percolation segregation in multi-size and multi- component ...

The Pennsylvania State University

The Graduate School

College of Engineering

PERCOLATION SEGREGATION IN MULTI-SIZE AND MULTI-

COMPONENT PARTICULATE MIXTURES: MEASUREMENT,

SAMPLING, AND MODELING

A Thesis in

Agricultural and Biological Engineering

by

Anjani K. Jha

© 2008 Anjani K. Jha

Submitted in Partial Fulfillment of the Requirements

for the Degree of

Doctor of Philosophy

May 2008

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The thesis of Anjani K. Jha.was reviewed and approved* by the following

Virendra M. Puri Distinguished Professor of Agricultural Engineering Thesis Advisor Chair of Committee Douglas B. Beegle Professor of Soil and Crop Sciences Eileen F. Wheeler Professor of Agricultural Engineering Steven F. Arnold Professor of Statistics Roy E. Young Professor of Agricultural Engineering Head of the Department of Agricultural and Biological Engineering

*Signatures are on file in the Graduate School

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ABSTRACT

Particulate materials are routinely handled in large quantities by industries such as,

agriculture, electronic, ceramic, chemical, cosmetic, fertilizer, food, nutraceutical,

pharmaceutical, power, and powder metallurgy. These industries encounter segregation due to

the difference in physical and mechanical properties of particulates. The general goal of this

research was to study percolation segregation in multi-size and multi-component particulate

mixtures, especially measurement, sampling, and modeling.

A second generation primary segregation shear cell (PSSC-II), an industrial vibrator, a

true cubical triaxial tester, and two samplers (triers) were used as primary test apparatuses for

quantifying segregation and flowability; furthermore, to understand and propose strategies to

mitigate segregation in particulates. Toward this end, percolation segregation in binary, ternary,

and quaternary size mixtures for two particulate types: urea (spherical) and potash (angular) were

studied. Three coarse size ranges 3,350-4,000 µm (mean size = 3,675 µm), 2,800-3,350 µm

(3,075 µm), and 2,360-2,800 µm (2,580 µm) and three fines size ranges 2,000-2,360 µm (2,180

µm), 1,700-2,000 µm (1,850 µm), and 1,400-1,700 µm (1,550 µm) for angular-shaped and

spherical-shaped were selected for tests. Since the fines size 1,550 µm of urea was not available

in sufficient quantity; therefore, it was not included in tests. Percolation segregation in fertilizer

bags was tested also at two vibration frequencies of 5 Hz and 7Hz. The segregation and

flowability of binary mixtures of urea under three equilibrium relative humidities (40%, 50%,

and 60%) were also tested. Furthermore, solid fertilizer sampling was performed to compare

samples obtained from triers of opening widths 12.7 mm and 19.1 mm and to determine size

segregation in blend fertilizers.

Based on experimental results, the normalized segregation rate (NSR) of binary mixtures

was dependent on size ratio, mixing ratio, material, strain rate, and strain. Segregated fines mass

of potash and urea particles was significantly different for the same size ratio (p<0.05). The

(NSR) and segregation rate of fines for binary mixtures were higher for larger size ratios, as

expected (2.4:1.0>2.0:1.0>1.7:1.0). Segregation rate was the highest and lowest for mixing ratios

33:67 and 67:33, respectively, when coarse mean size was 3,675 µm. The NSR decreased when

the strain rate was decreased from 1.0 Hz>0.5 Hz>0.25 Hz for the binary size ratios 1.7:1.0,

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2.0:1.0, and 2.4:1.0 (p<0.05). The NSR was dependent on multi-size mixtures

(binary>ternary>quaternary). At strain rate of 0.5 Hz for the size ratio 2.0:1.7:1.0 in ternary

mixture, the NSR for potash (0.83 kg/kg-h) was higher than the NSR for urea (0.21 kg/kg-h)

(p<0.05). The NSR increased with the increase in strain from 2% to 10%. At strain of 6% and

strain rate of 0.5 Hz, for the size ratio 2.0:1.7:1.0 in ternary mixture, the NSR for potash (0.83

kg/kg-h) was higher than the NSR for urea (0.21 kg/kg-h) in ternary mixtures (p<0.05).

For size ratios 2.0:1.0 and 1.7:1.0, only 2.8% and 7.0% of decrease in NSRs were

recorded for increase in relative humidity by 10 points (from 40% to 50%), respectively, whereas

36.0% and 45.0% decrease in NSRs were recorded for increase in relative humidity by 20 points

(from 40% to 60%), respectively (p<0.5). Additionally, flowability was quantified using a

Cubical Triaxial Tester (CTT) for size ratios 2.0:1.0 and 1.7:1.0, angle of internal friction

increased from 31.3° to 35.9° to 39.0° and 27.4° to 32.0° to 36.0° when relative humidity

increased from 40% to 50% to 60%, respectively (p<0.05), whereas cohesion remained close to

zero (p>0.05).

An innovative time-sequence procedure for sampling of bags was devised and

implemented. The size guide numbers (SGNs) of 10-10-10 blend samples using 19.1 mm width

trier were larger than those obtained using the 12.7 mm width trier, there were no substantial

differences between the SGNs and uniformity index (UIs) of the two different width triers, i.e.,

except for 10-10-10 (sample from second quarter) from blend plant 1, all SGNs and UIs were

within 7 and 2, respectively. Eleven out of the twelve samples from bagged fertilizers using 12.7

mm vs. 19.1 mm had the same outcomes, i.e., only one sample from blend plant 3, of

10-10-10 (sample from third quarter) using 12.7 mm vs. 19.1 mm had a conflicting outcome –

the sample obtained using 19.1 mm width trier (SGN=259, UI=47) passed, whereas, the sample

with 12.7 mm trier (SGN=256, UI=47) failed the AOAC chemical analysis test.

Two triers of opening widths 12.7 mm and 19.1 mm were used to determine percolation

segregation under vibration conditions. The percent mass retained on sieve number 8 (opening

width = 2.36 mm) was the highest (28%). Sieve numbers 7 (2.80 mm) and 10 (2.00 mm) retained

21% and 17% and followed the sieve number 8 (2.36 mm). The particle size distributions were

not significantly affected at the frequency of 5 Hz (p>0.05). The SGN and UI increased with

time at the frequency of 7 Hz. The SGN and UI of samples collected by 12.7 mm and 19.1 mm

triers were not significantly different (p>0.05).

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Results of binary size ratios of potash at three strains of 2%, 6%, and 10% each at strain

rates of 0.25 and 0.5 Hz and for urea at strains of 2%, 6%, and 10% each at strain rates of 0.25

and 1.0 Hz were used to develop and validate a convective and diffusive model. Based on

validation results the segregated fines mass values for size ratio 2.0:1.0 were: (1) within the 95%

CI for potash at 6% strain and 0.5 Hz strain rate, (2) similar but not within the 95% CI for potash

at 10% strain and 0.5 Hz strain rate, and (3) close but not within the 95% CI for urea at 6% strain

and 0.5 Hz strain rate.

A dimensional analysis model included the binary, ternary, quaternary mixtures of urea

and potash at strains of 2%, 6%, and 10% and strain rates of 0.25, 0.5, and 1.0 Hz. Strain rate of

1.0 Hz was included at strain of 6% for binary mixtures only. Developed dimensional analysis

model was validated for binary and ternary size ratios of urea and potash at strain rate of 0.5 Hz.

Based on the experimental data, it seems binary mixtures of potash results were sufficient to

represent the percolation segregation in binary, ternary, and quaternary mixtures of urea and

potash with reasonable accuracy (CoV of ±15%). The validation results showed that the CoV of

the modeled values to the experimental values were 18%, 15%, and 11% for binary mixtures of

urea and potash at strains of 2%, 6%, and 10% and strain rate of 0.25 Hz.

In conclusion, the binary, ternary, and quaternary mixtures provided the needed

framework to predict the segregation behavior in continuous mixtures under different motion

conditions. Based on initial results, only a limited number of tests need to be performed using

multi-size and multi-component mixtures to determine the extent of segregation in continuous

mixtures, the number of sizes and components should be determined based on operating

conditions. Percolation segregation in blended fertilizer could be minimized by changing

physical, mechanical and environmental parameters of particulate materials. The percolation

segregation was modeled for time-dependent and time-independent conditions to minimize the

number of tests to improve materials and process efficiency.

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TABLE OF CONTENTS LIST OF FIGURES ....................................................................................................................... xi LIST OF TABLES........................................................................................................................ xv ACKNOWLEDGEMENTS........................................................................................................ xvii 1. CHAPTER – INTRODUCTION ............................................................................................ 1

1.1 References............................................................................................................................. 3 2. CHAPTER - REVIEW OF LITERATURE............................................................................ 5

2.1 Flowability ............................................................................................................................ 5 2.1.1 Flowability tester apparatuses and their comparison ..................................................... 5 2.1.2 Physical property difference effect ................................................................................ 9 2.1.3 Relative humidity effect............................................................................................... 10

2.2 Mixing................................................................................................................................. 11 2.2.1 Mechanisms of mixing................................................................................................. 11 2.2.2 Quality of mixing: statistical approach ........................................................................ 12

2.3 Sampling ............................................................................................................................. 14 2.4 Concept of Segregation....................................................................................................... 23

2.4.1 Segregation mechanisms.............................................................................................. 23 2.4.2 Minimizing segregation ............................................................................................... 24 2.4.3 Quantifying segregation............................................................................................... 25

2.4.3.1 Binary mixture ...................................................................................................... 25 2.4.3.1.1 Homogeneous binary mixture........................................................................ 25 2.4.3.1.2 Heterogeneous binary mixture....................................................................... 31

2.4.3.2 Multi-size mixtures ............................................................................................... 31 2.4.4 Fertilizer segregation ................................................................................................... 33

2.4.4.1 Homogeneity of fertilizer...................................................................................... 33 2.4.4.2 Blend quality evaluation ....................................................................................... 33

2.4.5 Size segregation mathematical models ........................................................................ 34 2.4.5.1 Comprehensive MDT model................................................................................. 35 2.4.5.2 Convective/diffusive model .................................................................................. 36 2.4.5.3 Hopper model........................................................................................................ 37 2.4.5.4 Granular flow model ............................................................................................. 38 2.4.5.5 Drum model .......................................................................................................... 41

2.5 Second Generation Primary Segregation Shear Cell (PSSC-II) ......................................... 43 2.6 Vibration-induced Segregation ........................................................................................... 44 2.8 State-of-the-Art ................................................................................................................... 51 2.9 References........................................................................................................................... 51

3. CHAPTER - GOAL AND OBJECTIVES............................................................................ 59 4. CHAPTER - PERCOLATION SEGREGATION IN BINARY SIZE MIXTURES OF SPHERICAL AND ANGULAR-SHAPED PARTICLES OF DIFFERENT DENSITIES ......... 60

4.1 Abstract ............................................................................................................................... 60 4.2 Introduction......................................................................................................................... 60 4.3 Materials and Methods........................................................................................................ 62

4.3.1 Test material selection and parameter determination .................................................. 62 4.3.2 Test condition and experimental design ...................................................................... 63

4.4 Results and Discussion ....................................................................................................... 65

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4.4.1 Segregated fines mass .................................................................................................. 66 4.4.1.1 Mixing ratio effect ................................................................................................ 66 4.4.1.2 Size ratio effect ..................................................................................................... 67 4.4.1.3 Coarse size effect .................................................................................................. 68 4.4.1.4 Comparison between angular and spherical-shaped material ............................... 69

4.4.2 Normalized segregation rate ........................................................................................ 70 4.4.2.1 Mixing ratio effect ................................................................................................ 70 4.4.2.2 Effect of size ratio................................................................................................. 72 4.4.2.3 Effect of coarse size .............................................................................................. 73 4.4.2.4 Comparison between angular and spherical-shaped material ............................... 74

4.5 Conclusions......................................................................................................................... 75 4.6 Key Findings....................................................................................................................... 76 4.7 References........................................................................................................................... 76

5. CHAPTER - PERCOLATION SEGREGATION OF BINARY MIXTURES UNDER PERIODIC MOVEMENT............................................................................................................ 78

5.1 Abstract ............................................................................................................................... 78 5.1 Introduction......................................................................................................................... 78 5.3 Materials and Methods........................................................................................................ 80 5.4 Results and Discussion ....................................................................................................... 81

5.4.1 Segregated fines mass .................................................................................................. 81 5.4.1.1 Strain rate effect on size ratio ............................................................................... 84 5.4.1.2 Comparison between angular and spherical-shaped material ............................... 87

5.4.2 Normalized segregation rate ........................................................................................ 90 5.4.2.1 Strain rate effect on size ratio ............................................................................... 90 5.4.2.2 Comparison between angular and spherical-shaped material ............................... 93

5.5 Conclusions......................................................................................................................... 96 5.6 Key Findings....................................................................................................................... 96 5.7 References........................................................................................................................... 97

6. CHAPTER - PERCOLATION SEGREGATION IN BINARY SIZE MIXTURES UNDER DIFFERENT SHEAR AND INTENSITY OF MOTION ............................................................ 99

6.1 Abstract ............................................................................................................................... 99 6.2 Introduction......................................................................................................................... 99 6.3 Materials and Methods...................................................................................................... 100

6.3.1 Test material selection and parameter determination ................................................ 101 6.3.2 Test condition and experimental design .................................................................... 101

6.4 Results and Discussion ..................................................................................................... 103 6.4.1 Segregated fines mass ................................................................................................ 104

6.4.1.1 Strain and strain rate effects................................................................................ 104 6.4.1.2 Size ratio effect ................................................................................................... 106 6.4.1.3 Comparison between angular-shaped potash and spherical-shaped urea ........... 109

6.4.2 Normalized segregation rate ...................................................................................... 111 6.4.2.1 Strain and strain rate effect ................................................................................. 111 6.4.2.2 Effect of size ratio............................................................................................... 113 6.4.2.3 Comparison between angular and spherical-shaped material ............................. 115

6.5 Conclusions....................................................................................................................... 117 6.6 Key Findings..................................................................................................................... 117

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6.7 References......................................................................................................................... 118 7. CHAPTER - PERCOLATION SEGREGATION OF MULTI-SIZE AND MULTI-COMPONENT PARTICULATE MATERIALS ....................................................................... 120

7.1 Abstract ............................................................................................................................. 120 7.2 Introduction....................................................................................................................... 121 7.3 Materials and Methods...................................................................................................... 122 7.4 Results and Discussion ..................................................................................................... 124

7.4.1 Segregated fines mass ................................................................................................ 124 7.4.1.1 Effect of multi-size ratio ..................................................................................... 128 7.4.1.2 Material comparison ........................................................................................... 132

7.4.2 Normalized segregation rate ...................................................................................... 135 7.4.2.1 Strain rate effect on size ratio ............................................................................. 135 7.4.2.2 Comparison between angular and spherical-shaped materials ........................... 138

7.4.3 Binary, ternary, quaternary, and continuous mixtures............................................... 140 7.5 Conclusions....................................................................................................................... 141 7.6 Key Findings..................................................................................................................... 141 7.7 References......................................................................................................................... 142

8. CHAPTER - PERCOLATION SEGREGATION OF MULTI-SIZE AND MULTI-COMPONENT PARTICULATE MATERIALS: UREA AND POTASH AT MULTIPLE STRAIN AND STRAIN RATES ............................................................................................... 143

8.1 Abstract ............................................................................................................................. 143 8.1 Introduction....................................................................................................................... 143 8.2 Materials and Methods...................................................................................................... 144 8.4 Results and Discussion ..................................................................................................... 147

8.4.1 Segregated fines mass ................................................................................................ 147 8.4.1.1 Effect of strain and strain rate............................................................................. 147 8.4.1.2 Size ratio effect ................................................................................................... 151 8.4.1.3 Material comparison ........................................................................................... 156

8.4.2 Normalized segregation rate ...................................................................................... 160 8.4.2.1 Strain effect......................................................................................................... 160 8.4.2.2 Size ratio effect ................................................................................................... 162 8.4.2.3 Comparison between angular and spherical-shaped materials ........................... 166

8.4.3 Binary, ternary, quaternary, and continuous mixtures............................................... 170 8.5 Conclusions....................................................................................................................... 171 8.6 Key Findings..................................................................................................................... 172 8.7 References......................................................................................................................... 173

9. CHAPTER - PERCOLATION SEGREGATION AND FLOWABILITY MEASUREMENT OF UREA UNDER DIFFERENT RELATIVE HUMIDITIES ................................................. 174

9.1 Abstract ............................................................................................................................. 174 9.2 Introduction....................................................................................................................... 175

9.3 Materials and Methods.................................................................................................. 176 9.3.1 Test material selection, preparation, and parameter determination ........................... 176 9.3.2 Segregation ................................................................................................................ 177 9.3.3 Flowability ................................................................................................................. 179

9.4 Results and Discussion ..................................................................................................... 180 9.4.1 Physical properties determination.............................................................................. 180

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9.4.2 Percolation Segregation ............................................................................................. 181 9.4.3 Normalized segregation rate (NSR)........................................................................... 185 9.4.4 Distribution of segregation rate ................................................................................. 185 9.4.5 Flowability ................................................................................................................. 192

9.5 Conclusions....................................................................................................................... 194 9.6 Key Findings..................................................................................................................... 195 9.7 References......................................................................................................................... 196

10. CHAPTER - SOLID FERTILIZER SAMPLING AND COMPARISON OF SINGLE TUBE TRIERS OF 12.7 mm AND 19.1 mm OPENING WIDTHS ..................................................... 197

10.1 Abstract ........................................................................................................................... 197 10.2 Introduction..................................................................................................................... 197 10.3 Materials and Methods.................................................................................................... 199

10.3.1 Trier specification .................................................................................................... 200 10.3.2 Sampling procedures and preparation...................................................................... 201

10.4 Results and Discussion ................................................................................................... 204 10.4.1 Size distribution of raw ingredient and 10-10-10 blend .......................................... 204 10.4.2 Blend Plant 1 (BP1) ................................................................................................. 207 10.4.3 Blend Plant 2 (BP2) ................................................................................................. 209 10.4.4 Blend Plant 3 (BP3) ................................................................................................. 211 10.4.5 Theoretical and experimentally measured SGN and UI .......................................... 212

10.5 Summary of Observations............................................................................................... 214 10.6 Key Findings................................................................................................................... 215 10.7 References....................................................................................................................... 216

11. CHAPTER – VIBRATION-INDUCED SIZE SEGREGATION IN BAGGED FERTILIZER .............................................................................................................................. 217


11.3.1 Test condition and experimental design .................................................................. 219 11.3.2 Sampling procedures and preparation...................................................................... 223

11.4 Results and Discussion ................................................................................................... 224 11.4.1 Comparison of samples from three blend plants...................................................... 224 11.4.2 Size distribution of fertilizers from three blend plants ............................................ 226 11.4.3 Comparison of size distribution at 7 Hz frequency ................................................. 227

11.5 Key Findings................................................................................................................... 228 11.6 References....................................................................................................................... 228

12. CHAPTER - CONTINUUM THEORY BASED SIZE-SEGREGATION MODEL DEVELOPMENT AND VALIDATION ................................................................................... 231


12.3.1 Test material selection and parameter determination .............................................. 234 12.3.2 Test condition and experimental design .................................................................. 235 12.3.3 Convective and diffusive model development......................................................... 237

12.4 Results and Discussion ................................................................................................... 247 12.4.1 Convective and diffusive segregation model development ..................................... 247

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12.4.2 Validation of convective and diffusive segregation model...................................... 250 12.5 Conclusions..................................................................................................................... 252 12.6 Key Findings................................................................................................................... 253 12.7 References....................................................................................................................... 253

13. CHAPTER – MECHANISTIC THEORY BASED DIMENSIONAL ANALYSIS PERCOLATION SEGREGATION MODEL DEVELOPMENT AND VALIDATION .......... 255


13.3.1 Test material selection and parameter determination .............................................. 257 13.3.2 Test condition and experimental design .................................................................. 258 13.3.3 Dimensional analysis model development............................................................... 260

13.4 Results and Discussion ................................................................................................... 264 13.5 Validation of the dimensional analysis segregation model............................................. 269 13.6 Conclusions..................................................................................................................... 277 13.6 Key Findings................................................................................................................... 277 13.7 References....................................................................................................................... 277

14. CHAPTER - CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK . 279 14.1 Quantification of Percolation Segregation in Binary Mixtures ...................................... 280 14.2 Quantification of Percolation Segregation in Ternary and Quaternary Mixtures........... 280 14.3 Quantification of Segregation and Flowability in Binary Mixtures ............................... 281

14.3.1 Size ratios 2.0:1.0 and 1.7:1.0.................................................................................. 281 14.3.2 Flowability of binary mixtures................................................................................. 281

14.4 Sampling of Solid Fertilizers and Comparison of Samples from Two Triers of Opening Widths 12.7 and 19.1 mm....................................................................................................... 282

14.4.1 Raw ingredient samples ........................................................................................... 282 14.4.2 10-10-10 blend samples using 12.7 and 19.1 mms triers: ....................................... 282

14.5 Quantification of Percolation Segregation of Fines from Fertilizer Bags during Vibration................................................................................................................................................. 283 14.6 Convective and Diffusive Percolation Segregation Model............................................. 283 14.7 Mechanistic Theory Based Dimensional Analysis Percolation Segregation.................. 284 14.7 Recommendations for Future Work................................................................................ 285

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LIST OF FIGURES

Figure 2.1 Mohr-Coulomb model ................................................................................................... 7 Figure 2.2 Cross-sectional view of CTT test cell (Kamath and Puri, 1997) (not to scale)............. 8 Figure 2.3 Exploded view of one side of the assembled CTT test cell (Kamath and Puri, 1997) (not to scale).................................................................................................................................... 8 Figure 2.4 A heap divided into sampling regions (McGlinchey, 2004) ....................................... 27 Figure 2.5 Vertical motion segregation shear cell (Duffy and Puri, 2002)................................... 30 Figure 2.6 Schematic of two-dimension experimental apparatus for multi-component size segregation (Shinohara et al., 2001) ............................................................................................. 32 Figure 2.7 Schematic of global coordinates (Duffy and Puri, 2003) ............................................ 37 Figure 2.8 Percolation segregation mechanism and calculation domain (Boateng and Barr, 1996)....................................................................................................................................................... 40 Figure 2.9 Material conservation control volume in the active layer (Boateng and Barr, 1996) 40 Figure 2.10 (a) Rotating drum in rolling mode, (b) active-passive interface, and (c), and flow mode volume derivation (Ding et al., 2002) ................................................................................. 42 Figure 4.1 Comparison of percent segregated fines at three different mixing ratios of angular-shaped potash for size ratio 2.0:1.0, with ±SD as error bars ........................................................ 67 Figure 4.2 Comparisons of segregated percent fines for three different size ratios of binary mixtures of angular-shaped potash prepared using coarse size 3,675 µm, with ±SD as error bars....................................................................................................................................................... 68 Figure 4.3 Comparisons of percent segregated fines for three coarse sizes of angular-shaped potash binary mixtures for size ratio 1.7:1.0, with ±SD as error bars .......................................... 69 Figure 4.4 Comparisons of percent segregated fines for angular-shaped potash and spherical-shaped urea: size ratio 2.0:1.0 and coarse size 3,675 µm, with ±SD as error bars ....................... 70 Figure 4.5 Comparison of NSR at three different mixing ratios of angular-shaped potash: for size ratio 2.0:1.0 and coarse size 3,675 µm, with ±SD as error bars ................................................... 71 Figure 4.6 Comparison of SR at three different mixing ratios for angular-shaped potash: size ratio 2.0:1.0 and coarse size 3,675 µm, with ±SD as error bars ................................................... 72 Figure 4.7 Normalized segregation rate comparisons for different size ratios for the coarse size (3,675 µm) of angular-shaped potash, with ±SD as error bars ..................................................... 73 Figure 4.8 Normalized segregation rate comparisons for three coarse sizes for size ratio of 1.7:1.0 of angular-shaped potash, with ±SD as error bars ............................................................ 74 Figure 4.9 Segregation rate comparisons of spherical urea and angular potash materials size ratio 2.0:1.0 and coarse size 3,675 µm, with ±SD as error bars............................................................ 75 Figure 5.1 Comparison of percent segregated fines for three size ratios of potash when coarse size was 3,675 µm at strain rates (a) 1.0 Hz, (b) 0.5 Hz, and (c) 0.25 Hz, with ±SD as error bars....................................................................................................................................................... 86 Figure 5.2 Comparison of percent segregated fines between potash and urea for size ratio 2.0:1.0 when absolute coarse size was 3,675 µm at strain rates (a) 1.0 Hz, (b) 0.5 Hz, and (c) 0.25 Hz, with ±SD as error bars .................................................................................................................. 89 Figure 5.3 Comparison of NSR for three size ratios of potash when mean coarse size was 3,675 µm at strain rates (a) 1.0 Hz, (b) 0.5 Hz, and (c) 0.25 Hz, with ±SD as error bars ...................... 92 Figure 5.4 Comparison of NSR between potash and urea for size ratio 2.0:1.0 when coarse size was 3,675 µm at strain rates (a) 1.0, (b) 0.5 Hz, and (c) 0.25 Hz, with ±SD as error bars........... 95

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Figure 6.1 Comparison of strains on size ratio 2.4:1.0 at strain rates (a) 0.25 Hz and (b) 0.5 Hz, with ±SD as error bars ................................................................................................................ 105 Figure 6.2 Comparison of percent segregated fines for three size ratios of potash when coarse size was 3,675 µm at strain rate of 0.5 Hz under strains of (a) 2%, (b) 6%, and (c) 10%, with ±SD as error bars ........................................................................................................................ 108 Figure 6.3 Comparison of percent segregated fines for size ratio 2.0:1.0 of potash and urea when coarse size was 3,675 µm at strain rate of 0.5 Hz under strains of (a) 2%, (b) 6% Hz, and (c) 10%, with ±SD as error bars ....................................................................................................... 110 Figure 6.4 Comparison of strains on size ratio 2.4:1.0 at strain rates (a) 0.25 Hz and (b) 0.5 Hz, with ±SD as error bars ................................................................................................................ 112 Figure 6.5 Comparison of NSR for three size ratios of potash when coarse size was 3,675 µm at strain rate of 0.5 Hz under strains of (a) 2%, (b) 6%, and (c) 10%, with ±SD as error bars ...... 114 Figure 6.6 Comparison of NSR for size ratio 2.0:1.0 of potash and urea when coarse size was 3,675 µm at strain rate of 0.5 Hz under strains of (a) 2%, (b) 6%, and (c) 10%, with ±SD as error bars.............................................................................................................................................. 116 Figure 7.1 Comparison of percent segregated fines for multi-size ratios for potash at strain rate of 0.5 Hz in (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars.............. 129 Figure 7.2 Comparison of percent segregated fines for multi-size ratios for potash at strain rate of 0.25 Hz in (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars............ 130 Figure 7.3 Comparison of percent segregated fines between angular (potash) and spherical (urea) at strain rates 0.5 Hz and 0.25 Hz for (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars ........................................................................................................................ 134 Figure 7.4 Comparison of NSR between size ratios at strain rate 0.5 Hz for (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars..................................................... 136 Figure 7.5 Comparison of NSR between size ratios at strain rate 0.25 Hz for (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars..................................................... 137 Figure 7.6 Comparison of NSR between potash and urea at strain rates 0.25 Hz and 0.5 Hz for (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars ............................. 139 Figure 7.7 Comparison of NSR among binary, ternary, quaternary, and continuous mixtures (10-10-10), with ±SD as error bars.................................................................................................... 140 Figure 8.1 Comparison of binary, ternary, and quaternary size ratio at strain rate of 0.25 Hz and strains (a) 2%, (b) 6%, and (c) 10%, with ±SD as error bars...................................................... 149 Figure 8.2 Comparison of binary, ternary, and quaternary size ratio at strain rate of 0.5 Hz and strains (a) 2%, (b) 6%, and (c) 10%, with ±SD as error bars...................................................... 150 Figure 8.3 Comparison of percent segregated fines for multi-size ratios for potash 2% at strain rate of 0.5 Hz in (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars .. 153 Figure 8.4 Comparison of percent segregated fines for multi-size ratios for potash 6% at strain rate of 0.5 Hz in (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars .. 154 Figure 8.5 Comparison of percent segregated fines for multi-size ratios for potash 10% at strain rate of 0.5 Hz in (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars .. 155 Figure 8.6 Comparison of percent segregated fines between potash and urea 2% at strain rate of 0.5 Hz for (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars ............ 157 Figure 8.7 Comparison of percent segregated fines between potash and urea 6% at strain rate of 0.5 Hz for (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars ............ 158 Figure 8.8 Comparison of percent segregated fines between potash and urea 10% at strain rate of 0.5 Hz for (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars ............ 159

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Figure 8.9 Comparison of NSR for binary, ternary, and quaternary size ratios at strain rate of 0.25 Hz and strains (a) 2%, (b) 6%, and (c) 10%, with ±SD as error bars ................................. 161 Figure 8.10 Comparison of NSR for multi-size ratios for potash 2% at strain rate of 0.25 Hz in (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars ............................. 163 Figure 8.11 Comparison of NSR for multi-size ratios for potash 6% at strain rate of 0.25 Hz in (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars ............................. 164 Figure 8.12 Comparison of NSR for multi-size ratios for potash 10% at strain rate of 0.25 Hz in (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars ............................. 165 Figure 8.13 Comparison of NSR for multi-size ratios for potash 2% at strain rate of 0.5 Hz in (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars................................... 167 Figure 8.14 Comparison of NSR for multi-size ratios for potash 6% at strain rate of 0.5 Hz in (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars................................... 168 Figure 8.15 Comparison of NSR for multi-size ratios for potash 10% at strain rate of 0.5 Hz in (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars ............................. 169 Figure 8.16 Comparison of percent segregated fines among binary, ternary, quaternary, and (10-10-10) mixtures at strain of 6% and strain rate of 0.5 Hz, with ±SD as error bars..................... 171 Figure 8.17 Comparison of percent segregated fines among binary, ternary, and quaternary mixtures at strain of 2% and strain rate of 0.5 Hz, with ±SD as error bars ................................ 171 Figure 9.1 Collection pan for fines showing eight load cell locations, (a) top view of shear box and eight load cell positions for data collection, (b) top view of collection pan (all dimensions in mm) ............................................................................................................................................. 179 Figure 9.2 Typical segregated fines mass of binary size urea mixture for size ratio 2.0:1.0 equilibrated at 50% relative humidity environment with bed depth of 85 mm. The curves are for different load cell locations shown in Figure 9.1........................................................................ 183 Figure 9.3 Typical segregated fines mass of binary size urea mixture for size ratio 1.7:1.0 equilibrated at 50% relative humidity environment with bed depth of 85 mm. The curves are for different load cell locations shown in Figure 9.1........................................................................ 183 Figure 9.4 Typical distributed fines mass of binary size urea mixtures for (a) size ratio 2.0:1.0 and for (b) size ratio 1.7:1.0 equilibrated at 50% relative humidity ........................................... 184 Figure 9.5 Segregation rate at 40% ERH for size ratio 2.0:1.0, with ±SD as error bars ............ 185 Figure 9.6 Typical distributed segregation rate of fines mass of binary urea mixtures at, (a) 60 s, (b) 120 s, and (c) 180 s for size ratio 2.0:1.0 at 50% RH ........................................................... 187 Figure 9.7 Typical distributed segregation rate of fines mass of binary urea mixtures at, (a) 60 s, (b) 120 s, and (c) 180 s for size ratio 1.7:1.0 at 50% RH ........................................................... 187 Figure 9.8 Failure stress difference for binary mixtures of size ratios of 2.0:1.0 and 1.7:1.0 and confining pressures of 3.5 and 7.0 kPa ....................................................................................... 192 Figure 10.1 Schematic of different triers: (a) single and double tube, (b) Missouri D tube, (c) sampling cup, (d) stream sample with sampling cup, and (e) sampling front end loader (TFI, 1996) ........................................................................................................................................... 203 Figure 10.2 Typical size distribution of urea samples from bin of SGN (a) 270, (b) 271, (c) 271, and front end loader (d) 266........................................................................................................ 206 Figure 10.3 Typical size distribution of 10-10-10 (a) 1, (b) 2, (c) 3, and (d) 4 quarters, broken line 12.7 (252-1, 256-2, 251-3, and 246-4) and solid line 19.1 (252-1, 268-2, 252-3, 249-4) ... 206 Figure 11.1 Vibrating table with bag placed on vibration plate ................................................. 220 Figure 11.3 Preliminary calibration using empty table and 22.68 kg bag on table .................... 222 Figure 11.4 Schematic of AOAC single tube sampler (trier) (TFI, 1996).................................. 224

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Figure 11.5 Typical size distribution profiles of samples from blend plants BP1, BP2, and BP3 for (a) 19.1 mm and (b) 12.7 mm................................................................................................ 225 Figure 11.6 Typical size distribution profiles of samples from blend plants at frequency 5 Hz (a) 0 (b) 15, (c) 30 minutes............................................................................................................... 227 Figure 11.7 Typical size distribution profiles of samples from blend plants at frequency 7 Hz (a) 15 and (b) 30 minutes ................................................................................................................. 228 Figure 12.1 Primary segregation shear cell (PSSC-II)................................................................ 234 Figure 12.2 Schematic of the shear box..................................................................................... 238 Figure 12.3 Binary mixtures in shear box showing 12 equal size layers for model development..................................................................................................................................................... 238 Figure 12.4 Three dimensional mass balances ........................................................................... 239 Figure 12.5 Modeled and experimental data of potash at strain rate of 0.5 Hz (a) size ratio 2.4:1.0 under 6%, (b) size ratio 1.7:1.0 under strain of 6%, (c) size ratio 2.4:1.0 under 10%, (d) size ratio 1.7:1.0 under strain of 10%, and urea of size ratio 2.0:1.0 under strain of 6% at strain rates of (e) 0.25 Hz, (f) 1.0 Hz, 95%CI+ and 95%CI- upper and lower limits of CI.................................... 249 Figure 12.6 Validation at strain rate of 0.5 Hz for size ratio 2.0:1.0 (a) potash-6%, (b) potash-10%, and (c) urea-6%, 95%CI+ and 95%CI- upper and lower limits of CI ............................... 251 Figure 13.1 Validation of dimensional analysis model by comparison of modeled values to experimental values for potash at strain rate of 0.5 Hz, with ±SD as error bars ........................ 275 Figure 13.2 Validation of dimensional analysis model by comparison of modeled values to experimental values for urea at strain rate of 0.5 Hz, with ±SD as error bars ............................ 275 Figure 13.3 Validation of dimensional analysis model by comparison of modeled values to experimental values for potash at strain rate of 0.5 Hz, with ±SD as error bars ........................ 276 Figure 13.4 Validation of dimensional analysis model by comparison of modeled values to experimental values for urea at strain rate of 0.5 Hz, with ±SD as error bars ............................ 276

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LIST OF TABLES Table 2.1 Recommended sampling intensities (Miles and Quackenbush, 1950) ......................... 16 Table 2.2 Net standard deviations (Randle, 1955)a,b .................................................................... 17 Table 2.3 Specifications of the five triers used for comparison in securing samples from dry blended fertilizers (Baker et al., 1967).......................................................................................... 19 Table 2.4 Trier specifications used in sampling bias study by Caine and Hancock (2002) ........ 21 Table 2.5 Sequence of the use of three triers for securing samples from twelve 22.8 kg bags using the same hole*..................................................................................................................... 21 Table 4.1 Design of experiment for binary size mixtures for potash and urea*........................... 65 Table 4.2 Segregation results for binary size mixtures with three coarse sizes*.......................... 66 Table 5.1 Experimental design for binary size mixtures for potash and urea*............................. 81 Table 5.2 Segregation results for binary mixtures with three coarse sizes for potash*................ 82 Table 5.3 Segregation results for binary mixtures with three coarse sizes for urea* ................... 83 Table 6.1 Design of experiment for binary size mixtures for potash and urea*......................... 103 Table 7.1 Experimental design for binary size mixtures for potash and urea (Jha and Puri, 2007)*..................................................................................................................................................... 123 Table 7.2 Experimental design for ternary and quaternary size mixtures for potash and urea*. 123 Table 7.3 Segregation results for binary, ternary, and quaternary mixtures for potash*............ 125 Table 7.4 Segregation results for binary, ternary, and quaternary mixtures for urea* ............... 126 Table 8.1 Experimental design for binary size mixtures for potash and urea (Jha and Puri, 2007a)* ....................................................................................................................................... 146 Table 8.2 Experimental design for multi-size size mixtures for potash and urea*..................... 146 Table 9.1 Binary size mixtures of urea used for both segregation and flowability studies ........ 177 Table 9.2 Experimental design for segregation testing of binary size mixtures of urea............. 178 Table 9.3 Experimental design for flowability testing of binary size mixtures of urea.............. 180 Table 9.4 Physical property of binary size mixtures of urea (sphericity = 0.97*) at three different equilibrium relative humidity conditions.................................................................................... 181 Table 9.5 Segregated fines, mean segregation rate and mean NSR for binary size mixtures urea..................................................................................................................................................... 182 Table 9.6 Flowability parameters for binary size mixtures at three equilibrium relative humidities*.................................................................................................................................. 193 Table 10.1 Capacity of material locations at three blending plants ............................................ 199 Table 10.2 Blending formula for 10-10-10 at three different blend plants (kg) ......................... 200 Table 10.3 Specifications of the five triers used for collecting samples of dry solid fertilizer ingredients and from bagged 10-10-10 blends............................................................................ 200 Table 10.4 Sequence of the use of two triers for securing samples from 22.68 kg and 33.29 bags using the same hole*................................................................................................................... 202 Table 10.5 Size and chemical analyses of different materials at various sampling locations for blend plant BP1........................................................................................................................... 208 Table 10.6 Size and chemical analyses of different materials at various sampling locations for blend plant BP2........................................................................................................................... 210 Table 10.7 Size and chemical analyses of different materials at various sampling locations for blend plant BP3........................................................................................................................... 212 Table 10.8 Theoretical SGN and UI based on samples from bin, front end loader, and stream sampling at BP1, BP2, and BP3 ................................................................................................. 213

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Table 11.1 Experimental design for vibration of 10-10-10 bags ................................................ 223 Table 11.2 Specifications of the triers used for collecting samples from bagged fertilizer........ 223 Table 11.3 Sequence of the use of two triers for securing samples from 22.68 kg and 33.29 kg bags using the same hole*........................................................................................................... 224 Table 12.1 Experimental design for binary size mixtures for potash and urea*......................... 236 Table 12.2 Validation schedule for binary size mixtures for potash and urea*.......................... 237 Table 12.3 Convective, diffusive, and time parameters for potash and urea.............................. 247 Table 13.1 Experimental design for binary size mixtures for potash and urea*......................... 259 Table 13.2 Experimental design for multi-size size mixtures for potash and urea*................... 259 Table 13.3 Validation design for binary size mixtures for potash and urea* ............................. 260 Table 13.4 Results of linear regression analysis of variance for binary mixtures of potash* .... 265 Table 13.5 Results of linear regression analysis of variance for ternary mixtures of potash* ... 266 Table 13.6 Results of linear regression analysis of variance for binary mixtures of urea*........ 267 Table 13.7 Results of linear regression analysis of variance for binary mixtures of potash and urea when porosity was kept constant* ...................................................................................... 268 Table 13.8 Results of linear regression analysis of variance for binary mixtures of potash and urea when porosity was included*.............................................................................................. 269 Table 13.9 Comparison of the experimental and modeled values for binary mixtures of potash and urea at strain of 2% and strain rate of 0.25 Hz..................................................................... 270 Table 13.10 Comparison of the experimental and modeled values for binary mixtures of potash and urea at strain of 6% and strain rate of 0.25 Hz..................................................................... 271 Table 13.11 Comparison of the experimental and modeled values for binary mixtures of potash and urea at strain of 10% and strain rate 0.25 Hz ....................................................................... 271 Table 13.12 Comparison of the experimental and modeled values for ternary mixtures of potash and urea at strain of 2% and strain rate of 0.25 Hz..................................................................... 272 Table 13.13 Comparison of the experimental and modeled values for ternary mixtures of potash and urea at strain of 10% and strain rate of 0.25 Hz................................................................... 272 Table 13.14 Comparison of the experimental and modeled values for binary mixtures of potash and urea....................................................................................................................................... 273 Table 13.15 Comparison of the experimental and modeled values for ternary mixtures of potash and urea....................................................................................................................................... 274

xvii

ACKNOWLEDGEMENTS

I would like to take the opportunity to thank all of them who have helped me to complete

my Ph.D. research; due to space limitations, only few are listed here.

It has been my great honor to pursue Ph.D. under the keen supervision of Professor

Virendra M. Puri. I extend my sincere gratitude for his invaluable and unparalleled guidance for

over last three years. I am grateful to my Ph.D. advisory committee members Professor Douglas

B. Beegle, Professor Eileen F. Wheeler, and Professor Steven F. Arnold for their insightful

discussions and comments for improving the quality of my Ph.D. research.

Special thanks goes to Dr. Roderick Thomas, Randall G. Bock for providing technical

assistance needed to keep experimental set-up running without any major hindrance for almost

three years. Special thanks also goes to my friends Jaskaran S. Gill, Chandan Kumar, and Dr.

Hojae Yi for their help to complete such a voluminous work without compromising with the

quality within a limited time-frame. Thanks goes to my other friends Anuranjan Pandeya,

Deepak Jaiswal, Pankaj Jha, Praveen Kumar, Rituraj Nandan, Rohit Rai, Saed Roudsari, and

Varij Saurabh for their help and for making my stay enjoyable at Penn State, and old friends

back in India. I would like to thank Professor Roy E. Young, Head of the Department of

Agricultural and Biological Engineering, Pennsylvania Department of Agriculture, PennAG

Industries Associations, and Pennsylvania Experiment Station for providing the financial

assistance needed to complete this research.

Finally, special and sincere appreciation goes to my late grand-father Govind N. Jha who

has been my inspiration and always helped me to achieve my goals. Sincere appreciation also

goes to my parents, parents-in-laws for their blessings.

xviii

Dedicated to

my wife Maitri Jha and son Visu

for their unconditional love and support

1

1. CHAPTER – INTRODUCTION

Particulate materials are routinely handled in large quantities by industries such as,

agriculture, electronic, ceramic, chemical, cosmetic, fertilizer, food, nutraceutical,

pharmaceutical, power, and powder metallurgy. Unit operations involved to make products in

these industries from particulate materials include blending, sampling, conveying, handling,

mixing, processing, storage, and transportation of particulates. Rosato and Blackmore (2000)

mentioned that in 1999, the world-wide agricultural commodities production such as almonds,

barley, beans, buckwheat, cereals, grains, lentils, millet, maize, oats, rice, rye, sugarcane, and

sorghum were estimated to be approximately 5.34 × 1012 kg. On annual basis, the particulate

material production and related services contribute one trillion dollars to the US economy alone.

More than 80 percent of all pharmaceutical products are delivered as tablets or capsules that are

manufactured using powder blends (Muzzio et al., 2003). It is estimated that the pharmaceutical

industry in the U.S. alone invested $22.5 billion in research and development during the year

2000 for improving quality of tablets and capsules (Muzzio et al., 2002). Therefore, it is

worthwhile studying basic and applied research in the area of particulate materials.

Particulate materials are defined as a particle system composed of mutually contacting

solid particles, or structural units within a liquid and/or gaseous phase (Feda, 1982). This

definition of particulates represents an emerging branch of science and technology which applies

the principles of solid mechanics, fluid mechanics, and material science to study particle-particle

and particle-phase interactions for characterizing the physical and mechanical behavior of

particulate materials (Mittal, 2003). The physical and mechanical parameter that can influence

the behavior of particulates during previously mentioned unit operations include: particle size

and distribution, density, shape, morphology, structural properties and rheology of particle

packing, contact friction, elasticity, brittleness, ability to absorb moisture, size enlargement, size

reduction, electrostatic charges, vibration, intensity and displacement of motion, and magnetic

properties (Fayed and Otten, 1997 and Rosato et al., 2002). The processing dynamics of

particulate materials and known methods for characterizing the homogeneity of a granular blend

remain far from being well developed and understood. One of the key reasons is that the

2

essential mechanisms of segregation remain elusive, and a fundamental method to quantify

segregation occurring in a real-world particulate material has not been yet fully developed.

Segregation can be simply defined as de-mixing or reverse mixing (Popplewell et al.,

1989; and Rollins et al., 1995). In other words, segregation of a well mixed bulk solid composed

of particulates of differing constituent properties is defined as the resultant mixture that evolves

to a spatially non-uniform state (Rosato and Blackmore, 2000). One of the important facts about

segregation is that it occurs during dynamic instead of static condition and is primarily concerned

with the physical and mechanical characteristics of particulate materials. Segregation causes

uneven quality of fertilizers and tablets, fluctuating packet weights, low mechanical strength of

compacts and abrasives, poor refractory materials, and low rates of contact and reaction

(Shinohara, 1997). Of the above-mentioned industries, as an example to understand the impact of

segregation on product quality, pharmaceutical industry is very stringent concerning quality of

oral solid dosages. Strict U.S. quality control standards dictated by the Food and Drug

Administration (FDA) that some or even the entire batch may have to be discarded if it is found

that the amount of active ingredient or total weight of just five tablets in the batch varies outside

narrow limits (Carson et al., 1986). It is not unusual that the value of single batch of ingredients

to be in excess of $100,000. In the poultry industry, birds must get proper nutrients (protein,

energy, amino acids, vitamins, calcium, phosphorous, and manganese) for optimum quantity and

quality of egg production (Sainsbury, 2000). In most egg production systems, poultry mash feed

is widely practiced form of food for daily energy and nutrients requirement for birds (Zeigler,

1996). During conveying of poultry mash feed, even though well mixed, large particles separate

from small particles so birds are tend to and by selection eat large segregated mash feed

particulates resulting in less-than-optimum quality and quantity of egg (Tang, 2004). In the

fertilizer industry, 80% of the total fertilizer produced in the US is in the form of solid granules

and prills. Out of the total solid fertilizer produced in the US, 50% is sold in the blend (mixture

of two or more components of N, P, or K) form to meet the different plants nutrient requirement.

Different size fertilizer granules separate from one another during bagging, conveying, mixing,

transportation, and storage causing uneven distribution of fertilizer in the field that leads to

localized over- and under-supply. It can reduce the agronomic efficiency of fertilizers through

lower yields and reduced crop quality and may have detrimental environmental consequences.

3

This variation in the composition of tablets, capsules, fertilizer blend, and poultry mash feed has

been shown to be caused by segregation occurring in particulate materials.

In conclusion, handling, processing, conveying, storage, and production of powder (for

instance by spray drying and crystallization) and powder products are essential manufacturing

unit operations in the particulate material industries. These manufacturing operations continue to

challenge engineers due to the pervasive nature of segregation. Reduction of segregation in

handling and conveying operations is critically needed so as to produce better quality products.

Based on the above facts, segregation is a key bottleneck for industries handling particulate

materials, and there is high potential for successful research in this area. The current research is

focused on studying time-dependent percolation mechanism of broad size range powder mixtures

to minimize segregation. Percolation segregation may be defined as the migration of small size

particles through pore spaces of large size particles bed with external energy input (Williams,

1976). Wherever motion energy (i.e., vibration, shear and gravity) induced in the particulate

mixture occurs, segregation by the percolation mechanism is sure to occur (Vallance and Savage,

2000). To put it in perspective, percolation segregation exists in almost all the procedures of

particulate material processing, conveying, and storage. To minimize segregation, fundamental

understating of underlying mechanisms is essential. Physics and dimensional analysis-based

quantitative relationships between segregation and particle characteristics represent a rational

approach to mathematically model segregation mechanisms. Mathematical models are essential

to apply the results of quantitative relationships in the general area of segregation irrespective of

powder mixtures and applications. Therefore, results of this research can provide deeper insights

within the entire process of percolation segregation.

1.1 References

Carson, J. W., T. A. Royal, and D. J. Goodwill. 1986. Understanding and eliminating particle segregation problems. Bulk Solids Handling 6(1):139-144.

Fayed, M.E. and L. Otten.1997. Handbook of Powder Science and Technology. Van Nostrand Reinhold Company Inc. New York: Chapman & Hall.

Feda, J. 1982. Mechanics of particulate materials – The Principles. Elsevier, New York, NY. Mittal, B. 2003. An elasto-viscoplastic constitutive formulation for dry powder compression

analysis using finite elements. Ph.D. diss., The Pennsylvania State University, University Park, PA.

Muzzio, F. J., T. Shinbrot, and B. J. Glasser. 2002. Powder technology in the pharmaceutical industry: the need to catch up fast. Powder Technology 124: 1–7.

4

Muzzio, F. J., C. L. Goodridge, A. Alexander, P. Arratia, H. Yang, O. Sudah, and G. Mergen. 2003. Sampling and characterization of pharmaceutical powders and granular blends. International Journal of Pharmaceutics 250:51-64.

Popplewell, L. M., O. H. Campanella, V. Sapru, and M. Peleg. 1989. Theoretical comparison of two segregation indices for binary powder mixtures. Powder Technology 58: 55-61.

Rollins, D. K., D. L. Faust, and D. L. Jabas. 1995. A superior approach to indices in determining mixture segregation. Powder Technology 84: 277-282.

Rosato, A. D. and D. L. Blackmore. 2000. Preface. Eds: Rosato, A. D. and D. L. Blackmore. IUTAM Symposium on Segregation in Granular Flows 11-29. Norwell: Kluwer Academic Publishers.

Rosato, A. D., D. L. Blackmore, N. Zhang, and Y. Lan. 2002. A perspective on vibration induced size segregation of granular materials. Chemical Engineering Science 57: 265-275.

Sainsbury, D. 2000. Practical poultry feeding. Author: Sainsbury, D. Poultry Health and Management Chickens, Ducks, Turkeys, Geese, Quail. 4th ed. Chapter 4. 31-43. Blackwell Science, Inc. Commerce Place, 350 Main Street. Malden, MA.

Shinohara, K. 1997. Segregation of particles. Ed.: Gotoh, K. H. Masuda, and K. Higashitani. Powder Technology Handbook (2nd Ed.). Marcel Dekker Inc. New York. USA.

Tang, P. 2004. Percolation and sieving segregation patterns-quantification, mechanistic theory, model development and validation, and application. Ph.D.diss., The Pennsylvania State University, University Park, PA.

Vallance, J. W. and S. B. Savage. 2000. Particle segregation in granular flows down chutes. Eds: Rosato, A. D. and D. L. Blackmore. IUTAM Symposium on Segregation in Granular Flows 31-51. Norwell: Kluwer Academic Publishers.

Williams, J. C. 1976. The segregation of particulate materials- A review. Powder Technology 15: 245–251.

Zeigler, M. P. 1996. Sources of variance in feed distribution systems. Master of Science Thesis. The Pennsylvania State University, University Park, PA.

5

2. CHAPTER - REVIEW OF LITERATURE

In this chapter, literature review related to flowability test apparatuses, particle physical

property effect on flowability, effect of relative humidity on flowability, mixing mechanisms,

mixing quality evaluation, sampling of powder mixtures is presented. The segregation

mechanisms, techniques used for minimizing and quantifying segregation, mathematical

modeling of segregation, vibration induced segregation, and application of segregation theory in

industry have been reviewed in detail. The primary focus of the study was to minimize

segregation in multi-size and multi-component mixtures: experimental and mathematical model

development. Segregation, a very important aspect of powder technology, has limited

understanding. Most of the researchers define a segregation coefficient and explore segregation

for a particular process. The development of general quantitative relationships between particle

characteristics and segregation is of considerable importance. A shear apparatus was used to

study the percolation segregation, i.e., the movement along gravity direction of fine particles

through bed of coarse particles.

2.1 Flowability Segregation can be defined as a bulk solid composed of particulates of differing

constituent properties that evolves to a spatially non-uniform state (Rosato and Blackmore,

2000). Segregation does happen only in those bulk materials that are relatively free flowing.

Reviewing flowability of granular and powder materials is of great importance to understand the

ubiquitous phenomenon of segregation in-depth. In this section, flowability testing apparatuses,

effect of physical parameters on flowability, and effect of relative humidity on flowability of

particulates are reviewed.

2.1.1 Flowability tester apparatuses and their comparison Some of the commonly used testers for quantifying flow properties of powders include

the Jenike shear cell, the direct shear cell, the rotational shear cell, the true biaxial cell, the

conventional triaxial cell, and the true cubical triaxial cell. Based on the stress path used in the

testers, these can be broadly categorized into two: primary testers and secondary testers. Primary

testers are capable of measuring the flow behavior of particulate materials over a wide range of

6

stress paths, the true triaxial tester; and true biaxial testers, to a limited extent, fall under the

primary tester category. Whereas, secondary testers are capable of measuring one or more

specific types of stress paths, Jenike shear cell, the direct shear cell, the rotational shear cell fall

under this category. In the following paragraphs these testers were compared.

Kamath (1992) compared triaxial cell, direct shear cell, Jenike shear cell, and rotational

split-level shear cell to measure bulk flow properties of cohesive powders i.e., sugar and wheat

flour. Based on the preliminary tests, it was found that sugar was mildly cohesive (c < 1 kPa) and

wheat powder was cohesive (c > 1 kPa). Sugar results confirmed Feda’s (1982) findings. The

flow properties of wheat flour were not significantly different when the Jenike shear cell, the

direct shear cell, and the rotational split-level shear cell were compared. The flow properties of

sugar were not significantly different when the Jenike shear cell and the direct shear cell were

compared.

Kandala and Puri (2000) compared flow properties of Community Bureau of References

(BCR) limestone, glass fibers, ground silica, microcrystalline cellulose, and wheat flour using

computer controlled shear cell (CCJC and DYLT) and cubical triaxial tester (CTT) at low

consolidation loads (1-6 kPa). The detailed specifications and operating procedures of these two

devices can be found in Kandala (1999). Flow parameters were not significantly different

(p>0.05) for all five powders at consolidation stress of 1.2 kPa. Both the flow parameters were

different (p<0.05) for wheat flour at consolidation stresses of 5.2 and 3.2 kPa. The results of

DYLT were more reproducible. The CTT results showed that cohesion at consolidation stress of

12.5 kPa and consolidation and angle of internal friction at consolidation stress of 6.6 kPa were

comparable to values from other two testers. The flow parameters were similar for ground silica

at the two low consolidation stresses 2.8 and 8.4 kPa for these three testers.

Cubical Triaxial Tester (CTT)

A low pressure (<100 kPa) cubical triaxial tester (CTT) developed by Kamath and Puri

(1997) was used to measure flowability using the Mohr-Coulomb model. This CTT uses flexible

boundary which allows unrestrained deformations in the samples and minimizes die-wall friction

effect. The low pressure CTT is capable of measuring the three-dimensional response of

cohesionless and cohesive particulate materials (Li and Puri, 1996).

7

The Mohr-Coulomb model (Figure 2.1), which states that the shear strength increases with

normal stress on the failure plane, is the most commonly used yield criterion in bulk solids flow

theory. It can be represented by equation (2.1).

φστ tan+= c (2.1)

where, is the effective shear stress on the failure plane, c is the cohesion of the material, is

the effective normal stress on the failure plane and is the angle of internal friction.

Figure 2.1 Mohr-Coulomb model

The intrinsic properties cohesion and angle of internal friction are indicators of the

flowability of a powder. In this research, cohesion (c) and angle of internal friction (φ), see

equation (2.1), were used to quantify the flowability characteristics within a narrow size range of

blend constituents. For both parameters, lower values indicate higher flowability and higher

flowability implies higher segregation (Duffy and Puri, 1997).

The flexible-boundary CTT developed by Kamath and Puri (1997) are given in Figure 2.2

and Figure 2.3, which show schematic and exploded view of the (CTT), respectively. The

cubical triaxial tester uses two individual pressure controllers (Proportion-Air Inc.

QB1TFEE015), which can produce pressures from 0 to 100 kPa with ± 0.2% of accuracy over

the entire range. Individual pressure controller regulates horizontal pressure and vertical pressure

independently by triaxial test software developed with LabView (Kandala and Puri, 2000). The

flowability parameters were measured using the conventional triaxial compression (CTC) stress

path (i.e., test). CTC test begins with hydrostatic compression at pressure σc, or confining

pressure. While this confining pressure is kept constant in horizontal directions, the pressure in

τ σ

φτ

8

the vertical direction (i.e., gravity direction) was increased until the sample failed. The failure

stress was denoted as σf. These pressures (σc and σf) are the principal stresses and were plotted

on the normal stress versus shear stress diagram to produce corresponding Mohr circles.

Cylinder capLMP protection cylinder

Test cell wall

Pore pressureport

Test cell frame

Pressureapplicationmembrane

Fastener

Gaskets Sample

Pressureinlet

Electricalwire

feed-through

LMP

Figure 2.2 Cross-sectional view of CTT test cell (Kamath and Puri, 1997) (not to scale)

Frame

Pressure

inletPressure

application

membrane

Wall gasket

Test cell wall

LMP

LMP enclosing cylinder assembly

LMP wires feedthrough

Figure 2.3 Exploded view of one side of the assembled CTT test cell (Kamath and Puri, 1997) (not to scale)

9

2.1.2 Physical property difference effect Hsiau et al. (2002) conducted experiments in a circular container of diameter 12 cm to

characterize the flow behavior of granular material under vibratory conditions using bronze

disks. The thickness and density of disks were 3 mm and 8,780 kg/m3, respectively, and

diameters of disks were 4 mm (100 disks) and 5 mm (120 disks). The circular container was

filled upto 0.35 cm. A sinusoidal horizontal vibratory electromagnetic shaker was used for

producing desired vibrations. A constant vibration frequency of 12.5 Hz and vibrational

acceleration of 1, 2, 3, 4, 5 and 6 were used for vibration study on flowability of particulate

material. Two symmetric convection cells were found based on long-term velocity fields. Higher

vibrational intensity or rough walls can induce stronger convection so as to increase flowability.

With the increase in granular temperature, the convection strength was found to increase linearly.

Chen et al. (2005) analyzed the effect of surface composition of four spray-dried dairy

powders. The four industrial powders tested were spray-dried dairy powders: skim milk powder

(SMP), whole milk powder (WMP), cream powder (CP), and whole protein concentrate (WPC).

The flowability of powders was determined by measuring the angle of repose (a static measure

of relative flowability). The surface composition was determined by electron spectroscopy for

chemical analysis and found different for all these four powders. Although, several parameters

including: size, shape, and density can influence the flowability of powders. But these

parameters were almost the same for these four powders. So, it was concluded that the

flowability of these four dairy powders may be directly related to their surface composition.

Price et al. (2004) studied the effect of size and shape on flowability of powders using

paracetamol, ethanol, cyclohexane, magnesium stearate, microcrystalline cellulose, and talc were

used as supplied. Powder blends were prepared using untreated paracetamol and two small

particle sized samples, one micronized and one SAXS-processed, (49.25%), MCC (49.25%), talc

(1%) and magnesium stearate (0.5%). Angle of repose was measured to characterize the

flowability. Around 2.5 g was filled in the funnel and end of the funnel was placed 2 cm above

the flat base so that after releasing powder from the funnel the top of the resulting cone reached

the end of the funnel. The flowability of blend formed with untreated paracetamol was found to

be better than other two paracetamol. The effect of shape on flowability was found almost

negligible.

10

2.1.3 Relative humidity effect Furuuchia et al. (2005) determined the influence of relative humidity on flowability of

different size and shape glass beads. Two different size ranges of glass beads 500–700 µm and

250–355 µm of density 2,490 kg/m3 were used as the test material. The size and shape of

particles from each sample were measured using an image analyzer of resolution 1,024×1,024

pixels. Three indices were measured to determine the size and shape of test materials, DH =

equivalent area circle diameter, R = aspect ratio (ratio of maximum length to perpendicular

width), PM2/A = (perimeter length)2/(4π (area)), which increases with irregularity and becomes

unity for a circle. The angle of repose was measured to determine the flowability of different size

and shape glass beads under the influence of humidity by both discharge and tilting plane

methods. Results showed that flowability of glass beads was influenced by both size and shape.

The angle of repose value showed that the flowability of both glass beads changed when relative

humidity was in the range of 60-70% relative humidity. The effect of humidity was found to be

dominant on small size particles. The small size beads were more severely affected compared

with large size particles at the same relative humidity.

Rhodes et al. (2002) determined the flowability of glass spheres of particle size ranging

from 25 to 3,000 µm when partially filled in a small glass beaker under different relative

humidity conditions. Test started at 50% RH and 23°C temperature, and slowly relative humidity

increased in increments of 2% and sufficient time was allowed so that test chamber could be

equilibrated. Relative humidity was increased until glass spheres flowability substantially

reduced (called critical relative humidity) due to presence of moisture on the glass beads surface.

Critical relative humidity of large size particles was large whereas for small particles it was

lower. This behavior can be explained by van dar Waals force between two particles, for the

same magnitude of van der Waals force its effectiveness was more for small size particles

compared to large size particles. Drying of materials to the original humidity condition restored

the flowability and no hysteresis was observed

Teunou and Fitzpatrick (1999) studied the effect of relative humidity and temperature on

flowability of food powders (flour, tea, whey permeate) using annular shear cell. Three

parameters, such as instantaneous flow function, cohesion, and angle of internal friction, of

flowability were studied to determine flow behavior under varying relative humidity ranging

from 10% to 60%. Results showed that tea and whey permeate flowability was severely affected

11

with increase in relative humidity as compared to flour. The effect of relative humidity was more

on hygroscopic material compared (tea and whey permeate) to moderate hygroscopic material

(flour). The following paragraphs discuss the mechanisms of mixing and quality evaluation of

mixing.

2.2 Mixing Mixing and segregation go hand-in-hand or in other words segregation and mixing are

two extremes of the same process (Staniforth, 1982), and exist in dynamic equilibrium (Venables

and Wells, 2001). Understanding the mixing mechanism has great importance to understanding

segregation.

2.2.1 Mechanisms of mixing

Formulation of required solid blend is achieved by mixing two or more raw and/or

processed ingredients. The mixing of solids ingredients is governed by commonly three

mechanisms: convective, diffusive, and shear mixing. Most of the mixing of solids is governed

by one or more of these mechanisms in mixers.

Convective mixing: In this mechanism, particles of different properties (multi-component) are

transferred from one place to another in bulk, therefore mixing of particulates is accomplished at

macroscopic level. Particles of different properties in bulk behave differently under the course of

mixing, and changes at a microscopic level are not expected. Therefore, pure convection

considers being less effective in powder mixing, which may exhibit poor mixing characteristic at

microscopic level. Convective mixing is beneficial for batch mixing but provides unfavorable

results for continuous mixing (Barbosa-Cánovas et al., 2005).

Diffusive mixing: In diffusive mixing, an individual particle is randomly transferred from one

location to another either within the mass or on the surface developed on the top of the powder

mass. Pure diffusion, when possible, produces excellent mixing quality in solids at microscopic

level but at an exceedingly slow rate. Fan et al. (1970) concluded that diffusion is the best

mechanism for axial mixing analogous to diffusion of particles in gaseous and liquid phase. The

perfectly homogeneous mixture of multi-component solids can never be achieved at the

microscopic scale (Lindley, 1991).

12

Shear mixing: This mechanism is induced by the momentum exchange between layers of bulk

particulates having velocity gradient. Shear mixing can enhance semi-microscopic mixing and be

beneficial in both batch and continuous mixing operations. Actually shear mixing is combination

of convective and diffusive mixing (Hwang, 1978). Both diffusive mixing and shear mixing give

rise to size segregation in free-flowing powders, therefore, for such powders, convective mixing

is the major mechanism of promoting mixing (Rhodes, 1998).

2.2.2 Quality of mixing: statistical approach

The ideal homogenous mixture of solids can never be made in the real-world condition

because of limited understanding of solids mixing. The quality of mixing or mixture is how

much close to ideal mixture is commonly evaluated by statistical methods (Weinekotter and

Gericke, 2000). Ideal or perfect mixture can be defined as the composition of a component at

randomly selected point in the mixture is the same as that of the overall composition.

To physically evaluate the quality of a mixture, Dankwertz (1952) defined the two concepts, the

scale and intensity of segregation. The scale of segregation was defined as the description of

unmixed components, whereas intensity of segregation was defined as the deviation of

composition from the mean value of a mixture. A poor mix has large intensity and scale of

segregation, whereas a good mixture has smaller intensity and scale of segregation. In fact, more

than 30 criteria have been developed to express the degree of mixedness (Fan and Shin, 1979).

The degree of uniformity of a mixture is commonly evaluated by taking a number of spot

samples. If spot samples are taken at random for analysis, the standard deviation of the analysis,

s, the average value of the fraction of a specific mixture x is estimated by a general statistical

formula (equation (2.2)).

( )

11

2

−

−=∑=

N

xxs

N

ii

(2.2)

where,

N is the number of spot samples, and

ix is the powder composition of ith sample

The standard deviation of a sample is meaningless unless compared to some standard

samples, i.e., completely segregated (so) or completely randomized (sr). The actual standard

13

deviation of a mixture is found between these two extremes, i.e., completely segregated and

randomly mixed. The minimum standard deviation attained for a mixture is sr. Furthermore, if a

mixture is stochastically ordered, sr would equal to zero. Lacey (1954) defined a mixing index

M1, based on these two limiting standard deviations and mixing index is given below (equation

(2.3)):

22

22

1ro

o

ssss

M−

−= (2.3)

In practice, the values of standard deviation, even for a very poor mixture, lie much closer to sr

than to so. Poole et al. (1964) suggested an alternative mixing index M2:

rssM =2 (2.4)

For binary mixtures, the theoretical upper and lower limits of variance of a mixture can be

represented as given in equations (2.5) and (2.6), respectively:

Upper limit (completely segregated): ( )cco xxs −= 12 (2.5)

Lower limit (randomly mixed): n

xxs cc

r)1(2 −

= (2.6)

where,

n is the size of the sample, and

cx and ( )cx−1 are proportions of the two components determined from the sample.

The actual value of mixture variance lies between these two variance extremes (Rhodes, 1998).

Poole et al. (1964) considered a multi-component mixture as a binary mixture and variance is

given in equation (2.7):

( ) ( )[ ]⎥⎥⎦⎤

⎢⎢⎣

⎡

+=

∑ qaapaar wfpwfqw

pqs/

2 (2.7)

where, p and q are the proportion of components by weight within a total sample weight w and

af is the size fraction of one component of average weight aw in a particle size distribution. For

a given component in a multi-component system, Stange (1963) represented an expression for

rs , and is given in equation (2.8):

14

( ) ( ) ( )⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

+++⎥⎦

⎤⎢⎣

⎡ −= ∑∑∑ ...1

222

raaqaapaar wfrwfqwfpp

pwps (2.8)

For a multi-component mixture, the degree of mixedness can also be represented by a

covariance matrix in the same way as in the binary mixture, but its measurement and calculation

procedure are complicated. In practice, the multi-component system is regarded as a mixture of

the single most important component and the others, and it is treated as a binary mixture

(Miyanami, 1997)

2.3 Sampling

Quality of mixing is evaluated by analyzing the samples by destructive and non-

destructive methods. The discussion of non-destructive method is beyond the scope of this

research. The destructive method of sampling is reviewed in the following paragraphs.

The published articles that have contributed toward the evolution and development of the

current sampling method for bagged fertilizers have been reviewed. In 1996, the AOAC

International revised and adopted the sampling method for bagged fertilizers (Kane, 1997). In

section 2.1.01 entitled AOAC Official Method 929.01 – Sampling of Solids Fertilizers, Final

Action 1974 (Revised: March 1996) the official method is presented. As the AOAC official

sampling method deals with both bagged fertilizes and bulk fertilizers, only the bagged fertilizer

method is given below. In addition, the most recent Bulk Blend Quality Control Manual

produced by The Fertilizer Institute (TFI, 1996) has the AOAC Official Method 929.01 (Kane,

1997) summarized.

Bagged fertilizers. – Use slotted single or double tube trier with solid cone tip, constructed of

stainless steel or brass. (Do not use unplated brass for samples on which micronutrients are to be

determined.) Trier length, exclusive of handle, should be approximate length of filled bag to be

sampled, but > 63 cm; length of slot, > 58 cm; width of slot ≥ 12.7 mm; and id ≥ 15.9 mm.

Take sample as follows: Lay bag horizontally and remove core diagonally from end to end. From

lots of ≥ 10 bags, take core from each of 10 bags. When necessary to sample lots of < 10 bags,

take 10 cores but at least 1 core from each bag present.

For small packages (≤4.53 kg) and rigid containers such as buckets or boxes (containing

≥ 4.53 kg and 15.86 kg), take 1 entire package or container as sample.

15

Preparation of sample. – Place composite sample in airtight container and deliver entire sample

to laboratory. Reduce composite sample in laboratory, using riffle.

The AOAC official sampling method has gone through several revisions since its inception in

circa 1880 (Brackett, 1929). Therefore, a brief historical perspective would serve as a useful

framework to better understand the evolution of the current AOAC sampling method. This

summary, presented in proceeding paragraphs, was prepared by perusing the major references

used in the AOAC Official Sampling Method.

Although the fertilizer/feed related-sampling seemed to date back to circa 1880, a definitive

set of recommendations for sampling was proposed by the Association of Official Agricultural

Chemists in 1919 (Brackett, 1929). These recommendations were as follows:

1. That a sampler be used that removes a core from the bag from top to bottom.

2. That at least a pound of the material should constitute each official sample sent to

headquarters.

3. That the entire sample submitted to the chemist be passed through a 10-mesh sieve

previous to its subdivision for analysis.

4. That cores shall be taken from not less than 10 per cent of the bags present, unless this

necessitates cores from more than 20 bags, in which case a core shall be taken from 1 bag

from each additional ton represented. If there are less than 100 bags, not less than 10 bags

shall be sampled, provided that lots of less than 10 bags all bags shall be sampled.

During the 39th meeting of the Association of Official Agricultural Chemists meeting in

1923, the Executive Committee appointed a new committee to study the sampling methods of

sampling for fertilizers (Brackett, 1929). This committee was to review the recommendations

made in 1919 for sampling, enunciated above. Based on the records, these recommendations

remained unchanged through 1947; when by official action, large samples were taken from lots

of less than 200 bags. The minimum number of bags to be sampled was changed to 20, unless

the lot contained fewer than 20 bags, in which case a core was to be taken from each bag.

Miles and Quackenbush (1950) indicated that they were unable to find data to support

either intensity of sampling. In fact, Miles and Quackenbush paper seemed to be the first

interstate (in all seven states), comprehensive study to systematically consider factors that affect

16

the precision of samples and chemical analyses of fertilizers. Furthermore, this study dealt with a

key issue whether a particular lot of fertilizer met the manufacturer’s guarantee. From seven

states, official samples were taken from 106 batches of fertilizers at 41 plants. In this

comprehensive study, four sources of variation were investigated: (1) bags within batch, (2)

cores from same path, (3) positions within bag, and (4) chemical analysis. Based on the

measured variations of these four sources contributing toward uncertainty, the following

recommendations were made for adoption as part of the official sampling procedure for

fertilizers:

1. From a lot of 1 to 10 bags, sample all bags;

2. From a lot of 11 to 20 bags, sample 10 bags;

3. From a lot of 21 to 40 bags, sample 15 bags;

4. From a lot of 41 or more bags, sample 20 bags.

Furthermore, take one full-length diagonal core per bag sampled, except that for lots of 1 to 4

bags, take enough cores per bag – from the same path – to total 5 or more cores from the lot.

For convenience, the above recommendations by Miles and Quackenbush (1950) are

summarized in Table 2.1.

Table 2.1 Recommended sampling intensities (Miles and Quackenbush, 1950)

Bags in Lot Bags to Sample Cores per Bag Sampled Number Number Number

1 1 5 2 2 3 3 3 2 4 4 2 5 5 1

6 to 10 All 1 11 to 20 10 1 21 to 40 15 1

41 or more 20 1

Subsequently Miles and Quackenbush (1955), studied the reliability (i.e., precision) of

chemical analyses for estimating the composition from samples. In their study, three sources of

variation were considered: (1) bag to bag, (2) reduction of large sample to small sample

(especially, riffle vs. manual cone-and-quartering), and (3) technique for chemical analysis. It

was noted that: (1) for all major fertilizer constituents, NPK, the estimated bag to bag deviation

17

(based on measurements) when sampling 20 bags vs. 10 bags was almost similar. In fact,

comparison of deviations from 2 and 400-bag lots was not noticeable; i.e., deviations for the lots

of large sizes were recommended to be applied to a lot of any size. For lot sizes with number of

bags > 20, it was recommended that 10 bags be sampled. (2) Riffle method resulting in better

precision than the manual method was recommended. (3) Although no specific number was

provided, guidance in tabular form for repeating chemical analysis was presented for analyst’s

consideration based on measured deviations.

In a parallel study, Randle (1955) investigated in-depth the variation among true analyses

of laboratory samples prepared by hand vs. riffle reductions. In general, riffle-reduced samples

had less variation compared with true analysis of the original composite sample vs. hand-reduced

samples. Furthermore, the variations associated with riffle-reduced samples were comparable to

those associated with chemical analysis (Table 2.2). Based on this study, the following

recommendations were made for consideration and adoption:

1. That fertilizer samples be reduced to appropriate size through the use of a riffle

2. That sampling and sample preparation of fertilizers be studied further

Table 2.2 Net standard deviations (Randle, 1955)a,b

Net Standard Deviation of Reduction of Samples by:

Nutrient

Hand Riffle

Net Standard Deviation of Chemical Analysis

Nitrogen 0.061 0.049 0.052 Total P2O5 0.194 0.103 0.096

Soluble Potash 0.207 0.134 0.095 aThe unit is percent of the nutrient and not percent of percent bSquare root of components of variance

Gehrke (1972) reviewed the equipment and procedures used by 34 states in sampling

bagged fertilizers. Based on analysis of data, it was recommended that sampling instructions be

amended to include clearer sampler specifications. These were as follows:

Use slotted single or double trier with solid cone tip constructed of stainless steel or

brass. (Do not use unplated brass for samples on which micronutrients are to be determined.)

Trier length, exclusive of handle should be approximately length of the filled bag to be sampled,

but > 63 cm; length of slot > 58 cm; width of slot ≥ 12.7 mm; and id ≥ 15.9 mm.

18

The above recommendation is consistent with the most current AOAC official sampling

method (Kane, 1997). The remainder of the major references cited in the AOAC Sampling

Method deal with bulk fertilizers (Anonymous, 1967; Gehrke et al., 1967 and 1968).

The Association of American Plant Food Control Officials (AAPFCO) Inspection

Manual summarizes the official procedure for sampling methods for fertilizers (AAPFCO,

1999). The AAPFCO official procedure is consistent with the AOAC International procedure in

all but two important dimensional measurements for trier: in AAPFCO, the recommended slot

width is greater than or equal to 19.1 mm (vs. 12.7 mm in AOAC), and the recommended inside

diameter of the trier is equal to or greater than 28.6 mm (vs. 15.9 mm in AOAC). In a recent

development, the AOAC International committee on fertilizer sampling has adopted, apparently,

the trier width to be greater than or equal to 19.1 mm for bagged fertilizers.

The published articles that have contributed toward the most recent AAPFCO

(Association of American Plant Food Control Officials)-adopted trier dimensions for use in

sampling bagged fertilizers were critically reviewed. The AAPFCO official procedure is

consistent with the Association of Official Agricultural Chemists (AOAC) International

procedure (TFI, 1996) in all but two key dimensional measurements for the trier: in AAPFCO,

the recommended slot width is greater than or equal to 19.1 mm (vs. 12.7 mm in AOAC), and the

recommended inside diameter of the trier is equal to or greater than 28.6 mm (vs. 15.9 mm in

AOAC). Recently, the AOAC also adopted the AAPFCO recommendation (Kane, 2005). In the

following paragraphs, summary and critique of the two relevant articles that formed the basis for

the recent recommendation of trier dimensions are presented (Caine and Hancock, 1998, and

Baker et al., 1967).

Baker et al. (1967) were among the first to plan and complete a comprehensive study that

compared and evaluated the performance of five different trier-types available and in-use around

1966. Baker et al.’s study provided the framework and motivation for the most recent

undertaking by Caine and Hancock (1998) in 1996. The findings of Caine and Hancock formed

the basis for adoption of the most recent recommendation of AAPFCO and AOAC concerning

trier dimensions for securing samples from bagged fertilizers that are representative of the blend.

Since the Baker et al.’s seminal study represents a fairly comprehensive experimental design, it

is reviewed first.

19

The basis of Baker et al.’s study was rooted in the key observation by the national

fertilizer group in mid-1960s that various triers and corresponding procedures used for sampling

of dry blended fertilizers were biased in both chemical analysis and physical properties. This

observation was the result of three completed reports: (1) in 1958, Fiskell et al. showed that the

AOAC trier secured more fines (below 20 mesh, SGN=85) compared with the coarse particles in

the dry blend, (2) in 1961, Sauchelli and Duncan reported that the AOAC single and double tube

12.7 mm width triers secured more particles finer than 14 mesh (SGN=140) and less of particles

large than 6 mesh (SGN=335) compared with 22.2 mm slot width Archer Tube, and (3) in 1967,

Gehrke et al. reported the same tendency, i.e., more fines in the AOAC trier compared with

coarse particles representative of the dry blend.

In order to gain a deeper understanding of the mechanisms of segregation that contributed

toward the sampling bias when using the triers, a study was planned by Baker et al. (1967) to test

the effect of four key factors. These factors, deemed responsible for differences in chemical

analysis and physical properties, were:

1) bridging of large particles at the trier opening,

2) selective filling with the more free flowing particles,

3) differential movement of particles in the vicinity of the core to be drawn when disturbed

by the insertion of the sampler, and

4) selective drag-off of larger particles as an open trier is withdrawn from the dry blended

mix.

In all, five samplers, with specifications given in Table 2.3, were tested.

Table 2.3 Specifications of the five triers used for comparison in securing samples from

dry blended fertilizers (Baker et al., 1967) Sampler Specifications

Compartment Openings Trier

Length (mm)

OD (mm)

ID (mm) Number Width

(mm) Length (mm)

AOAC Double Tube 914.4 20.6 14.3 1 12.7 673 AOAC Single Tube 914.4 20.6 17.5 1 12.7 673 524 Grain Probe 1600.2 34.9 28.6 11 23.8 88.9 Missouri 1498.6 28.6 22.2 8 19.1 76.2 Experimental D-tube 1320.8 28.6 41.3 1 25.4 1092.2

20

For their study, Baker et al. prepared three lots (one ton each) by blending in

predetermined proportions binary and ternary mixtures (with known constituents’ particle size

distributions and chemical analysis) to test particle size, size distribution, and shape effects

including chemical analysis. The key concluding observations were:

Bridging of larger particles – In every case, the larger 524 Grain Probe (i.e., trier) of 23.8 mm

slot width secured more of the large size and less of the smaller size fractions when compared

with other four triers. However, the samples by the 23.8 mm slot width 524 Grain Probe more

nearly resembled the calculated (i.e., actual) analysis than the 12.7 mm AOAC triers. In no case

were the differences statistically significant at the 0.05 level of significance.

Selective filling with the more free flowing particles – Surface adhesiveness of particles was

determined to be a key factor influencing the sample bias, i.e., moisture absorption should be

minimized.

Differential movement of particles when disturbed – The gravitational movement of smaller

particles was very clearly demonstrated by the Experimental D-tube trier, i.e., the calculated

analysis was most closely approximated when the sample retaining face was held vertical vs.

upward or downward.

Selective drag-off – This factor was not found to be significant toward sampler bias at the 0.05

level of significance.

Three decades later in 1996 Caine and Hancock (1998) noted that there was an increase

in the absolute particle size of ingredients. The absolute size increase implied that trier-secured

samples may yield chemical analysis and physical particle size distributions, which are not likely

to be representative of the dry blended fertilizer. In other words, use of trier slot width of

12.7 mm may bias the samples with more fines. Toward this end, Caine and Hancock (1998)

designed a study similar to Baker et al.’s to compare sample portions from bagged fertilizers

obtained with three triers (Table 2.4):

(1) AOAC single tube trier with slot width of 12.7 mm wherein the sample flows into the

slotted opening,

(2) Kentucky trier with slot width of 19.1 mm wherein the sample portion is encompassed, and

(3) Indiana trier with slot width of 19.8 mm wherein the sample flows into the slotted opening.

21

Table 2.4 Trier specifications used in sampling bias study by Caine and Hancock (2002) Trier Length

(mm) OD

(mm) ID

(mm) Number of

Compartments Compartment Width (mm)

Compartment Length (mm)

AOAC Single Tube 968.4 22.2 19.1 1 12.7 798.5 Kentucky Trier 777.9 25.4 19.1 1 19.1 635.0 Indiana Trier 976.3 31.8 28.6 1 19.8 798.5

Samples with the three triers given in Table 2.4, were obtained from a large blend

fertilizer plant in Ohio in August 1996. Five products filled in 22.8 kg bags were sampled that

consisted of: (i) high N grade (20-10-10), (ii) High P2O5 grade (8-32-16), (iii) high K2O grade (6-

18-36), (iv) 1-1-1 grade (19-19-19) with least amount of filler, and (v) 1-1-1 grade (12-12-12)

with significant amount of filler. In the sequence designated in Table 2.5, twelve horizontal cores

were drawn from 12 bags. The same sampling hole was used for all three triers. Raw materials

(Urea, TSP, DAP, MOP, and filler), from which these formulations were prepared, were sampled

as well. Upon completion, sample portions from the same triers were collected in separate

containers, which were riffled to obtain analytical and particle size analysis portions using sieve

number 6 (Size Guide Number, SGN=335), 8 (SGN=236), 10 (SGN=200), 14 (SGN=140), and

20 (SGN=85) mesh, where SGN is particle median size upto second decimal in mm*100.

Table 2.5 Sequence of the use of three triers for securing samples from twelve 22.8 kg bags using the same hole*

Bag Number 1 2 3 4 5 6 7 8 9 10 11 12 A K I A K I A K I A K I K I A K I A K I A K I A

Trier Sequence**

I A K I A K I A K I A K *Material condition: Free flowing **A = AOAC trier, K = Kentucky trier, and I = Indiana trier

Chemical analysis and particle size distribution results led to the following key observations:

(1) The Kentucky trier in every case encompassed materials with higher SGN vs. AOAC and

Indiana triers.

(2) The AOAC trier with slot width of 19.1 mm rejected larger particles to a greater extent than

did the Indiana trier with slot width of 19.8 mm.

22

(3) For all three triers, urea samples were not secured as readily when DAP was present in

substantial amounts in the grade. This was attributed to surface adhesion between particles

of the two materials.

Based on this study, Caine and Hancock (1998) recommended that the AOAC standard be

amended to define an acceptable trier as one with minimum slot width of 19.1 mm.

While the study by Caine and Hancock (1998) presents results that are in line with those

summarized by Baker et al. (1967), there are a few significant differences between the two

studies, i.e., some analyses were either not presented in the publication or done in the study by

Caine and Hancock. Accordingly, these are listed below, which require further consideration.

(1) Control formulation for calibration of triers to establish mean and variance of chemical

analysis and SGN and UI of particle size distribution of dry blends prepared from

ingredients – Unlike Baker et al.’s study, Caine and Hancock did not preselect the particle

sizes with known chemical analysis (i.e., control formulation) for preparing the dry blends.

The use of preset sizes and known chemical analysis of ingredients to prepare the blends

(i.e., control formulation) is an important step that is necessary for calibrating the triers,

which are to be subsequently used for securing samples. The trier-secured samples from

control formulation should have been used as the basis for calibrating (i.e., establishing

uncertainty of) the triers for chemical analysis (i.e., mean and variance) and particle size

distribution (i.e., SGN and UI). In addition, variations in particle size and chemical

analyses from storage through pre- and post-mixing are equally important. Therefore, the

uncertainty in mean and variance of chemical analysis and particle size distribution when

using the three triers given in Table 2.4 remain unknown.

(2) Statistical analysis – Statistical analysis was not reported by Caine and Hancock for either

the chemical analysis or particle size analysis to determine if the results based on samples

obtained using the three triers were significantly different. Therefore, Caine and

Hancock’s conclusion, at best, is only an indicator that the three triers result in differing

size and chemical analysis, which is consistent with Baker et al.’s findings; however, Baker

et al. specifically mentioned that the particle size did not lead to significant differences in

chemical and size analysis for trier-secured sample results (based strictly on particle size

distribution effect). Since blends experience different motion conditions during handling

and conveying, the relative movement of particles could result in significant differences in

23

size distribution and chemical analyses. Note that in Baker et al.’s study, particle shape-

related samples did result in some statistically significant differences; though not all.

2.4 Concept of Segregation Researchers have defined segregation from different perspectives. Popplewell et al.

(1989) and Rollins et al. (1995) define segregation as de-mixing or reverse mixing; whereas,

Rosato and Blackmore (2000) define segregation as a “term used to describe the ubiquitous

phenomenon in which bulk solid, composed of particulates with differing constituent properties,

evolves to a spatially non-uniform state.” These three assumptions have been made when

defining segregation:

1) Segregation is primarily concerned with the physical and mechanical characteristics of

particulate materials

2) Segregation occurs only during dynamic phase of particulate materials

3) Segregation occurs only in solid-solid phase

2.4.1 Segregation mechanisms

Tang and Puri (2004) reviewed the thirteen segregation mechanisms based on different

parameters, such as: physical properties of particles (size, density, or shape segregation)

(Venables and Wells, 2001), energy input (vibration, gravity, or shear segregation) (Rosato et al.,

2002) particle movement direction (vertical, i.e., top-to-bottom, and horizontal, i.e., side-to-side,

segregation) (Prescott and Hossfeld, 1994), and the devices used during particulate material

processing (hopper, drum, and chute segregation) (Khakhar et al., 2001; Vallance and Savage,

2000; Shinohara et al., 2002). Based on the above-mentioned parameters and some new findings

by Mosby et al. (1996), Salter (1998) and de Silva et al. (2000), a re-categorization of the

segregation mechanisms (trajectory, air current, rolling, sieving, impact, embedding, angle of

repose, push-way, displacement, percolation, fluidization, agglomeration, and concentration

driven displacement) has been proposed.

Understanding segregation mechanisms is very important in order to minimize

segregation (Johanson, 1978). Carson et al. (1986) simplified the thirteen mechanisms into five

main mechanisms of segregation responsible for all segregation. These five mechanisms of

segregation are briefly described below:

24

1) Sifting- Sifting mechanism can be described as the movement of smaller particles

through a mixture of larger particles. This mechanism occurs under certain conditions

and these are large to small particle ratio more than 1.3:1, mean particle diameter more

than 200 µm, free flowing material, and interparticle motion.

2) Trajectory- In the particulate material mixtures, fine particles or particles irregular in

shape have higher frictional drag. The higher frictional drag and their position near the

chute surface cause shorter trajectories for fine and irregular particles than that of the

coarse and regular size particles, respectively, during chute flow.

3) Fluidization- This mechanism occurs due to permeability difference between coarse and

fine particles. During bin charging and discharging, coarse particles reach the bed but

fine particles remain in the fluidized condition near the top surface.

4) Air stream- During charging and discharging of bin, small particles (≤50 µm) may

remain in air stream. As a result, the secondary air currents can carry airborne particles

away from a fill/discharge point toward outer areas of bin. These fine particles are

scattered in way that there is no resemblance to the calculated trajectory.

5) Dynamic characteristics- Most often, mixture of particle differ in their resilience, inertia

and other dynamic characteristics. The difference in dynamic characteristics of material

mixtures cause them to segregate.

2.4.2 Minimizing segregation

Carson et al. (1986) reported three techniques either to reduce or to eliminate segregation.

These are: 1) change of material, 2) change of process, and 3) change of equipment design.

1) Change of material- Segregation occurs in most of the cohesionless particulate

materials, because they separate from each other very easily. This problem can be

overcome by changing the material properties. The material properties can be changed by

increasing the cohesiveness of materials by adding oil or water and/or by changing the

particle size distribution. Lowering the particle size ratio to 1.3:1 or reducing the particle

diameter below 100 µm will reduce the segregation. Small particle ratio and small size

will also help in reducing fluidization segregation.

2) Change of process- The process can be changed to minimize segregation. Materials used

for product formulations are different in their characteristics. Some are less while others

25

are highly prone to segregation. In these cases, each of these materials should be handled

individually upto final processing step and then proportion and mix them just before the

final step. During mechanical handling operations, some materials have tendency to

segregate from side to side and some have tendency to segregate from top to bottom. In

these cases, transfer of materials should be avoided.

3) Change of equipment design- Two patterns are mostly found in bin flow i.e., mass flow

and funnel flow. Mass flow and funnel flow can also be recognized as first-in, first-out

flow pattern and first-in, last-out flow pattern, respectively. Materials having segregation

potential from side to side while filling are suggested to be handled using mass flow

pattern during discharge to minimize segregation, whereas funnel flow discharge makes

segregation worse.

2.4.3 Quantifying segregation A number of attempts have been made to quantify segregation using particulate materials.

In this section, quantitative study of segregation has been reviewed for binary and multi-size and

multi-component particle mixtures.

2.4.3.1 Binary mixture Researchers have studied segregation using homogeneous and heterogeneous binary

mixtures of particulate materials. These are summarized in the following subsections.

2.4.3.1.1 Homogeneous binary mixture Porion et al. (2004) used nuclear magnetic resonance (NMR) technique to characterize

the kinematics of size segregation of dry binary mixtures (either poppy seeds or sugar beads)

(diameter dmin and dmax) in turbula mixer, where, dmin represents the fine particle diameter and

dmax represents the coarse particle diameter. Turbula mixer uses inversion kinematics for mixing

solids and liquids. It works on three-dimensional motion principle (Paul Schatz principle)

combining a possible eight-directional motion. In this experiment, binary mixtures were

investigated, and results were compared to the ideally mixed identical particles. For 50–50%

mixtures, a segregation index S was defined and computed from the MRI images for quantitative

analysis. Segregation index can be defined as the standard deviation of the spatial distribution of

26

the concentration and mathematically presented in the following equations (2.9), (2.10), (2.11),

and (2.12):

∑=

−

=vN

ii

v

xN

x1

1 (2.9)

22 )(1

1 ∑−

−−

= xxN i

v

σ (2.10)

Segregation index (S) = ∑∑=

−

− −−

=VN

ii

Vi

V

xN

xxNx 1

2 1/)(1

1σ (2.11)

222ram σσσσ ++= (2.12)

where,

xi = local concentration of reference probe beads,

NV = total number of voxels

σ = sample variance

σm = mixing error variance

σa = analysis variance

σr = error done to limited number of particles

The results showed that container should not be filled above 80% of the height.

Segregation in the binary mixtures was influenced by two mechanisms. The first, surface effect,

works at any rotation speed of turbula mixer cylinder due to shear-induced percolation. Shear-

induced percolation motion extracts the coarse particles outside the mixture and percolates the

fine particles in a mixture. The second, bulk mechanism whose strength depends on the rotation

speed and disappears at fast rotation speed

McGlinchey (2004) used the binary coal mixtures to quantify heap segregation (also

known as poor mixing) using statistical technique ANOVA. The experiment was done by using a

double feeding two layers of coal of different size fractions directly over the conveyor belt. The

dimension of conveyor belt was 2.5 × 0.5 m2. The heaps were formed on the conveyor belt

because of free flowing coal mixture from the double cone hopper. Each heap was divided into

six sampling regions (Figure 2.4). Segregation was quantified and compared using coefficient of

variation proposed by several researchers such as Syskov and Lyan (1960), Jenike (1960), Lacey

(1943), Ashton and Valentin (1985), Carley-McCauly and Donald (1962), Harris and Hildon

27

(1970), and F-value of Rollins et al. (1995) methods. The F-value of Rollins et al. was the best

among statistical methods mentioned above.

Figure 2.4 A heap divided into sampling regions (McGlinchey, 2004)

Tang (2004) designed and fabricated second generation primary segregation shear cell

(PSSC-II) for percolation segregation. The PSSC-II was the improved version of PSSC-I used by

Duffy and Puri (2000). Additionally, Tang (2004) used fine and coarse glass beads and poultry

mash feed to quantify percolation segregation. Glass beads (GG) and poultry mash feed (FF)

were used for homogeneous binary mixtures to quantify percolation segregation. In these binary

mixtures, first letter represents coarse particle and second letter represents fine particle. Letter G

was used for glass beads (representative of an ideal material) and letter F was used for poultry

mash feed (representative of a real-world material).

Binary mixture of glass beads (GG combination)- Tang (2004) studied the time-

dependent percolation segregation using binary mixture of glass beads and found the

following:

1) Size ratio, absolute size, and their interactions have a significant effect on normalized

segregation rate (NSR) (p<0.05). In addition, a linear relationship with NSR was

Top

Heap

Cor

e N

orth

So

uth

Wes

t

East

28

observed. Before defining NSR, segregation rate was defined as the mass of fine

particles discharged through the sieve screen per unit time during operation of second

generation primary segregation shear cell (PSSC-II). The normalized segregation rate

(NSR) was defined as rate of the ratio of collected fines mass to feed fines mass (unit:

g/g/s). The NSRs were measured to overcome the limitations of the measurement

system such as limited number of sampling points, limited number of space positions,

and limited quantity of segregated fines. The total segregated fines mass was

measured using an accurate balance (±0.01 g) and the total time with a stop watch (±1

s). Total time was the discharge time taken by entire fine particles from vertical

funnel under the action of gravity.

2) Both duration of lag phase (DLP) and duration of acceleration phase (DAP) decreased

with increasing size ratio as well as absolute size. Time taken by fine particles to start

discharge from sieve screen after following tortuous path through coarse particle bed

was known as duration of lag phase (DLP). Duration of increasing segregation rate

due to increasing void spaces in a coarse particle bed was defined as duration of

acceleration phase (DAP). As the maximum segregation rate (MSR) increased, DLP

and DAP decreased. Generally, the segregation rate attains a maximum value known

as MSR.

3) The distributed segregation rate (DSR) for larger size ratios such as 8:1 and 6:1 was

concentrated in the center region of the shear box and uniformly distributed for size

ratios 4:1.

Binary mixture of poultry mash feed particles (FF combination)- Tang (2004) studied

time-dependent segregation using poultry mash feed and found the following:

1) In the FF combination, a linear relationship between NSR and absolute size was

observed but not for size ratio. The absolute size ratio and size ratio effects were

significant (p<0.05).

2) The DSR was concentrated along the two sides of the shear box.

Duffy and Puri (2003) used fine and coarse glass beads to quantify percolation

segregation with a primary segregation shear cell (PSSC) (Figure 2.5). Primary segregation shear

cell was designed and built on the basis of percolation mechanism, which occurs in a mixture of

29

fine and coarse particles due to external disturbance. Two different sizes (small and large) of

glass beads were used in this experiment, small and large particles were called fine and coarse

particles, respectively, in this study. Duffy (2001) found that 5% and 25% are the two extremes

of shear strain for primary segregation shear cell for percolation segregation. For a given strain

and cycle speed, three depths of coarse particles, i.e., 2.54 cm, 5.08 cm and 7.62 cm were tested.

The main conclusions drawn by Duffy and Puri (2000) were as follows:

1) Two percolation mechanisms such as free-fall and diffusive were identified for binary

mixture of glass beads

2) Size ratio was the most dominant factor that influenced the percolation mechanism

3) The percolation of fines through a bed of coarse particles was isotropic

4) Strain and cycle speed were found to be critical in the type of percolation exhibited

5) The first generation primary segregation shear cell (PSSC-I) was a suitable device for

studying percolation segregation.

30

Motor

Cam

Nylon Walls

Collection Pan

Shear Box

Air Inlet

Figure 2.5 Vertical motion segregation shear cell (Duffy and Puri, 2002)

31

2.4.3.1.2 Heterogeneous binary mixture Tang (2004) studied time-dependent segregation of heterogeneous binary mixtures of

glass beads and poultry mash feed in two sub-combinations. The key findings are summarized

below.

Binary mixture of coarse feed and fine glass beads (FG combination)- Both absolute

size and size ratios have a linear relationship with normalized segregation rate (NSR).

The normalized segregation rate is defined as the ratio of collected fine mass to feed fine

mass divided by total time. However, this relationship did not hold for particle

combination FG710. FG710 represents the binary mixtures of coarse poultry mash feed

particle and fine glass beads and size of coarse particles was 710 µm. Like GG

combination, distributed segregation rate (DSR) concentrated in the center region of the

shear box for larger size ratios such as 8:1 and 6:1 and relatively uniform for size ratio

4:1. Distribution of segregation rate is defined as distribution of segregated fines. These

results indicated that fine particles in higher size ratios followed the shortest path in the

coarse particle bed

Binary mixture of coarse glass and fine feed particles (GF combination)- Like FF

combinations, the DSR concentrated along the two side regions of the shear box. Both

absolute size and size ratio effects are significant (p<0.05) but linear relationships

between the NSR and size ratio and between NSR and absolute size do not exist. Unlike

FF combination, a smaller NSR was obtained for larger absolute size.

2.4.3.2 Multi-size mixtures Shinohara et al. (2001) used spherical glass beads of size varying from 174 to 1660 µm to

make different composition mixtures (two to five) for quantifying size segregation. Two-

component mixtures consisted of GB1 and GB4, three-component mixtures consisted of GB1,

GB2, and GB4, four-component mixtures consisted of GB1, GB2, GB3, and GB4, and five-

component mixtures consisted of GB1, GB2, GB3, GB4, and GB5. Various sizes GB1, GB2,

GB3, GB4, and GB5 are given in Figure 2.6. Overall characteristics of segregation for multi-

component were defined by segregation index. Mathematically, segregation index (Is) was

defined and given in equations (2.13) and (2.14):

Is = σ/M1 (2.13)

32

where,

σ = deviation of concentration of the smallest component at different sampling positions

along the heap line

M1 = initial concentration

21

11

2 )(1

1 MMn

n

jj −−

= ∑=

σ (2.14)

jM1 = concentration of component j

j = 1, 2, 3, 4, and 5

n = number of components

In this study, it was found that segregation increased with an increasing number of

components from two to three and then decreased for the four and five-component mixture. As

the relative size difference of the components decreased with increasing number of components,

the possibility of penetration of fine particles into the voids became lower with increasing

number of components in the mixture. Segregation of multi-component mixtures during vessel

filling revealed that the degree of segregation was significant at low initial fine particle

concentration and low mixture feed rate (Figure 2.6). Segregation initially increased and then

decreased with increasing number of different sized particle components in the feed mixture.

Figure 2.6 Schematic of two-dimension experimental apparatus for multi-component size

segregation (Shinohara et al., 2001)

Particle diameter, cm GB1 0.0174 GB2 0.0358 GB3 0.0507 GB4 0.0784 GB5 0.166

33

2.4.4 Fertilizer segregation

2.4.4.1 Homogeneity of fertilizer Lance (1996) mentioned that there is no European standard for determining fertilizer

homogeneity. In Europe, fertilizer homogeneity is determined by French standard NF U 42-405.

In this method the fertilizer is split into three size fractions, the top 10% (oversize), the middle

80%, and the bottom 10% (fines) and analyzed chemically for N, P, and K. If the results for the

fines and oversize are close to the declared analysis, the fertilizer is called homogeneous.

Lance (1996) also mentioned that sizes and density are responsible for segregation during

storage and transportation in conditions where relative motion of the particles is possible. But the

effect of fertilizer density on segregation is almost negligible as compared to size ratio of the

particles. Responsibility of shape for the fertilizer segregation is almost non-existent. Surface

roughness appears merely to retard the process of segregation without influencing the final

result.

2.4.4.2 Blend quality evaluation The fertilizer blending quality is defined by the size grade number (SGN), the uniformity

index (UI), and mixing quality index (MQI). The SGN is the calculated mean diameter expressed

in millimeters and multiplied by 100. In other words it is equal to 100 times the d50. The UI is the

ratio of the sizes of small and large particles expressed as percentage. Small in this context is the

5% level and large means the 90% level. In other words it is (d5/d90) × 100. The MQI is the

combination of the UI and the SGN and it is calculated from the coefficients of variation (CV) of

the SGNs and UIs between the individual raw materials used in the particular blend and given in

equation (2.15).

MQI = 1.0 – CV of SGNs – CV of UIs (2.15)

The MQI is less reliable system than the SGN or UI when only two raw materials are involved as

the CV has little statistical significance.

Williams and Shields (1967) used a binary mixture of granulated fertilizer granules of

two sizes and fed into a vibrated channel so that vertical size segregation took place. The amount

of segregation onto a rectangular vibrated plate was studied by splitting the stream into upper

and lower halves. The downward slope was 11° to the horizontal. Speed of the flywheel to

produce vibration in the bed was 1425 r.p.m. The amount of segregation was given by the

coefficient of segregation, equation (2.16).

34

Coefficient of segregation (Cs) = 100×+

−

B

B

T

T

B

B

T

T

Ww

Ww

Ww

Ww

(2.16)

where,

WT = total weight in the top half

wT = weight of large particles in the top half

WB = total weight in the bottom half

wB= weight of large particles in the bottom half

2.4.5 Size segregation mathematical models Mathematical study of segregation plays an important role in evaluating the processing

operations for powders, such as, handling, storage, manufacturing, and processing. Moakher et

al. (2000) divided the mathematical models for granular flows into three categories, i.e.,

continuum, kinetic theory, and discrete models.

Continuum models- These models neglect the discrete nature of grains and assume a continuous

variation of matter that obeys conservation laws of mass, momentum and energy. Examples of

continuum models are soil plasticity and fluid mechanics

Kinetic theory- Kinetic theory models using the property of colliding molecules of a dense gas

to explain the phenomena of particulate materials interaction. This theory is based on the

averaging methods of conservation laws of mass, momentum, and kinetic energy of particulate

materials.

Discrete models- Discrete models admit numerous classifications, but all take the constituent

grains to be distinct and to move according to prescribed rules. Two types of particle dynamics

methods are commonly used in these models, i.e., hard-particle (instantaneous collision) and

soft-particle (lasting and multiple collision). The behavior of particulate materials is very

complex because it follows the law of solids, liquids and gases at the same time. A single type of

model cannot cover the overall picture of segregation in particulate materials.

In the following subsections, five percolation segregation mathematical models under the

category of continuum, kinetic, and discrete models are reviewed. These five percolation

segregation models are: 1) Comprehensive mechanistic theory-based segregation model (MDT)

(Tang 2004), 2) Convective and Diffusive model (Duffy and Puri, 2003), 3) Hopper model

35

(Asmar et al., 2003), 4) Granular flow model (Boateng and Barr, 1996), and 5) Drum Model

(Ding et al., 2002).

2.4.5.1 Comprehensive MDT model Tang (2004) developed a comprehensive mathematical model for GG and FG particle

combinations. The porosity of coarse particles was utilized to quantify the coarse particle shape

effect. The use of porosity may not be nearly as accurate as using individual particle shapes

measured through ratio of dimensions (length, width) or index compared with an ideal spherical

shape particle (Gotoh, 1997). However, with consideration of the bulk solids continuum

assumption and extensive time and resources needed to quantify the individual particle shape

parameter, as a first approximation, porosity was used to quantify the coarse particle shape for

larger particle sizes. This can be more clearly explained by using interstitial void space theory.

For instance, Yi et al. (2001) stated that: 1) irregular shaped particles can readily lodge in

the interstitial void spaces, and 2) void spaces formed from irregularly-shaped coarse particles is

larger than that for sphere-shaped particles. Therefore, it is reasonable to use porosity to quantify

the shape effect.

Based on the shape effect, a model of the following form was developed, equation (2.17),

and verified:

( ) ( )nm

absp SRatioH

DShpcStRateNSR

⋅⎟⎠⎞

⎜⎝⎛⋅⋅= (2.17)

where,

Shp= porosity (%),

NSR= normalized segregation rate (kg/kg/s),

StRate= strain rate (m/m/s),

c= constant coefficient, dimensionless,

Dabs = absolute size of coarse particle (m),

H= coarse bed depth (m),

SRatio= size ratio of the binary mixture (m/m),

m= the power indicates the contribution of absolute size to NSR/StRate, and

n= the power indicates the contribution of absolute size to NSR/StRate.

With the consideration of the effect of other factors such as relationship of passed fine

particle number to the void space, relationship of gravity force to fine particle size, and porosity

36

variation, the regressed coefficients for the four terms of the model were slightly adjusted as

shown in equation (2.18).

( ) ( )SRatioH

DShpStRateNSR abs ln5.2)ln(5.1ln75.04)ln( +++= (2.18)

Namely, the comprehensive model for GG and FG combinations is:

( ) ( )252

3

43

6.54 SRatioH

DShp

StRateNSR abs ⋅⎟

⎠⎞

⎜⎝⎛⋅⋅= (2.19)

2.4.5.2 Convective/diffusive model Duffy and Puri (2003) developed two segregation models, i.e., PSSC convective model

and PSSC convective/diffusive model. The glass micro-spheres (glass beads) of two different

sizes were used in this experiment. The small and large glass beads were called as fine and

coarse particles, respectively. The motion of the fine particles was divided into two phases such

as initial phase and final phase. These two models were developed based on the Fick’s second

law of diffusion and the Fokker-Planck equation. The first percolation segregation model was

considered as convective mechanism because convection had dominant role in the initial phase

of fine particle motion. With reference to Figure 2.7, the convective model is presented in

equation (2.20).

⎪⎩

⎪⎨⎧

>>

>

∂∂

−=∂∂

0cos

0

θθ

θθ ht

mutm (2.20)

where, m = mass of fines (kg)

t = time (s)

θ = location (degree)

θu = coefficient (unit: length per unit time)

h= bed depth (mm)

The second model, PSSC convective/diffusive model, is derived from the Fick’s second

law of diffusion and the Fokker-Planck equation, i.e., both convective and diffusive mechanisms

are considered in the percolation segregation, equation (2.21).

⎪⎩

⎪⎨⎧

>>

>

∂∂

−∂∂

=∂∂

0cos

0

2

2

θθ

θθ θθ ht

mumDtm (2.21)

37

θD = the diffusive components or coefficient (unit: area per unit time)

Both Model 1 and Model 2 quantify the mass of fines (m) at any given time (t) and

location along the θ-direction of the bed depth (h) using the material parameters θD and θu

(Figure 2.7).

Duffy and Puri (2003) found that the PSSC convective/diffusive model represented the

normalized mass versus time relationships better than the PSSC convective model especially for

the smaller size ratios.

Collection Pan

i

j

k

(0,0,0)

Mesh Screen

h

50.8 mm

101.6 mm

#1

#2

#3

#4

#5

#6

#7

#8

#9

#10

#11

#12

#13

#14

#15

#16

#17

#18

θ - Direction

θ

Figure 2.7 Schematic of global coordinates (Duffy and Puri, 2003)

2.4.5.3 Hopper model Asmar et al. (2003) used discrete element method to model the percolation segregation of

binary mixtures in a hopper filling process. The fine particle and coarse particle had different

characteristics. The percolation of fine particles in a bed of coarse particles was studied. This

model included the particulate material characteristics such as absolute size, density, initial

38

velocity, initial position and friction. The normalized height (varies from 0 to 1) of the fine

particle could be expressed and given in equation (2.22) as follows:

max,max z

ssn rZ

rZH

−−

= (2.22)

where,

Zs = height of the fine particle

Zmax = height of the highest particle in the bed excluding the fine particle

rs= radius of the fine particle

rz = radius of the highest particle in the bed excluding the fine particle

The movement of fine particle was dependent on its normal height location:

Rise: Hn > 0:4

Neutral: 0:4 > Hn > 0:3

Sink: Hn < 0:3

In the DEM, selection of time step plays an important role for stability and accuracy of the

numerical integration. Time step was expressed in mathematical form and given in equation

(2.23).

kmCt =∆ (2.23)

where,

m = mass of the fine particle

k = spring constant of fine particle

C = proportionality constant (0.1 or 2 or 2π/10)

The following assumptions were made in the development of this model:

1) The materials were cohesionless and results valid for particles having sizes greater than

1,000 µm.

2) Particles had constraint motion in x-y plane and free motion in z-direction.

2.4.5.4 Granular flow model Boateng and Barr (1996) developed granular flow segregation model to predict the

movement of particles in the shearing active layer (Figure 2.8). The granular flow model was

able to determine the extent of fine particle segregation based on the principle of percolation in

39

the active layer of coarse particles. The rheological properties of particles such as size, shape and

surface characteristics, rotation rate of cylinder, degree of fill of cylinder, bed motions in

transverse plane (centrifuging, cataracting, cascading, rolling, slumping and slipping) were

considered for developing this model (Henein et al., 1983).

Using continuity equation, diffusion and convection concepts, a governing equation was

developed to predict the segregation of fines in the bed of coarse particles in the active region of

steady-state flow (Figure 2.9), equation (2.24).

0)()21(2

2

=∂∂

−∂∂

−+∂∂

xC

yuy

CCvp

yC

D JJJ

Jy (2.24)

where,

3

3

1 σησρ+

=JC

pl

ps

dd

=σ

F

J

ηη

η =

ρ = solid concentration

Jη = number of fine particles

Fη = number of coarse particles

psd = diameter of fine particles

pld = diameter of coarse particle

u(y) = velocity profile

vp = the percolation velocity

Dy = diffusion coefficient

40

Figure 2.8 Percolation segregation mechanism and calculation domain (Boateng and Barr,

1996)

Figure 2.9 Material conservation control volume in the active layer

(Boateng and Barr, 1996)

41

The following assumptions were made for the above model:

1) The mechanism of segregation was considered as steady-state

2) The segregation process was continuous and there was constant discharge of fines from

the plug flow region into the active layer

3) The tongue formed by the segregated material contains both fine and coarse particles so

there was concentration gradient in the mixture (Henein et al., 1983)

4) The bed behavior remains unchanged with addition of fines (Henein, 1980)

5) The percolation velocity of fine particles depends on the size of the voids formed in an

underlying layer of particles; these voids are formed in a random manner (Savage and

Lun, 1988)

6) For particles below some critical size, spontaneous percolation may also occur in the plug

flow region thereby resulting in a possible collection of fines near the bed-wall interface

(Bridgwater and Ingram, 1971)

7) Downward movement of segregating particles in the active layer is compensated by an

equal volumetric upward movement of bulk particles in the active layer I-squeeze

expulsion mechanism (Savage and Lun, 1988)

2.4.5.5 Drum model Ding et al. (2002) used a non-invasive positron emission particle tracking (PEPT)

technique to follow the motion of different sized particles during percolation segregation.

Segregation potential of binary mixtures of glass beads were studied in the transverse plane of a

rolling rotating drum (Figure 2.10a). The developed mathematical model was two-dimensional

and based on the Eulerian approach and thin layer approximation, equation (2.25). The bed

structure of a binary mixture consisted of two regions, i.e., active region and passive region (near

the drum wall) (Figure 2.10b). Segregation model developed by Savage and Lun (1988) for

inclined chute was the reference for this model. The net percolation velocity in y-direction was

only taken into account because mass flux in x-direction overcame the percolation segregation in

this direction (Figure 2.10c).

42

Figure 2.10 (a) Rotating drum in rolling mode, (b) active-passive interface, and (c), and

flow mode volume derivation (Ding et al., 2002)

⎟⎟⎠

⎞⎜⎜⎝

⎛=

dydudvv plpop (2.25)

where,

( )

( ) ( )( )

E

NM

kE

NMk

v

AV

LT

po ∆×

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡⎟⎠⎞

⎜⎝⎛

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+

+++

++

+⎟⎠⎞

⎜⎝⎛

=−

2

2

23

11)1(1)1(

14

ησησηησηπ

ησ

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

−

−−+−+−

⎪⎭

⎪⎬⎫

⎪⎩

⎪⎨⎧

−

−−+−+=∆ −

−

−

−

m

mama

m

mbmb

EE

EEEEE

EE

EEEEEE exp)1(exp)1(

( ))1(

1ηση

++

=aE

43

( ))1(

1ησση

++

=bE

pl

ps

dd

=σ

psd = diameter of small particle

pld = diameter of large particle

η = size ratio of large to small particles

LTk = layer thickness constant

NM = constant (depending on particle packing)

mE = constant (depending on particle packing)

−

E = mean void ratio diameter

AVk = constant (depending on particle packing)

The velocity difference between small and large particles was negligible at low rotational

speeds but velocity difference was small in the active region and negligible in passive region at

high rotational speeds. The surface velocity normal to the bed surface direction was less than

15% of their counterpart in parallel direction in the active part of the flow region.

2.5 Second Generation Primary Segregation Shear Cell (PSSC-II) Tang and Puri (2004) developed a PSSC-II to quantify segregation caused by various

factors such as, particle size, size distribution or size ratio, particle density, shape, surface

texture, and electrostatic charge. With this innovative test device, the segregation potential of

binary combinations of two test materials, glass beads and laying hen mash feed, was examined.

Tang (2004) concluded the following:

1) PSSC-II is capable of quantifying size segregation of a variety of powder mixtures with

different particle size distribution

2) The percolation procedure can be observed and recorded visually

3) PSSC-II is able to simulate the segregation occurring under real world conditions through

adjustment of particle bed depth, strain, and strain rate

44

4) Percolation distribution (isotropic or anisotropic) and percolation rate are recorded in real

time, i.e., during the process

5) PSSC-II data enables the development of size segregation constitutive model for powders

and powder mixtures.

Tang (2004) mentioned the limitations of the PSSC-II by assessing the versatility of

PSSC-II in the quantification of segregation potential of different test materials (glass beads and

poultry feed). On the basis of the above facts, Tang (2004) recommended to improve

measurement systems (capacity, 2 g, and accuracy) and also to modify upright wall compartment

of shear cell into sloped wall (pyramid shaped) compartment to minimize the effect of wall

friction.

2.6 Vibration-induced Segregation Williams and Shields (1967) considered particle size and density as the main factors

responsible for segregation under vibration. Results showed that size was the most dominant

parameter contributing towards segregation. Two mechanisms of size segregation were identified

for particle segregation under vibration: 1) percolation of fines through the coarse and fine

particles bed and 2) vibration-induced segregation causing large particles to move upward

through a mass of finer particles. Number of experiments had been carried out for different size

ratios of binary mixtures onto a rectangular vibrated plate so that a bed of particles along the

plate as it would on a vibrated screen. The extent of segregation was measured by splitting the

stream into lower and upper halves for analyzing composition after vibration. The slope of the

plate was 11 degree throughout the experiment to assist flow along straight line in the to and fro

motion under simple harmonic motion. An a.c motor of 1/3 h.p. at constant speed of 1425 r.p.m

was used, speed of the motor could be controlled by a variable speed control gear that permits

variation from 400 to 1600 r.p.m. The three channels of length 15.24, 30.48, and 45.72 cm with a

0.64 cm thick base and 5.08 cm perpex. To prevent the slip of whole bed along the slope of the

channel, the surface of the channel was roughened by sticking to it a 0.32 cm thick layer of the

granules using a perspex cement. Fertilizer of round shape was used for the tests because of its

free-flowing, resistant to attrition and availability in the required size range. The density of the

fertilizer was ranged from 1041 to 1105 kg/m3. Binary mixture mass (80 g each time) in weight

proportion 1:1 (large to small) was poured into rectangular hopper in layers. Individual streams

45

of large and small particles collected side by side onto a firmly clamped inclined plate. The

trajectories of streams were selected in such a way that streams intermixed after leaving the

plate. The mean diameters of large and small granules used were 2.23 and 0.78 mm, respectively.

The direction of vibration was 30 degree to the horizontal at constant amplitude of 0.35 cm and

six different frequencies ranging from 836 to 1,400 rpm. The direction of vibrations varied from

15 to 45 degrees at the interval of 7 1/2 degrees with the horizontal and four different amplitudes

while frequency kept constant. The amplitudes were also varied from 0.25 to 0.55 cm and

frequencies from 700 to 1600 rpm, when channel was vibrated at an angle of 30 degree to

horizontal. Three size ratios i.e., 2.87, 4.0 and 5.6 were tested, the mean particle dia being kept

constant at 1.6 mm when direction was 30 degrees, amplitude 0.35 cm and frequency varied. It

was found that the effect of the type of vibration on the amount of segregation could not be

uniquely described in terms of either the maximum acceleration of the bed or the vertical

component of this acceleration. Most of the segregation was found to take place in the first six

inches of the bed. Segregation was the maximum when direction of vibration made an angle of

about 30 degrees to the horizontal; the frequency of vibration was 1,300 rpm and the amplitude

0.35 cm.

Lawrence and Beddow (1968) studied the segregation mechanism using absolute coarse

(2,000 and 177 µm) and fine sizes (500 and 325 µm) lead shot in the size ratio of 4:1. The

vibration conditions varied between 0-1.52 cm amplitude and 0-100 Hz vibration frequency.

Three regions of differing composition were observed:

1) at low frequency and amplitude dilation was minimal and powder mass was relatively

quiescent.

2) at high frequency and amplitude, the entire powder was moving out of phase with the die

and was actually bouncing in the die

3) at intermediate frequency and amplitude the powder mass was moving relative to die

producing a churning action.

The effects of vibration upon radial segregation in the binary mixture consists of large coarse and

fine particles show that

1) Normal segregation in the outer zone was reduced by vibration.

46

2) Inverse segregation was not noticeably increased by vibration but occurs in coarser

mixtures more than in the case without vibration.

The effects of vibration upon vertical segregation given

1) at low frequency and amplitude low segregation was observed

2) at high amplitudes low segregation was observed

3) at intermediate amplitude segregation was high and particularly at higher frequency

Ahmad and Smalley (1973) studied the vibration induced segregation of a large lead

particle in a bed of fine sand particles using a cylinder container. The diameter of lead and sand

particles were 12.7 mm and 500-600 µm, respectively. The frequency and acceleration under

which binary mixtures studied were 50-150 Hz and 1-10 g, respectively. The six parameters were

studied: 1) initial position of large particles in the bed, 2) frequency of vibration, 3) acceleration

(r.m.s), 4) size of large particles, 5) density of large particles, and 6) shape of large particles.

The obtained results were concluded as the followings:

1) Position of large particle in a bed of fine particles affects the rising time so as the

segregation. Large particle placed in the bottom took longer time than the particle

positioned in the middle of the bed to rise to the top.

2) Lower accelerations and higher frequencies may be useful in controlling segregation of

large particles.

3) Larger the sand bed depth higher the segregation time. There was no direct relationship

found between segregation time and depth of sand bed under the same identical vibratory

conditions.

4) The extent of segregation increased with increasing the size of large particles.

5) The tendency to segregate decreased with increasing density of large particles.

6) No significant effect of shape was observed on the segregation of large particle.

Harwood (1977) studied vibration-induced segregation of a radioactive marker sand in a

bed of each of the free flowing (flint and banding sand), incipiently cohesive (lactose), and

cohesive (milled zircon) powders. The size distributions of the each of above mentioned material

can be found (Harwood, 1977). Oslen and Rippie (1964) showed the effect of size and density on

47

vibration-induced segregation using binary mixtures of glass and steel spheres. They also found

that size of particle has dominant effect on segregation compared to density of spheres. In this

article, parameters of tested particles were chosen accordingly to show the effect of size and

density on segregation. The dimension of the cylinder used in the study was 19.1 mm in diameter

and 152.4 mm in length. Segregation was found minimal when binary mixtures of marker sand

and free flowing sand of the same size and density were used and also when marker sand used

with incipient cohesion material in binary mixture. At intermediate level of amplitude and high

frequencies, segregation was found maximum in the binary mixtures. Truly cohesive powder

(zircon) showed little effect frequency once the powder had packed down to its final bulk

density.

Rosato et al. (2002) reviewed the size segregation in binary mixture. They mentioned that

the first qualitative study was done by Williams (1963) to study the effect of vibration on motion

of a single large sphere in a bed of sand when vibrated vertically. Williams found that locking of

small particles underneath a large particle prevent large particle to move down when subjected

vibration. In a subsequent paper (Williams, 1976), four physical properties i.e., size, density,

shape and elasticity were studied-and three mechanisms of segregation were also identified:

trajectory, percolation of fines and the rise of coarse particles due to vibration. The effect of

different physical properties such as particle size and distribution, density, shape agitation

studied was studied under sinusoidal frequency (Oslen and Rippie, 1964; Rippie, 1964; Faimen

and Rippie, 1965; Rippie et al., 1967). It was also found that the presence of an intermediate size

reduces the extent of segregation. This was confirmed by the results found by Jha and Puri

(2005) using sugar mixtures of different sizes under shear motion.

Generally, segregation is governed by combinations of mechanisms, which themselves

depend on the nature of the flow, particle properties and environmental conditions. The

properties which usually affect segregation are particle sizes and distributions, shape,

morphology, contact friction, elasticity, brittleness, shape, density, chemical affinities, ability to

absorb moisture, magnetic properties, different time and length scale, vibration under vertical

vibrations applied to bulk solids of different sizes. Bridgwater and his colleagues were the

pioneers in identifying the dominant mechanisms responsible for segregation (Bridgwater et al.,

1969, Bridgwater and Ingram, 1971, Scott and Bridgwater, 1975 and 1976, Bridgwater, 1976 and

1999, Cooke et al., 1976, Cooke et al., 1978, Stephens and Bridgwater, 1978, Cooke and

48

Bridgwater, 1979; Foo and Bridgwater, 1983; Bridgwater et al., 1985). They found that size was

the most dominant parameter contributing toward segregation under vibratory conditions.

Granular materials were also studied under horizontal shaking by numerous researchers

(Herrmann, 1994; Liffman et al., 1997). Vallance and Savage (2000) indicated that density

segregation was far weaker than that promoted by size. Based on the review of the above

mentioned articles, Rosato et al. (2002) mentioned size as the major parameter contributing

towards segregation and confirmed the result by a simple experiment. An acrylic cylinder of

diameter 6.35 cm rigidly mounted onto an electromagnetic shaker to move up and down. The

diameter of acrylic beads was 3.175 mm and filled upto 9.151 cm in the cylindrical container.

The amplitudes and frequencies varied from (0.0375<a/d<0.24) and f(25 Hz<f<100 Hz), the

time of operation kept constant at 10 minutes.

The binary mixtures of glass beads and steel of the same size were studied to observe the

effect of vertical vibration on segregation (Yang, 2006a). Three main mechanisms have been

proposed by which segregation does happen due to vibration. These are a) geometrical

organization, b) size percolation, and c) convection. Among these three, the size difference of the

granular material was the most dominant parameter responsible towards segregation under

vibration. A sinusoidal electromagnetic vibration system (Gearing and Watson, V-20) firmly

attached to rectangular tank was used for vertical vibration in the granular particles bed. The

dimension rectangular tank was 21.6×10.8×0.35 cm3 and all sides, except top, were roughened

by a layer of #400 papers so that materials can not slip along these walls when subjected to

vibration. The size of the spherical glass beads and steel balls was 3 mm. The ratio of number of

steel ball and glass beads was 0.5 and total number of particles was varied by adjusting the

height of the bed in the tank. The acceleration amplitude and frequency used in the test were 3.0

and 15 Hz, respectively. After a few seconds of vibration, the steel balls started to mix with

glass beads in the interior of the bed. Finally, a segregated state of the mixture evolved to a well

mixed state within 70 seconds. When a binary granular mixture was subjected to a vertical

vibration, the flow behaviors and mixing phenomenon contributed significantly to the

momentum exchange of each species causing the granular temperature gradient of components.

The maximum densities for particles were concentrated around center region, while the

concentrations of light particles in this region were small. Hsiau and Yang (2003) experimentally

studied the segregation process of binary mixture with different density ratios in a granular bed.

49

They also found that heavier particles tended to move towards the center region of the two

convection cells of the lighter particles. Binary results show that the steel balls (heavy) had

higher concentrations at the intermediate levels, while the light particles had lower concentration

in this region. Concentration of lighter particles were found more than the heavy particles and

concluded that light particles obtained more energy from heavy particles in the particle-particle

collision.

Γ (dimensionless acceleration amplitude) = ( ) gfa /2 2π

where a and f were vibration amplitude, vibration frequency, respectively and g = gravitational

acceleration.

When a mixture of different size particles was vibrated, largest size particles rose to the

top or sank to the bottom depending upon vibration frequency and amplitude (Ellenberger et al.,

2006). The rising and sinking of largest size particles is known as Brazil nut effect and reverse

Brazil nut effect, respectively. The condition under which BNE and RBNE occur is still hotly

disputed. Shinbrot and Muzzio (1998) found that in a vertically vibrated granular bed, large

heavy intruder rise to the top under large amplitude of vibration. Yan et al. (2003) discovered

using granular of different density that intruder density should be less than the granular bed in

order to sink intruder. In contrast, Breu et al. (2003) found that RNBE only occurs when the

intruder density was greater than the granular bed density. In this line, Huerta and Ruiz-Suarez

(2004) explained the rising and sinking phenomena by proposing that at high frequency, heavy

particles sink and light particles rise due to buoyancy. The rise time of large particles depend on

the ratio of density of intruder to bed particles. The maximum rising time was observed when

density ratio was about 0.5 and this result was confirmed by many researchers. Experiments were

extensively carried out in a pseudo-2D polyacrylate container having dimension of 0.2 m× 0.15

m× 0.0045 m. The diameter and density of polystyrene beads were 0.85 mm and 1,080 kg/m3,

respectively. The container was filled upto a height of 0.06 m measured from bottom. The

rectangular container was vibrated by an air-mount vibration exciter (TIRAvib 5220, Germany),

which can produce sinusoidal wave of different amplitudes and frequency. Seven amplitudes

were used ranging from 0.25 to 5 mm and frequency ranged from 20 Hz to 110 Hz. Nine-disk

shaped brass intruders of different inner and outer diameters were used in carrying out the

50

experiments. Based on the experimental results following conclusions were drawn by the

authors:

1. At a fixed vibration amplitude, the frequency required to cause an intruder to rise was

always lower than that required to let it sink.

2. The position of intruder in a granular bed also effects its rise or sink behavior

3. The rise and sink velocity of an intruder is a function of its position in the granular bed

and the diameter of the intruder. Furthermore, at a fixed amplitude, the mean rise velocity

of an intruder is always much higher than the mean sink velocity.

4. High-speed video movies support the void-filling mechanism as the underlying

phenomenon responsible for the rise of large particles in a vertically vibrated granular

bed.

There are many physical variables such as size, shape, density, and friction contributing

to the granular material segregation under vibration (Rosato et al., 1987, Jullien et al., 1992,

Hong et al., 2001, Burtally et al., 2002, Huerta and Ruiz-Suárez, 2004). So far three mechanisms

have been identified for segregation to happen in a vibrated granular bed: geometrical

reorganization (Jullien et al., 1992), size percolation (Williams, 1963) and convection (Knight et

al., 1993, Duran et al., 1994). Rise and sink of an intruder in a granular material bed depends on

the particles properties and intensity of vibrations (Ciamarra et al., 2006). Yang (2006b) studied

the rise and sink behavior of an intruder in a vertically vibrated cohesive granular material bed

using DEM simulation. There were four forces mentioned for imparting cohesive force

including: van der Waals force, electromagnetic forces or the capillary forces in the wet granular

material bed. Scheel et al. (2004) studied the effect of small amounts of liquid on the dynamic

behavior of vertically vibrated granular materials. They found that the amount of liquid in

granular system affects by increasing the acceleration of fluidization. Soda-lime glass beads of

particle density 2,500 kg/m3 with an average diameter of 1 mm were used as an experimental

material. The large disks (or intruders) with various diameters and similar density of glass beads

were used. Water with surface tension of (0.0725 N/m) and viscosity of 0.0012 Pa-s was chosen

to provide liquid in the glass beads bed. They found that segregation of wet glass was strongly

dependent on the convection motion of small particles and amount of liquid added to the small

51

and large particles bed. Segregation was the maximum at intermediate level of liquid due to

decreased convection and slows down as liquid proportion increased in the bed as compared to

dry material.

2.8 State-of-the-Art

The aim of this research was to study time-dependent segregation using multi-size and

multi-component granular mixtures. Literature review revealed that many researchers have

studied segregation, either as time-dependent response for binary mixtures or cohesionless (ideal

material) multi-size mixtures using segregation index. The quantitative study of segregation for

multi-size and multi-component powders is of considerable interest to researchers in academia

and practitioners in industry. Most of the previously developed mathematical models incorporate

the characteristics of segregation of either binary mixtures or cohesionless material mixtures.

These models are not sufficient to explain the segregation mechanism for continuous size

particulate mixtures. Almost all previously developed segregation mathematical models were

validated in the laboratory. One of the aims of this research was to validate developed

mathematical model by applying to an industrial process.

The purpose of the review-of-literature presented in the preceding sections was to

critically evaluate the scientific work to develop background and to gain in-depth knowledge in

the proposed field of study. A critical analysis of the powder segregation quantification and

modeling revealed that many researchers worked in the above-mentioned areas but they have

used either binary mixtures or ideal multi-size mixtures and these results cannot be applied to

industrial situations. If the real-world (i.e., those used in industry) materials could be used and

representative segregation studied, the above limitations would be overcome and results could be

applied to industrial problems.

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Harwood, C. F. 1977. Powder segregation due to vibration. Powder Technology 16: 51-57. Henein, H. 1980. Bed behavior in rotary cylinders with applications to rotary kilns. Ph.D. diss.,

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Herrmann, H. J. 1994. Simulating moving granular media. In E. Gauzzelli, & L. Oger (Eds.), Mobile particulate systems, Cargese, Corsica, France. Dordrecht: Kluwer Academic Publishers.

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3. CHAPTER - GOAL AND OBJECTIVES Goal

The overall goal of this research was to mitigate percolation segregation in multi-size and multi-

component cohesionless particulate mixtures leading to continuous mixtures using science and

engineering principles. The research goal was achieved by the following five objectives:

Objectives

1) To develop an experimental design, based on fertilizer plant visits, for testing select

fertilizer mixtures under conditions similar to those during the filling, handling, and

storage of bagged fertilizers using the Primary Segregation Shear Cell-II (PSSC-II),

2) To analyze the data from Objective 1 leading to the development and verification of

mathematical models for percolation segregation,

3) To correlate the effect of equilibrium relative humidity on flowability and percolation

segregation of hygroscopic materials,

4) To study the sampling variations from raw material to the filling of fertilizer bags through

each of the handling and processing steps and compare two single tube triers of opening

width 12.7 mm and 19.1 mm,

5) To design and conduct an experiment for studying the effect of vibration frequency and

amplitude on percolation segregation of fines.

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4. CHAPTER - PERCOLATION SEGREGATION IN BINARY SIZE MIXTURES OF SPHERICAL AND ANGULAR-SHAPED

PARTICLES OF DIFFERENT DENSITIES

4.1 Abstract Percolation segregation in binary size mixtures for two particulate types: urea (spherical-

shaped) and potash (angular-shaped) were studied. Materials chosen were major raw ingredients

of blended fertilizer that represented two extremes based on shape and density. In this study, the

coarse and fine particles were classified using particle size larger and smaller than 2,360 µm,

respectively. Three coarse mean sizes 3,675 µm, 3,075 µm, and 2,580 µm for both spherical and

angular particles and three fines mean sizes 2,180 µm, 1,850 µm, and 1,550 µm for angular

particles and two fines mean sizes 2,180 µm and 1,850 µm for spherical particles were selected

for tests. Size ratio for binary size mixture is defined as the ratio of mean size of coarse to fine

particles. Binary mixed samples of coarse and fine particles were placed into shear box of the

primary segregation shear cell (PSSC-II) very gently to avoid segregation. Percolation

segregation was quantified using PSSC-II. Based on experimental results, the segregated fines

mass, normalized segregation rate (NSR), and segregation rate of fines for binary mixtures were

higher for larger size ratios (2.4:1.0>2.0:1.0>1.7:1.0). The NSR is defined as the amount of fines

percolated from initial fines present in the binary mixture based on total time of PSSC-II

operation (kg/kg-h). Segregation rate was the highest and lowest for mixing ratios 33:67 and

67:33, respectively, when coarse mean size was 3,675 µm, where mixing ratio for binary

mixtures is the ratio of mass of coarse particles to the mass of fine particles. For the same size

ratio, segregated fines mass for coarse-fine size combinations in the binary mixtures of urea and

potash were significantly different (p<0.05). Segregated fines mass of potash and urea particles

was significantly different for the same size ratio and the same coarse sizes (p<0.05). Percent

segregated fines of angular particles (59%) was higher vs. spherical particles (45%) for the size

ratio 2.0:1.0 and coarse mean size 3,675 µm.

4.2 Introduction Several industries such as agriculture, ceramic, construction, food, mineral and mining, and

pharmaceutical are known to handle, convey, mix, flow-by-gravity, and store granular solids in

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bulk. During the above unit operations, granular solids tend to segregate due to physical and

mechanical properties difference, which results in poor mixing and lower product quality. Several

researchers have reported that size of granular materials is the most dominant parameter

responsible for segregation (for instance, Rosato et al., 2002, Bridle et al., 2004, Tang and Puri,

2004, Bradley and Farnish, 2005). Shape and density effect in binary size mixtures was quantified

using two materials of the same size range (glass beads and poultry mash feed) by Tang and Puri

(2007). They found that particles having irregular shape and higher density are more segregation

prone compared with spherical and lower density particles. Segregation in particulate solids due to

size effect in association with other physical and mechanical properties have greater detrimental

effect on product quality and mixing than size alone (Jha and Puri, 2006). To date, thirteen

segregation mechanisms have been identified for processing and manufacturing of granular solids,

i.e., trajectory, air current, rolling, sieving and sifting, impact, embedding, angle of repose, push-

way, displacement or floating, percolation, fluidization, agglomeration, and, concentration driven

displacement (Mosby et al., 1996; Salter, 1998; de Silva et al., 2000). Out of the thirteen listed

mechanisms, the percolation segregation mechanism was selected for study due to its wide

application during handling, conveying, mixing, transportation, and storage (Tang and Puri, 2005).

Percolation segregation always occurs under dynamic conditions induced by shear and vibration in

bulk solids (Vallance and Savage, 2000).

Based on the above facts, the aim of this research was to study time-dependent

percolation segregation in binary mixtures of granular materials. Only a limited number of

researchers have studied the time-dependent percolation segregation in binary mixtures (Duffy

and Puri, 2002 and 2003; and Tang and Puri, 2005). Tang and Puri, and Duffy and Puri used

point feed and a layer of feed of fines in the coarse particle bed, respectively. The present study

extends the work of previous researchers by conducting segregation experiments on well mixed

systems, which is common in industrial operations. In this study, urea (CON2H4) and muriate of

potash (KCl) were used to quantify the effect of particle size, size ratio and size in association

with shape and density. The particle densities of spherical urea and angular potash were 1,459

kg/m3 (Standard deviation, SD = 2 kg/m3) and 2,291 kg/m3, (SD = 3 kg/m3), respectively.

Herein, potash and urea were representatives of irregular or angular-shaped and spherical-shaped

particles, respectively (Baker et al., 1967). The mean measured sphericity of urea and potash

particles of size range 3,350-4,000 µm were 0.97 (SD = 0.02) and 0.78 (SD = 0.08), respectively

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(Mohsenin, 1986). In this article, all the tests were conducted at strain of 6% and strain rate of

0.5 Hz, and bed depth of 85 mm in the shear box. The specific objectives of this study were to

determine the effect of: 1) size ratio, 2) coarse size and fines size, 3) amount of initial fines mass,

and 4) materials used to formulate binary size mixtures.

4.3 Materials and Methods

The PSSC-II was developed and fabricated by Tang (2004) and has five main

components: shear box, measurement system, sieve system, drive system, and main frame. The

details, capabilities, and limitations of the PSSC-II can be found in Tang (2004) and Tang and

Puri (2005). The modified measurement system, and sieving system is given in Jha and Puri

(2006). A sieve of opening size 2,360 µm was used throughout the experiments after preliminary

tests with different size ratios (binary and multi-size mixtures) to ensure that coarse size particles

did not block the sieve openings.

Binary, ternary, and quaternary size distributions were made and studied at different

strains and strain rates. The motivation for binary and multi-size study was to formulate mixtures

representative of continuous size distribution when studying percolation response under different

motion conditions. Binary size mixture is considered to be the foundation of multi-size and

continuous mixture study. Therefore, results are presented for binary mixture in this article. This

study will pave the way for other binary and multi-size mixture at different strain and strain

rates. In the present article, nine different binary size ratios of potash and six different size ratios

of urea in different mixing ratios were studied. The segregation results were analyzed using

segregation determining metrics such as the effect of size ratio and mixing ratio on segregation,

collected segregated fines mass, segregation rate (SR), and normalized segregation rate (NSR).

4.3.1 Test material selection and parameter determination

Urea and muriate of potash, from now on referred to as potash, were selected for studying

percolation segregation due to their extreme shape and density among the three major raw

ingredients: urea, potash, and phosphate, used in the manufacture of different fertilizer blends.

For segregation study, three parameters including material bed depth, particle bed strain, and

strain rate were selected for operating PSSC-II based on published results (Tang and Puri, 2005).

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Bed depth of 85 mm (shear box height = 100 mm) was used to represent percolation of fines

within bagged fertilizers in normal orientation, i.e., depth direction along gravity, during

conveying, handling, and transportation. The selected strain of 6% and strain rate of 0.5 Hz

represent the unfilled bag volume (≤ 15%) and intensity of motion experienced by the blend in

the bag during processing operations (<10 Hz) (Vursavus and Ozguven, 2004). Results of other

strains and strain rates are to be presented in subsequent articles.

Different coarse and fine size ranges of the test material were obtained using US standard

sieve of (2)1/4 series. Potash and urea were received from local fertilizer blend plant facilities.

Three size ranges (3,350-4,000, 2,800-3,350, and 2,360-2,800 µm) were designated as coarse

and while three fine size ranges (2,000-2,360, 1,700-2,000, and 1,400-1,700 µm) were

designated as fines in the present study (Table 4.1). Since size spread of urea was small

compared with potash, fines size range 1,400-1,700 µm were not found in sufficient quantity,

therefore, this fines size was not included in the segregation study of urea. Size ratio of binary

mixture was defined as the ratio of mean size of coarse particles to mean size of fine particles.

For potash, three size ratios for each coarse sizes 3,675 µm, 3,075 µm, and 2,580 µm were

2.4:1.0, 2.0:1.0, 1.7:1.0, and 2.0:1.0, 1.7:1.0, 1.4:1.0, and 1.7:1.0, 1.4:1.0, 1.2:1.0, respectively,

(Table 4.1). For urea, two size ratios for each coarse size 3,675 µm, 3,075 µm, and 2,580 µm

were 2.0:1.0, 1.7:1.0, and 1.7:1.0, 1.4:1.0, and 1.4:1.0, 1.2:1.0, respectively. Different mixing

ratios (MR) were used for different size ratios based on weight proportion of different size

(Table 4.1) distributions found in low analysis fertilizer blend sample collected from blend plants

(such as low analysis 10-10-10).

4.3.2 Test condition and experimental design Coarse size particles were mixed with fine size particles in a 225-W six-speed bench-top

mixer (Model-106772N, Type-M27, General Electric, Marketed by Wal-Mart Stores Inc.,

Bentonville, AR). Initial tests showed that 30 s at lowest rpm was sufficient to uniformly mix the

binary size samples. Mixed binary sizes were placed in shear box of the PSSC-II very gently

with a scoop to avoid segregation. From statistical analysis of data, a separate experimental

design was considered for both angular and spherical-shaped materials including dissimilar

amount of fines (Table 4.1). Based on published results (Duffy and Puri, 2002, and Tang and

Puri, 2005) and preliminary testing with fertilizer blends, six replications were done for each set

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of experiments for testing percolation segregation using PSSC-II. A complete block design was

selected for data analysis. A set of coarse particles was considered as a block of experiment.

Within each block, all treatments (replicate = 1 × 6 = 6) were randomly assigned. Of the six

replicates, three replicates for each set were completed using load cells and three replicates were

completed by collecting segregated fines in a pan. Results of segregation determining metrices

are given in tabular form based on six replications. However, only three replications were

included for the graphical representation of results because of limited capacity of load cells (<3.5

g), i.e., load cells were not able to collect data effectively upto 30 minutes with desired accuracy

for all the size ratios. The segregated fines mass values were measured and two segregation

determining parameters, segregation rate (SR) and normalized segregation rate (NSR), were

deduced from the fines mass values. SR was defined as amount of fines collected in unit time

(kg/h), and NSR was defined as the amount of fines percolated from the initial fines in a binary

mixture for the total time of operation of PSSC-II (kg/kg-h). The SR and NSR provided similar

results; however, when different MRs were used, differing results for SR and NSR were obtained

for some MRs. Therefore, the two segregation rate metrics were considered whenever needed.

All tests were conducted in the environment-controlled laboratory with average temperature of

22°C ± 3°C and relative humidity less than 40%.

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Table 4.1 Design of experiment for binary size mixtures for potash and urea* Material Coarse size

(µm) Fine Size (µm) Size

Ratio Mixing Ratio Number

1,400-1,700 (mean = 1,550)

2.4:1.0 50:50

1,700-2,000 (mean = 1,850)

2.0:1.0** 37:63

Potash

3,350-4,000 (Mean = 3,675)

2,000-2,360 (mean = 2,180)

1.7:1.0 37:63

3

1,400-1,700 (mean = 1,550)

2.0:1.0 67:33

1,700-2,000 (mean = 1,850)

1.7:1.0 50:50

Potash

2,800-3,350 (mean = 3,075)

2,000-2,360 (mean = 2,180)

1.4:1.0 50:50

3

1,400-1,700 (mean = 1,550)

1.7:1.0 67:33

1,700-2,000 (mean = 1,850)

1.4:1.0 60:40

Potash

2,360-2,800 (mean = 2,580)

2,000-2,360 (mean = 2,180)

1.2:1.0 60:40

3

1,700-2,000 (mean 1,850)

2.0:1.0 37:63

Urea

3,350-4,000 (mean = 3,675) 2,000-2,360

(mean 2,180) 1.7:1.0 37:63

2

1,700-2,000 (mean 1850)

1.7:1.0 50:50

Urea

2,800-3,350

(mean = 3,075) 2,000-2,360 (mean 2,180)

1.4:1.0 50:50

2

1,700-2,000 (mean 1,850)

1.4:1.0 60:40 Urea

2,360-2,800 (mean = 2,580) 2,000-2,360

(mean 2,180 1.2:1.0 60:40

2

Total (six replications) 15×6 =90 * All tests were performed at strain of 6% and strain rate of 0.5 Hz ** Three mixing ratios 33:67, 50:50, and 67:33

4.4 Results and Discussion Segregation results in terms of collected fines, average segregation rate and normalized

segregation rate are summarized in Table 4.2. The effect of mixing ratio, size ratio, coarse size

and fines size, and material (angular vs. spherical) on segregation are discussed in subsequent

paragraphs.

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4.4.1 Segregated fines mass

As expected, the segregated fines mass values were different for different mixing ratios

and size ratios. Furthermore, the segregated fines mass for the same size ratio but different

coarse and fine sizes were different.

Table 4.2 Segregation results for binary size mixtures with three coarse sizes* Material Coarse mean

size (µm)

Size ratio

Mixing ratio

Collected fines (g)

Average SR (kg/h)

NSR (kg/kg-h)

2.4:1.0 50:50 369.50 (6.5) 0.74 (0.01) 1.54 (0.03)2.0:1.0 37:63 280.20 (5.7) 0.56 (0.01) 0.90 (0.02)

Potash

3,675

1.7:1.0 37:63 39.00 (7.2) 0.08 (0.01) 0.13 (0.02)2.0:1.0 37:63 140.30 (4.0) 0.28 (0.01) 0.62 (0.02)

Urea

3,675 1.7:1.0 37:63 27.30 (2.8) 0.05 (0.01) 0.12 (0.01)2.0:1.0 67:33 216.60 (5.3) 0.43 (0.01) 1.17 (0.03)1.7:1.0 50:50 205.30 (24.7) 0.41 (0.05) 0.86 (0.10)

Potash

3,075

1.4:1.0 50:50 39.50 (1.4) 0.08 (0.00) 0.16 (0.01)1.7:1.0 50:50 41.20 (3.7) 0.08 (0.01) 0.24 (0.02)

Urea

3,075 1.4:1.0 50:50 19.76 (5.8) 0.04 (0.01) 0.11 (0.03)1.7:1.0 67:33 57.70 (6.5) 0.12 (0.01) 0.39 (0.04)1.4:1.0 60:40 43.77 (1.4) 0.09 (0.00) 0.23 (0.01)

Potash

2,580

1.2:1.0 60:40 12.79 (0.8) 0.03 (0.00) 0.07 (0.00)1.4:1.0 60:40 12.26 (0.7) 0.02 (0.00) 0.09 (0.01)

Urea

2,580 1.2:1.0 60:40 7.02 (0.4) 0.01 (0.00) 0.05 (0.00)* SD values in parentheses

4.4.1.1 Mixing ratio effect Percent segregated fines for three mixing ratios of 67:33, 50:50, and 33:67 for the mean

coarse size of 3,675 µm are shown in Figure 4.1. The binary size mixtures where subjected to

shear motion for 30 minutes because load cells were not designed to collect more than 3.5 g. Of

the total time, for the first 10 minutes fines were collected at 30-s interval and thereafter 120-s

interval due to the slow down in discharge of fines. For these three mixing ratios, percent

segregated fines increased with increasing time (Figure 4.1). Effect of mixing ratio on

segregation was determined based on three replications of each test and it was found that three

replications were sufficient for the data to be within the 95% confidence interval. The percent

67

segregated fines mass was the highest and lowest for mixing ratios 67:33 and 33:67, respectively.

As expected, percent segregated fines for mixing ratio 50:50 was in-between percent segregated

fines mass of mixing ratios 33:67 and 67:33. After 15 s, 1.5%, 1.5%, and 1.6% mass were

collected for mixing ratios 33:67, 50:50 and 67:33, respectively. At the end of 30 minutes, the

masses for these three mixing ratios were 45.3%, 53.3%, and 59.3%, respectively. The difference

in percent segregated fines for these three size ratios were significantly different (p<0.05). The

error bar on symbols shows standard deviation (SD) for the test.

0.0

20.0

40.0

60.0

80.0

100.0

0 5 10 15 20 25 30 35

Time (minutes)

Perc

ent s

egre

gate

d fin

es (%

)

Mixing ratio 67:33Mixing ratio 50:50

Mixing ratio 33:67

Figure 4.1 Comparison of percent segregated fines at three different mixing ratios of angular-shaped potash for size ratio 2.0:1.0, with ±SD as error bars

4.4.1.2 Size ratio effect Figure 4.2 shows the comparison of percent segregated fines for three different size ratios

when mean coarse size of 3,675 µm was used for angular-shaped particles. As expected, the

percent segregated fines for size ratio 2.4:1.0 was the highest while it was the lowest for size

ratio of 1.7:1.0. However, the percent segregated fines for size ratio 2.0:1.0 was closer to size

ratio 2.4:1.0 vs. 1.7:1.0. A plausible explanation is the mixing ratio difference, i.e., for size ratios

of 2.4:1.0 and 2.0:1.0 the mixing ratios were 50:50 and 33:67, respectively; whereas for 1.7:1.0

the mixing ratio was 33:67. This observation is in agreement with the hypothesis that binary

mixtures prepared with the same coarse size and size ratio but differing mixing ratios result in

68

greater amount of segregated fines for higher proportion of fines, i.e., 33:67 vs. 50:50. The

percent segregated fines for these three size ratios were significantly different (p<0.05). Similar

results were obtained for different size ratios when using coarse sizes 3,075 and 2,580 µm, i.e.,

segregated fines were also significantly different (p<0.05). Complementary results of SR and

NSR are justified, the SR for size ratios 2.0:1.0 and 1.7:1.0, when coarse size was 3,075 µm,

were almost the same (Table 4.2), although, SR should be more for size ratio 2.0:1.0 compared

with size ratio 1.7:1.0 because of smaller fines size. However, NSR for size ratio 2.0:1.0 was

higher compared to size ratio 1.7:1.0. Here NSR provides intuitive results compared to

segregation rate.

0.0

20.0

40.0

60.0

80.0

100.0

0 5 10 15 20 25 30 35

Time (minutes)

Perc

ent s

egre

gate

d fin

es (%

)

Size Ratio = 2.4:1.0



Figure 4.2 Comparisons of segregated percent fines for three different size ratios of binary mixtures of angular-shaped potash prepared using coarse size 3,675 µm, with ±SD as error

bars

4.4.1.3 Coarse size effect Figure 4.3 compares the effect of mean coarse sizes (3,675, 3,075 and 2,580 µm) for the

same size ratio 1.7:1.0 for angular potash particles; the corresponding mixing ratios were 33:67,

50:50, and 60:40, respectively. The percent segregated fines for coarse size 3,075 µm was the

highest, whereas, it was the lowest for 3,675 µm. Therefore, the segregated fines not only depend

on coarse size, fine size, and size ratio but also on the relative displacement of particles in the

69

bed during shear motion, i.e., the change in void sizes for strain of 6% was not sufficient in

binary mixtures formed using 3,675 µm coarse particles to allow larger size fines 2,180 µm to

percolate vs. 1,550 µm and 1,850 µm. Percent segregated fines was higher for 3,075 µm

compared with 2,580 µm (Figure 4.3). This can be attributed to the mixing ratio for 3,075 µm

being smaller (50:50) than 2,580 µm (67:33). The effect of these coarse sizes on percent

segregated fines was significantly different (p<0.05). Similar results were obtained other two size

ratios 2.4:1.0 and 1.4:1.0, which were also significantly different (p<0.05).

0.0

20.0

40.0

60.0

80.0

100.0

0 5 10 15 20 25 30 35

Time (minutes)

Perc

ent s

egre

gate

d fin

es (%

)

Coarse size 3,075 µm Coarse size 3,675 µm

Coarse size 2,580 µm

Figure 4.3 Comparisons of percent segregated fines for three coarse sizes of angular-

shaped potash binary mixtures for size ratio 1.7:1.0, with ±SD as error bars

4.4.1.4 Comparison between angular and spherical-shaped material Segregation potential of urea (spherical shaped particles) and potash (angular shaped

particles) were also compared for size ratio 2.0:1.0 when coarse size was 3,675 µm (Figure 4.4).

In the first few minutes (<2 minutes), the segregated fines mass for binary mixtures prepared

using spherical-shaped urea was very close to angular-shaped potash (8.9% and 8.0% of their

respective total fines); however, after 2 minutes, the percentage of fines increased very rapidly

for angular shaped potash in comparison with the spherical shaped urea binary mixtures

(p<0.05). More fines were expected in the case of potash because of angular-shaped particles

(porosity of 51%, i.e., larger void spaces) and higher particle density compared with spherical

shape urea particles (porosity of 44% i.e., smaller void spaces). At the end of 30 minutes, the

70

percentage of segregated fines for urea and potash were 45% and 59% of their, respective, initial

fines mass. The difference in percent segregated fines of urea and potash were significant

(p<0.05) Similar results were obtained for binary mixtures comprising different coarse sizes and

size ratios (p<0.05).

0.0

20.0

40.0

60.0

80.0

100.0

0 5 10 15 20 25 30 35

Time (minutes)

Perc

ent s

egre

gate

d fin

es (%

)

Potash

Urea

Figure 4.4 Comparisons of percent segregated fines for angular-shaped potash and spherical-shaped urea: size ratio 2.0:1.0 and coarse size 3,675 µm, with ±SD as error bars

4.4.2 Normalized segregation rate

As stated earlier, SR and NSR results are similar when comparing results with same

mixing ratio; however, different mixing ratios for some treatments lead to differing results.

Herein, the total time of operation was measured from the beginning of fine particle discharge at

30 s intervals up to 10 minutes, thereafter, 120-s intervals up to 30 minutes.

4.4.2.1 Mixing ratio effect It was hypothesized that more fines in a given mixture result in larger normalized

segregation rate when other test conditions were the same. The hypothesis was tested by using

binary size mixtures of angular-shaped potash for size ratio 2.0:1.0 of coarse size 3,675 µm in

three mixing proportions 67:33, 50:50, and 33:67. The results obtained are presented in Figure

71

4.5. At the end of 15 s, the NSR was 4.84 kg/kg-h, 3.68 kg/kg-h, and 3.37 kg/kg-h for mixing

ratios 67:33, 50:50, and 33:67, respectively (p<0.05). NSR decreased in the same fashion for

these three mixing ratios until data collection was stopped at 30 minutes. At the end of 30

minutes, the NSRs were found to be 1.29 kg/kg-h, 1.07 kg/kg-h, 0.90 kg/kg-h for MRs 67:33,

50:50, and 33:67, respectively (p<0.05). The obtained results were contrary to the hypothesis for

NSR; therefore, it could be concluded that more fines in a mixture provide interrupted pathways

for fines to percolate when external motion was applied. SR results for the size ratio 2.0:1.0 at

three mixing ratios 33:67, 50:50, and 67:33 followed the opposite trend compared with NSR

results (Figure 4.6). SR for mixing ratio 33:67 was found the highest whereas for mixing ratio

67:33 was the lowest, with mixing ratio 50:50 SR to be in-between these two extremes. This is

the only set of SR results different from NSR, i.e., results of other parameters were similar for

SR and NSR.

0.0

2.0

4.0

6.0

8.0

10.0

0 5 10 15 20 25 30 35

Time (minutes)

NSR

(kg/

kg-h

)

Mixing ratio 67:33


Figure 4.5 Comparison of NSR at three different mixing ratios of angular-shaped potash: for size ratio 2.0:1.0 and coarse size 3,675 µm, with ±SD as error bars

72

0.0

1.0

2.0

3.0

4.0

5.0

0 5 10 15 20 25 30 35Time (minutes)

Segr

egat

ion

rate

(kg/

h)


Mixing ratio 33:67

Figure 4.6 Comparison of SR at three different mixing ratios for angular-shaped potash: size ratio 2.0:1.0 and coarse size 3,675 µm, with ±SD as error bars

4.4.2.2 Effect of size ratio The NSR values also decreased rapidly with time for all the tested binary size ratios

(Figure 4.7). Relationship between NSR and time for three size ratios 2.4:1.0, 2.0:1.0, and

1.7:1.0 for coarse size of 3,675 µm is given in Figure 4.7. NSR decreased very rapidly, i.e.,

became less than 50%, within first 2 minutes for all size ratios and then decreased linearly. The

NSR of size ratio 2.4:1.0 was the highest followed by size ratio 2.0:1.0 and 1.7:1.0 in that order

for coarse size 3,675 µm. The NSR was significantly different for these three tested size ratios

with the coarse size of 3,675 µm (p<0.05). Similar results were obtained for all other size ratios

when using coarse sizes 3,075 µm and 2,580 µm with the NSR being significantly different

(p<0.05).

73

0.0

2.0

4.0

6.0

8.0

10.0

0 5 10 15 20 25 30 35

Time (minutes)

NSR

(kg/

kg-h

)


Size Ratio = 1.7:1.0Size Ratio = 2.0:1.0

Figure 4.7 Normalized segregation rate comparisons for different size ratios for the coarse

size (3,675 µm) of angular-shaped potash, with ±SD as error bars

4.4.2.3 Effect of coarse size For a given size ratio, the coarse size plays an important role in determining NSR in

binary size mixtures. Three coarse sizes (3,675 µm, 3,075 µm, and 2,580 µm) of angular-shaped

potash were compared for size ratio of 1.7:1.0 (Figure 4.8). The NSR of coarse size 2,580 µm

was higher than the NSR of coarse sizes 3,675 µm and 3,075 µm. Initially, the NSR of coarse

size 2,580 µm (6.17 kg/kg-h) was higher than the NSR of 3,075 µm (4.87 kg/kg-h) but after 45

seconds, NSR of 2,580 µm was lower than NSR of 3,075 µm but always higher than the NSR of

3,675 µm. The reason of initially higher and then lower NSR of 2,580 µm compared with NSR

of 3,075 µm was the smaller fine size of 1,550 µm compared with fine size 1,850 µm for 3,075

µm. In addition, the proportion of fines for 2,580 µm was small compared to 3,075 µm

combinations, i.e., mixing ratios were 67:33 and 50:50, respectively, for 2,580 µm and 3,075

µm. The effect of coarse size on NSR was significantly different for the tested size ratios

(p<0.05).

74

0.0

2.0

4.0

6.0

8.0

10.0

0 5 10 15 20 25 30 35

Time (minutes)

NSR

(kg/

kg-h

)

Coarse size 3,675 µmCoarse size 2,580 µm

Coarse size 3,075 µm

Figure 4.8 Normalized segregation rate comparisons for three coarse sizes for size ratio of

1.7:1.0 of angular-shaped potash, with ±SD as error bars

4.4.2.4 Comparison between angular and spherical-shaped material Figure 4.9 compares the NSR for urea and potash. After 15 s, NSR was 8.38 kg/kg-h and

4.25 kg/kg-h for spherical and angular binary mixtures, respectively. After 150 s, the NSR

values were very close to each other, i.e., 2.35 kg/kg-h and 2.38 kg/kg-h. Thereafter, NSR for

urea decreased rapidly compared with potash. As mentioned previously, the large decrease in

NSR can be attributed to urea’s spherical shape and lower porosity compared with potash binary

mixtures comprised of angular particles that form higher porosity assembly. Clearly, size

segregation in conjunction with other physical properties such as shape and density has greater

detrimental affect than size alone. The NSRs of urea and potash were significantly different

(p<0.05). Similar results for urea and potash were obtained for other size ratios (1.7:1.0 and

1.4:1.0) with NSR being significantly different (p<0.05).

The NSR results for both urea and potash are given in Table 4.2. A linear relationship

was found between size ratio and NSR (R2 ≥ 0.98) for each coarse sizes (3,675 µm, 3,075 µm,

and 2,580 µm) (equations (4.1) to (4.3)) for size ratio ranging from 1.2:1.0 to 2.4:1.0. Linear

relationship was not found between coarse size and NSR (R2 = 0.13) for the same size ratio.

75

Linear relationship was also not found between urea and potash for the same size ratio (R2 =

0.23). The effect of size ratio and coarse size on NSR was significant (p<0.05).

NSR = 1.99 size ratio - 3.19, for potash coarse size 3,675 µm (R2 = 0.98) (4.1)

NSR = 1.68 size ratio – 2.16, for potash coarse size 3,075 µm (R2 = 0.98) (4.2)

NSR = 0.65 size ratio – 0.70, for potash coarse size 3,075 µm (R2 = 0.99) (4.3)

0.0

2.0

4.0

6.0

8.0

10.0

0 5 10 15 20 25 30 35

Time (minutes)

NSR

(kg/

kg-h

)

Spherical

Angular

Figure 4.9 Segregation rate comparisons of spherical urea and angular potash materials size ratio 2.0:1.0 and coarse size 3,675 µm, with ±SD as error bars

4.5 Conclusions

The PSSC-II was capable of quantifying segregation in the binary size mixtures of urea

and potash, i.e., six size ratios of urea two for each coarse size 3,675 µm, 3,075 µm, and 2,580

µm and nine size ratios of potash three for each coarse size 3,675 µm, 3,075 µm, and 2,580 µm.

Three parameters, such as, collected segregated fines mass, segregation rate, and normalized

segregation rate were used to determine segregation potential of fines at strain rate of 0.5 Hz,

strain of 6%, and initial bed depth of 85 mm. Percolation segregation is affected by size ratio,

selection of size of coarse and fines, mixing ratio, and material. Based on analysis of results, it

was concluded: 1) Both NSR and SR depend on mixing ratio in binary mixtures, NSR decreased

with increasing amount of fines 67:33>50:50>33:67, however, SR increased with increasing

76

amount of fines 67:33>50:50>33:67 for the same size ratio. 2) NSR decreased from 1.54 kg/kg-h

for size ratio 2.4:1.0 to 0.13 kg/kg-h for size ratio 1.7:1.0, almost 96% of decrease NSR was

observed with decrease in size ratio from 2.4:1.0 to 1.7:1.0, 3) NSR was dependent on size of

coarse and fine particles, NSR decreased from 0.39 kg/kg-h to 0.13 kg/kg-h with increasing size

of fines 1,550 µm vs. 2,180 µm for the size ratio 1.7:1.0, and 4) NSR was dependent on type of

material selected, the NSR of spherical urea (0.62 kg/kg-h) was lower than the NSR of angular-

shaped potash (0.90 kg/kg-h) at the end of 30 minutes of PSSC-II operation.

4.6 Key Findings The binary mixtures of urea and potash were tested for percolation segregation of fines in

reference to size ratio, mixing ratio, coarse and fines size and materials comparison. Size ratio

was found to be the most dominant parameter responsible for segregation followed by size of

coarse and fines and mixing ratio. In addition, the percolation of fines of urea and potash showed

that the cumulative effect of size with shape and density has more detrimental effect (potash)

compared with size (urea) only.

4.7 References


Bradley, M. S. A. and R. J. Farnish. 2005. Segregation of blended fertilizer during spreading: the effect of differences in ballistic properties. In Proc 554. The International Fertilizer Society, York, UK. pp: 15.

Bridle, I. A., M. S. A. Bradley, and A. R. Reed. 2004. Non-segregating blended fertilizer development: A new predictive test for optimising granulometry. In Proc 547. The International Fertilizer Society, York, UK. pp: 27.

de Silva, S., A. Dyroy, and G. G. Enstad. 2000. Segregation mechanisms and their quantification using segregation testers. Eds: Rosato, A.D. and D.L. Blackmore. IUTAM Symposium on Segregation in Granular Flows 11-29. Kluwer Academic Publishers.

Duffy, S. P. and V. M. Puri. 2002. Primary segregation shear cell for size-segregation analysis of binary mixtures. KONA (Powder and Particle) 20:196-207.

Duffy, S. P. and V. M. Puri. 2003. Development and validation of a constitutive model for size-segregation during percolation. KONA (Powder and Particle) 21:151-162.

Jha, A. K. and V. M. Puri. 2006. Segregation in and flowability of blended fertilizers. ASABE Paper Number 064004. St. Joseph, MI: ASABE.

Mohsenin, N. N. 1986. Physical properties of plant and animal materials. 2nd Ed. Gordon and Breach, Science Publishers, Inc., New York, NY.

77

Mosby, J., S. R. de Silva, and G. G. Enstad. 1996. Segregation of particulate materials-mechanisms and testers. KONA (Powder and Particle) 14: 31-42.


Salter, G. F. 1998. Invetigations into the segregation of heaps of particulate materials with particular reference to the effects of particle size. Ph.D. diss. University of Greenwich.

Tang, P. 2004. Percolation and sieving segregation patterns-Quantification, mechanistic theory, model development and validation, and application. Ph.D. diss. The Pennsylvania State University, University Park, Penn.

Tang, P. and V. M. Puri 2004. Methods for minimizing segregation, a review. Particulate Science and Technology, An International Journal 22(4): 321-338.

Tang, P. and V. M. Puri. 2005. An innovative device for quantification of percolation and sieving segregation patterns – Single component and multiple size fractions. Particulate Science and Technology, An International Journal 23(4): 335-350.

Tang, P. and V. M. Puri. 2007. Segregation quantification of two component particulate mixtures – effect of particle size, density, shape, and surface texture. Particulate Science and Technology, An International Journal 25(6): 571-588.

Vallance, J. W. and S. B. Savage. 2000. Particle segregation in granular flows down chutes. Eds: Rosato, A.D. and D.L. Blackmore. IUTAM Symposium on Segregation in Granular Flows 31-51. Kluwer Academic Publishers. Norwell, USA.

Vursavus, K. and F. Ozguven. 2004. Determining the effects of vibration parameters and packaging method on mechanical damage in golden delicious apples. Turkey Journal of Agriculture 28: 311-320.

78

5. CHAPTER - PERCOLATION SEGREGATION OF BINARY MIXTURES UNDER PERIODIC MOVEMENT

5.1 Abstract Three strain rates of 0.25, 0.5, and 1.0 Hz were selected for studying percolation

segregation in binary mixtures of urea (spherical-shaped particles) and potash (angular-shaped

particles). The binary mixed samples were prepared from the three mean coarse sizes with their

corresponding three and two fines sizes for potash and urea, respectively. In this study, the three

coarse mean sizes 3,675 µm, 3,075 µm, and 2,580 µm and three mean fines sizes 2,180 µm,

1,850 µm, and 1,550 µm were selected for tests. Since the fines size 1,550 µm of urea was not

available in sufficient quantity; therefore, it was not included in tests. Percolation segregation in

the binary mixed sample was quantified using the primary segregation shear cell (PSSC-II).

Based on the experimental results, the segregated fines mass, the normalized segregation rate

(NSR), and the segregation rate of fines for binary mixtures increased when the strain rate was

increased from 0.25 Hz to 1.0 Hz; where NSR is defined as the amount of fines percolated from

initial fines present in the binary mixture based on total time of PSSC-II operation (kg/kg-h). The

NSR decreased when the strain rate was decreased from 1.0 Hz>0.5 Hz>0.25 Hz for the size

ratios 1.7:1.0, 2.0:1.0, and 2.4:1.0 (p<0.05). At these three strain rates and size ratio of 2.0:1.0,

the NSR of coarse size 3,675 µm with fines size 1,850 µm was smaller than the NSR of coarse

size 3,075 µm with fines size 1,550 µm in the binary mixtures (p<0.05). At the three strain rates:

1.0, 0.5, and 0.25 Hz, the NSR for potash was higher (56.5%, 49.5%, 31.9%) than the NSR for

urea (35.4%, 31.9%, and 18.1%) for the same size ratio 2.0:1.0 when coarse size was 3,675 µm

(p<0.05).

5.1 Introduction

Segregation is an unwanted phenomenon in particulates that affects the quality of

mixtures during material-related unit operations, such as mixing, conveying, filling, discharging,

and compaction. Segregation can be defined as a bulk solid composed of particulates with

differing constituent properties that evolves to a spatially non-uniform state (Rosato and

Blackmore, 2000). The importance of mitigating segregation can be gauged by the various

industries that are impacted; for instance, agriculture, ceramic, construction, food, nutraceutical,

79

metal powder and metallurgy and pharmaceutical. Researchers have reported that physical

property of particulates, such as size and size distribution, shape, density, surface texture,

morphology, contact friction, brittleness, density, chemical affinities, ability to absorb moisture,

magnetic properties, different time and length scale, relative displacement of two layers and

intensity of movements (Rosato et al., 2002) affects segregation. Segregation can be mitigated, if

not eliminated, by understanding the factors affecting the mechanisms. Bridgwater and his

colleagues were the pioneers in identifying the dominant parameters responsible for segregation

(Bridgwater and Ingram, 1971, Scott and Bridgwater, 1975 and 1976, Bridgwater, 1976 and

1999, Cooke et al., 1976, Cooke and Bridgwater, 1979; Foo and Bridgwater, 1983). Bridgwater

and his colleagues found that size of particulates is the most dominant parameter responsible

contributing towards segregation. Results were later confirmed by several researchers (for

instance, Rosato et al., 2002, Bridle et al., 2004, Tang and Puri, 2004, Bradley and Farnish, 2005,

and Jha et al., 2007a). It is also reported that shape and density have secondary effect on

segregation as compared to size. Effect of shape and density on segregation in binary mixtures

were quantified by Tang and Puri (2007). Percolation segregation always occurs under dynamic

conditions induced by shear and vibration in bulk solids (Vallance and Savage, 2000).

Based on the above literature review, the aim of this research was to study time-

dependent percolation segregation in binary mixtures of granules under three strain rates of 1.0

Hz, 0.5 Hz, and 0.25 Hz. Strain rate can be defined as the cycles of movement (intensity of to-

and-fro movements) of the shear box in a second. Limited understanding of time-dependent

percolation segregation has been achieved by these researchers (Duffy and Puri, 2002 and 2003;

and Tang and Puri, 2005, Jha et al., 2007a and b). Duffy and Puri (2002) conducted experiments

for limited number of binary size mixture of glass beads (ideal material) under two strain rates,

when a layer of fines was introduced at the surface of bed of coarse particles. The present study

overcomes the limitations of the work of previous researchers by conducting segregation

experiments for number of size ratios on well mixed systems of real-world materials; the

procedure of conducting tests is common in industrial operations. The particle densities of

spherical urea and angular potash were 1,459 kg/m3 (Standard deviation, SD = 2 kg/m3) and

2,291 kg/m3 (SD = 3 kg/m3), respectively and their corresponding sphericity were 0.97 (SD =

0.02) and 0.78 (SD = 0.08), respectively (Jha et el., 2007a). The significance of selection of

strain of 6%, strain rate of 0.5 Hz, and bed depth of 85 mm is given in Jha et al. (2007a). The

80

other two extremes of strain rate of 0.25 Hz and 1.0 Hz were selected for well mixed systems of

binary mixtures when placed in the shear box of the PSSC-II. The specific objectives of this

study were to determine the effect of strain rate on: 1) size ratio 2) coarse size and fines size, and

3) materials used to formulate binary size mixtures.

5.3 Materials and Methods In the present article, nine different binary size ratios of potash and six different size

ratios of urea in different mixing ratios at three strain rates were studied. The segregation results

were analyzed using three segregation determining metrics: percent segregated fines mass,

segregation rate (SR), and normalized segregation rate (NSR). For segregation study of binary

size urea and potash mixtures, three parameters including material bed depth, particle bed strain,

and strain rate at three levels (0.25 Hz, 0.5 Hz, and 1.0 Hz) were selected for operating PSSC-II.

Results of the other strains at these strain rates are to be presented in subsequent articles.

For potash, three size ratios for each of the coarse sizes 3,675 µm, 3,075 µm, and 2,580

µm were 2.4:1.0, 2.0:1.0, 1.7:1.0, and 2.0:1.0, 1.7:1.0, 1.4:1.0, and 1.7:1.0, 1.4:1.0, 1.2:1.0,

respectively (Table 5.1). For urea, two size ratios for each of the coarse size 3,675 µm, 3,075

µm, and 2,580 µm were 2.0:1.0, 1.7:1.0 and 1.7:1.0, 1.4:1.0, and 1.4:1.0, 1.2:1.0, respectively.

Different mixing ratios (MR) were used for the different size ratios based on the weight

proportion of different size (Table 5.1) distributions found in low analysis (such as 10-10-10)

fertilizer blend samples collected from three blend plants in the Commonwealth of Pennsylvania.

Test conditions and design of experiments followed in this article have been described in detail

(Jha et al., 2007a and 2007b). All tests were conducted in an environment-controlled laboratory

with average temperature of 22°C ± 3°C and relative humidity less than 40%.

81

Table 5.1 Experimental design for binary size mixtures for potash and urea* Material Strain Rate

(Hz) Coarse size

(µm) Fine Size

(µm) Size Ratio Mixing Ratio Number

1,550 2.4:1.0 50:50 1,850 2.0:1.0 37:63

Potash

0.25 0.50 1.00

3,675 2,180 1.7:1.0 37:63

9

1,550 2.0:1.0 63:37 1,850 1.7:1.0 50:50

Potash

0.25 0.50 1.00

3,075 2,180 1.4:1.0 50:50

9

1,550 1.7:1.0 63:37 1,850 1.4:1.0 63:37

Potash

0.25 0.50 1.00

2,580 2,180 1.2:1.0 63:37

9

1,850 2.0:1.0 37:63 Urea

0.25 0.50 1.00

3,675 2,180 1.7:1.0 37:63

6

1,850 1.7:1.0 50:50 Urea

0.25 0.50 1.00

3,075 2,180 1.4:1.0 50:50

6

1,850 1.4:1.0 63:37 Urea

0.25 0.50 1.00

2,580 2,180 1.2:1.0 63:37

6

Total (six replications) 45×6 = 270

*Strain of 6%

5.4 Results and Discussion The results of the segregated fines mass and normalized segregation rate are summarized

in two subsections, i.e., the effect of strain on size ratio and on materials. The results for potash

and urea at three strain rates 0.25, 0.5, and 1.0 Hz are presented in Tables 5.2 and 5.3,

respectively.


As expected, by increasing the strain rate from 0.25 Hz to 1.0 Hz, the percent segregated

fines mass increased with time for all binary mixtures tested.

82

Table 5.2 Segregation results for binary mixtures with three coarse sizes for potash* Coarse Size Size Ratio Mixing Ratio Strain Rate (Hz) Collected Fines (g) Segregation Rate (kg/h) NSR (kg/kg-h)

0.25 232.50 (5.1) 0.47 (0.01) 0.97 (0.02) 0.50 369.50 (6.5) 0.74 (0.01) 1.54 (0.03)

2.4:1.0

50:50 1.00 409.35 (4.2) 0.82 (0.01) 2.27 (0.02) 0.25 1 96.22 (6.1) 0.39 (0.01) 0.63 (0.02) 0.50 280.20 (5.7) 0.56 (0.01) 0.90 (0.02)

2.0:1.0

63:37

1.00 333.34 (14.0) 0.67 (0.03) 1.08 (0.05) 0.25 32.85 (4.8) 0.07 (0.01) 0.11 (0.02) 0.50 39.00 (7.2) 0.08 (0.01) 0.13 (0.02)

3,675

1.7:1.0

37:63 1.00 43.60 (3.5) 0.09 (0.01) 0.14 (0.01) 0.25 138.56 (9.2) 0.28 (0.02) 0.75 (0.05) 0.50 216.60 (5.3) 0.43 (0.01) 1.17 (0.03)

2.0:1.0

63:37

1.00 292.18 (7.2) 0.58 (0.01) 1.58 (0.04) 0.25 117.79 (5.5) 0.24 (0.01) 0.49 (0.02) 0.50 216.30 (8.3) 0.41 (0.05) 0.86 (0.10)

1.7:1.0

50:50 1.00 298.23 (8.7) 0.60 (0.01) 1.24 (0.03) 0.25 29.28 (1.1) 0.06 (0.00) 0.12 (0.00) 0.50 39.50 (1.4) 0.08 (0.00) 0.16 (0.01)

3,075

1.4:1.0

50:50 1.00 53.28 (3.4) 0.11 (0.01) 0.22 (0.02) 0.25 68.70 (1.0) 0.14 (0.00) 0.46 (0.01) 0.50 57.70 (6.5) 0.12 (0.01) 0.39 (0.04)

1.7:1.0

63:37

1.00 76.19 (8.8) 0.15 (0.02) 0.51 (0.06) 0.25 40.90 (0.5) 0.08 (0.00) 0.21 (0.00) 0.50 43.77 (1.4) 0.09 (0.00) 0.23 (0.01)

1.4:1.0

63:37 1.00 63.04 (3.0) 0.13 (0.01) 0.33 (0.03) 0.25 12.95 (1.7) 0.03 (0.00) 0.07 (0.01) 0.50 12.79 (0.8) 0.03 (0.00) 0.07 (0.00)

2,580

1.2:1.0

63:37 1.00 17.37 (0.9) 0.03 (0.00) 0.09 (0.00)

* SD values in parentheses

83

Table 5.3 Segregation results for binary mixtures with three coarse sizes for urea* Coarse Size Size Ratio Mixing Ratio Strain Rate (Hz) Collected Fines (g) Segregation Rate (kg/h) NSR (kg/kg-h)

0.25 81.56 (1.8) 0.16 (0.00) 0.36 (0.01) 0.50 140.30 (4.0) 0.28 (0.01) 0.62 (0.02)

2.0:1.0

37:63

1.00 150.86 (8.7) 0.30 (0.02) 0.67 (0.04) 0.25 31.18 (1.7) 0.06 (0.00) 0.14 (0.01) 0.50 27.30 (2.8) 0.05 (0.01) 0.12 (0.01)

3,675

1.7:1.0

37:63 1.00 30.52 (4.2) 0.06 (0.01) 0.14 (0.02) 0.25 27.49 (1.3) 0.05 (0.00) 0.16 (0.01) 0.50 41.20 (3.7) 0.08 (0.01) 0.24 (0.02)

1.7:1.0

50:50

1.00 47.35 (3.3) 0.09 (0.01) 0.27 (0.01) 0.25 21.90 (2.3) 0.04 (0.00) 0.13 (0.01) 0.50 19.76 (5.8) 0.04 (0.01) 0.11 (0.03)

3,075

1.4:1.0

50:50 1.00 16.72 (1.5) 0.03 (0.00) 0.10 (0.00) 0.25 9.80 (1.0) 0.02 (0.00) 0.07 (0.01) 0.50 12.26 (0.7) 0.02 (0.00) 0.09 (0.01)

1.4:1.0

63:37

1.00 17.34 (1.9) 0.03 (0.00) 0.12 (0.01) 0.25 9.91 (0.5) 0.02 (0.00) 0.07 (0.00) 0.50 7.02 (0.4) 0.01 (0.00) 0.05 (0.00)

2,580

1.2:1.0

63:37 1.00 7.33 (1.0) 0.01 (0.00) 0.05 (0.01)

* SD values in parentheses

84

5.4.1.1 Strain rate effect on size ratio Figure 5.1 compares the percent segregated fines at the three strain rates of 1.0, 0.5, and

0.25 Hz for the three size ratios 2.4:1.0, 2.0:1.0, and 1.7:1.0, respectively; when coarse mean size

of 3,675 µm was used for angular-shaped potash. Of the total time, for the first 10 minutes fines

were collected at 30 s interval and, thereafter, 120 s interval due to the slow down in discharge of

fines. The percent segregated fines mass was the highest and the lowest at 1.0 Hz and 0.25 Hz

strain rates, respectively, for the binary size ratios 2.4:1.0, 2.0:1.0, and 1.7:1.0 of potash. As

expected, the percent segregated fines mass at 0.5 Hz was in-between the percent segregated

fines mass at strain rates of 1.0 Hz and 0.25 Hz. At strain rate 1.0 Hz, after 15 s, 3.8%, 1.8%, and

0.6% of the total initial fines present in the binary mixtures were collected for the size ratios

2.4:1.0, 2.0:1.0, and 1.7:1.0, respectively. At the end of 30 minutes, the percent segregated fines

mass at these strain rates were 85.0%, 56.1%, and 7.3%, respectively (Figure 5.1a) (p<0.05). At

strain rate 0.5 Hz, after 15 s, 3.1%, 1.6%, and 0.5% of the total initial fines present in the binary

mixtures were collected for the size ratios 2.4:1.0, 2.0:1.0, and 1.7:1.0, respectively. At the end

of 30 minutes, the percent segregated fines mass at these strain rates were 79.6%, 49.5%, and

7.1%, respectively (Figure 5.1b) (p<0.05). At strain rate 0.25 Hz, after 15 s, 2.3%, 1.3%, and

0.3% of the total initial fines present in the binary mixtures were collected for the size ratios

2.4:1.0, 2.0:1.0, and 1.7:1.0, respectively. At the end of 30 minutes, the percent segregated fines

mass at these strain rates were 47.6%, 32.0%, and 4.7%, respectively (Figure 5.1c) (p<0.05).

The segregated fines mass for size ratio 1.7:1.0 was not significantly different at the three

level of strain rates (p>0.05) used in this study. At these three strain rates, however, the percent

segregated fines for the size ratio 2.0:1.0 was closer to size ratio 2.4:1.0 vs. 1.7:1.0, although,

difference decreased with decreasing strain rate from 1.0 Hz to 0.25 Hz. This observation is in

agreement with the hypothesis that binary mixtures prepared with the same coarse size and size

ratio but differing mixing ratios result in greater amount of segregated fines for higher proportion

of fines, i.e., 33:67 vs. 50:50 (Jha et al., 2007a). Consequently, the larger size of fines in the

binary size ratio 1.7:1.0 could also be the reason of lower percent of segregated fines. At the

three strain rates of 1.0, 0.5, and 0.25 Hz, the segregated fines mass for the size ratios 2.0:1.0,

1.7:1.0, and 1.4:1.0 of potash and the size ratio 2.0:1.0 of urea when fines sizes of 1,550 µm and

1,850 µm were used with their corresponding coarse sizes was significantly different (p<0.05)

(Tables 5.2 and 5.3). In general, the strain rate had minimal or no effect on the percent

85

segregated fines mass for the size ratio 1.2:1.0 of potash and the size ratios 1.7:1.0, 1.4:1.0, and

1.2:1.0 of urea (p>0.05) (Tables 5.2 and 5.3). This was attributed to the smaller pore sizes in the

coarse particles bed that were not large enough for fines to pass. These results showed that strain

rate has minimal or no effect when size difference and porosity were small. The results are in

agreement with the research findings that size is the dominant parameter responsible for

segregation.

86

0.0

20.0

40.0

60.0

80.0

100.0

0 5 10 15 20 25 30 35

Time (minutes)

Perc

ent s

egre

gate

d fin

es (%

)

Size ratio 2.4:1.0

Size ratio 2.0:1.0

Size ratio 1.7:1.0

0.0

20.0

40.0

60.0

80.0

100.0

0 5 10 15 20 25 30 35

Time (minutes)

Perc

ent s

egre

gate

d fin

es (%

)

Size ratio 2.4:1.0

Size ratio 2.0:1.0

Size ratio 1.7:1.0

0.0

20.0

40.0

60.0

80.0

100.0

0 5 10 15 20 25 30 35

Time (minutes)

Perc

ent s

egre

gate

d fin

es (%

)

Size ratio 1.7:1.0Size ratio 2.0:1.0

Size ratio 2.4:1.0

Figure 5.1 Comparison of percent segregated fines for three size ratios of potash when

coarse size was 3,675 µm at strain rates (a) 1.0 Hz, (b) 0.5 Hz, and (c) 0.25 Hz, with ±SD as error bars

(a)

(b)

(c)

87

5.4.1.2 Comparison between angular and spherical-shaped material Figure 5.2 compares the percent segregated fines of urea (spherical-shaped particles) and

potash (angular-shaped particles) at strain rates 0.25, 0.5, and 1.0 Hz for the size ratio 2.0:1.0

when the coarse size was 3,675 µm. In the first few minutes, the percent segregated fines mass

for binary mixtures prepared using the spherical-shaped urea and the angular-shaped potash was

very close to each other; however, after a few minutes, the percent segregated fines mass

increased very rapidly for the angular-shaped potash in comparison with the spherical-shaped

urea binary mixtures at the three strain rates: 0.25, 0.5, and 1.0 Hz. More fines were expected in

the case of potash because of the angular-shaped particles (porosity of 51%, i.e., larger void

spaces) and the higher particle density compared with the spherical-shaped urea particles

(porosity of 44% i.e., smaller void spaces).

The difference between the percent segregated fines mass of urea and potash increased

with the increase in strain rate from 0.25 Hz to 1.0 Hz. In first few minutes (<6 minutes), at

strain rate 0.25 Hz, the percent segregated fines for urea and potash were 10.3% and 9.9%,

respectively, however, at the end of 30 minutes, the percent segregated fines mass increased

rapidly for potash 31.9% compared to urea 18.1% . At strain rate of 0.5 Hz, in the first few

minutes (<2 minutes), the percent segregated fines for urea and potash were 8.9% and 8.0%,

respectively, however, at the end of 30 minutes, the percent segregated fines mass increased

rapidly for potash (49.5%) compared to 24.5%. At strain rate 1.0 Hz, in the first minute (<1

minute), the percent segregated fines for urea and potash were 7.9% and 6.6%, respectively,

however, at the end of 30 minutes, the percent segregated fines mass increased rapidly for potash

56.5% compared to 35.4%. The difference in percent segregated fines of urea and potash were

significant (p<0.05) when fines size 1,850 µm was used with three coarse mean size for size ratio

2.0:1.0, 1.7:1.0, and 1.4:1.0. The percent segregated fines mass difference between urea and

potash has minimal or no effect when the fines size 2,180 µm was used with the three different

coarse sizes for the size ratios 1.7:1.0, 1.4:1.0, and 1.2:1.0 and were not significantly different

(p>0.05) for strain rates from 1.0 Hz to 0.25 Hz (Tables 5.2 and 5.3).

At these three strain rates, for the size ratio 2.0:1.0, the percent segregated fines for

coarse size 3,075 µm was higher than the coarse size 3,675 µm during 30 minutes of testing. The

size of fines (1,550 µm) with the coarse size 3,075 µm was smaller compared with the size of

fines (1,850 µm) with the coarse size 3,675 µm in binary mixtures of the size ratio 2.0:1.0. A

88

plausible reason of the less segregated fines for the coarse mean size 3,675 µm than 3,075 µm

because of the small void spaces in the binary mixtures, i.e., the void spaces were not large

enough to let the fine particles percolate. The difference in the percent segregated fines mass for

these two coarse sizes decreased with the decreasing strain rate from 1.0 Hz to 0.25 Hz. For size

ratios larger than 4.0:1.0 for a given coarse size, Tang and Puri (2005) found that the percent

segregated fines mass for the larger size coarse particles was higher. But for size ratios smaller

than 2.4:1.0, the size of fine particles was also the determining factor for the percent segregated

fines from a well mixed binary mixtures. These results showed that the percent segregated fines

from a well mixed system is not only determined by the size of coarse particles but also by the

size of fine particles. However, the results obtained for the other two size ratios 1.7:1.0 and

1.4:1.0 were significantly different at the three strain rates of 1.0, 0.5, and 0.25 Hz (p<0.05). The

percent segregated fines for the size ratio 1.2:1.0 was not significantly different at these three

rates (p>0.05).

89

0.0

20.0

40.0

60.0

80.0

100.0

0 5 10 15 20 25 30 35

Time (minutes)

Perc

ent s

egre

gate

d fin

es (%

)

Angular

Shperical

0.0

20.0

40.0

60.0

80.0

100.0

0 5 10 15 20 25 30 35

Time (minutes)

Perc

ent s

egre

gate

d fin

es (%

)

Angular

Spherical

0.0

20.0

40.0

60.0

80.0

100.0

0 5 10 15 20 25 30 35

Time (minutes)

Perc

ent s

egre

gate

d fin

es (%

)

Angular

Spherical

Figure 5.2 Comparison of percent segregated fines between potash and urea for size ratio 2.0:1.0 when absolute coarse size was 3,675 µm at strain rates (a) 1.0 Hz, (b) 0.5 Hz, and (c)

0.25 Hz, with ±SD as error bars

(a)

(b)

(c)

90

5.4.2 Normalized segregation rate The SR and NSR results are similar at strain rates 1.0, 0.5, and 0.25 Hz when comparing

results for the same mixing ratio; however, different mixing ratios for some treatments yielded

differing results (Jha et al., 2007a). The mixing ratios for the tested binary size mixtures were

kept constant for testing the segregation potential of fines at the three mentioned strain rates.

Herein, only the NSR results are presented.

5.4.2.1 Strain rate effect on size ratio It was hypothesized that the voids created during higher intensity (strain rate) motions for

a bed of binary size mixtures, result in larger normalized segregation rate when the other test

conditions were the same. The hypothesis was tested by using the binary size mixtures at the

three strain rates of 1.0, 0.5, and 0.25 Hz for both urea and potash. The obtained results at these

three strain rates for the size ratios 2.4:1.0, 2.0:1.0, and 1.7:1.0 when the coarse particles size was

3,675 µm are presented in Figure 5.3. At the strain rate of 1.0 Hz, after 15 s, the NSR was 9.11,

4.41, and 1.54 kg/kg-h for the size ratios 2.4:1.0, 2.0:1.0, and 1.7:1.0. At the end of 30 minutes,

the NSR was found to be 1.70, 1.67, and 0.15 kg/kg-h in the same order. At the strain rate of 0.5

Hz, at 15 s, the NSR was 7.39, 3.95, and 1.14 kg/kg-h for the size ratios 2.4:1.0, 2.0:1.0, and

1.7:1.0. At the end of 30 minutes, the NSR was found to be 1.59, 0.99, and 0.14 kg/kg-h in the

same order. At the strain rate of 0.25 Hz, at 15 s, the NSR was 5.35, 2.96, and 0.75 kg/kg-h for

the size ratios 2.4:1.0, 2.0:1.0, and 1.7:1.0. At the end of 30 minutes, the NSR was found to be

0.95, 0.64, and 0.10 kg/kg-h in the same order.

At these three strain rates: 1.0, 0.5, and 0.25 Hz, similar results were obtained for the size

ratios 2.0:1.0, 1.7:1.0, and 1.4:1.0 of potash and the size ratio 2.0:1.0 of urea when the fines sizes

of 1,550 µm and 1,850 µm were used with their corresponding coarse sizes, i.e., the NSRs were

also significantly different (p<0.05). The three strain rates of 1.0, 0.5, and 0.25 Hz had minimal

or no effect on the NSR for the other size ratio 1.2:1.0 of potash and the size ratios 1.7:1.0,

1.4:1.0, and 1.2:1.0 of urea (p>0.05) (Tables 5.2 and 5.3). The reason of having minimal to no

effect of the strain rate on the NSR was due to small size difference in the coarse and fines sizes

and corresponding smaller spatial voids distributions. Figure 5.3 also compares the effect of

strain rate on the coarse size and the fines size in binary mixture for determining the NSR of

fines. At the three strain rates, for the size ratio 2.0:1.0 of potash, the coarse size 3,075 µm has

higher NSR compared with the coarse size 3,675 µm This observation is in agreement with the

91

hypothesis that binary mixtures prepared with the same coarse size and the size ratio but

different mixing ratios result in greater amount of the segregated fines for mixtures with higher

proportion of fines, i.e., 33:67 vs. 50:50 (Jha et al., 2007a). Consequently, the larger size of fines

(1,850 µm) with the coarse size 3,675 µm could also be the reason for lower percent of the

segregated fines. Similar results were obtained for the other size ratios 2.0:1.0, 1.7:1.0, 1.4:1.0

when the coarse mean sizes were 3,675, 3,075 and 2,580 µm (p<0.05); although, when the fines

size was 2,180 µm with the coarse sizes 3,675, 3,075 and 2,580 µm at the strain rates 0.25 Hz

and 0.5 Hz, there were no significant differences (p>0.05).

92

0.0

2.0

4.0

6.0

8.0

10.0

0 5 10 15 20 25 30 35

Time (minutes)

NSR

(kg/

kg-h

)

Size ratio 2.4:1.0


0.0

2.0

4.0

6.0

8.0

0 5 10 15 20 25 30 35

Time (minutes)

NSR

(kg/

kg-h

)

Size ratio 2.4:1.0


0.0

2.0

4.0

6.0

8.0

10.0

0 5 10 15 20 25 30 35

Time (minutes)

NSR

(kg/

kg-h

)

Size ratio 2.4:1.0


Figure 5.3 Comparison of NSR for three size ratios of potash when mean coarse size was

3,675 µm at strain rates (a) 1.0 Hz, (b) 0.5 Hz, and (c) 0.25 Hz, with ±SD as error bars

(b)

(a)

(c)

93

5.4.2.2 Comparison between angular and spherical-shaped material Figure 5.4 compares the NSR for urea and potash at three strain rates 0.25, 0.5, and 1.0

Hz for the size ratio 2.0:1.0. At the strain rate of 1.0 Hz, after 15 s, the NSR was 9.31 and 4.41

kg/kg-h for the spherical and angular binary mixtures, respectively. After 5 minutes, the NSR

values were very close to each other, i.e., 2.10 and 1.96 kg/kg-h. Thereafter, the NSR for urea

decreased rapidly compared with potash. At the end of 30 minutes, the NSR was 0.71 and 1.13

kg/kg-h for spherical and angular binary mixtures, respectively. At the strain rate of 0.5 Hz, after

15 s, the NSR was 7.14 and 3.95 kg/kg-h for spherical and angular binary mixtures, respectively.

After 5 minutes, the NSR values were very close to each other, i.e., 1.74 and 1.68 kg/kg-h. At the

end of 30 minutes, the NSR was 0.64 and 0.99 kg/kg-h for spherical and angular binary mixtures,

respectively. At the strain rate of 0.25 Hz, after 15 s, the NSR was 4.86 and 1.16 kg/kg-h for

spherical and angular binary mixtures, respectively. After 6 minutes, the NSR values were the

same, i.e., 1.03 and 1.03kg/kg-h. At the end of 30 minutes, the NSR was 0.36 and 0.64 kg/kg-h

for spherical and angular binary mixtures, respectively.

As mentioned previously, the large decrease in the NSR can be attributed to urea’s

spherical-shaped and lower porosity (i.e., initially, there is a large availability of low

coordination number particles) compared with potash binary mixtures comprised of angular-

shaped particles that form higher porosity assembly. Clearly, size segregation in conjunction

with other physical properties such as shape and density have greater detrimental affect than size

alone. The difference in percent segregated fines of urea and potash were significant (p<0.05)

when the fines size 1,850 µm was used with the three coarse mean size for the size ratios 2.0:1.0,

1.7:1.0, and 1.4:1.0. The percent segregated fines mass values were not significantly different

(p>0.05) at strain rates 1.0 Hz to 0.25 Hz (Tables 5.2 and 5.3) between the urea and potash

binary mixtures when the fines size 2,180 µm was used with the three different coarse sizes to

form the size ratios 1.7:1.0, 1.4:1.0, and 1.2:1.0. At the three strain rates used, the size ratio

2.0:1.0 was selected to show the effect of the coarse (3,675 µm vs. 3,075 µm) and fine (1,850 µm

vs. 1,550 µm) sizes on the NSR (Figure 5.4). The NSR of the coarse size 3,075 µm was higher

than the NSR of the coarse sizes 3,675 µm at all the three strain rates. In addition to the fines size

difference, the proportion of fines for 3,075 µm was small compared to 3,675 µm combinations,

i.e., the mixing ratios were 67:33 and 33:67, respectively (p<0.05). The results obtained for the

94

other two size ratios 1.7:1.0 and 1.4:1.0 were significantly different at the three strain rates 0.25,

0.5, and 1.0 Hz (p<0.05).

95

0.0

2.0

4.0

6.0

8.0

10.0

0 5 10 15 20 25 30 35

Time (minutes)

NSR

(kg/

kg-h

)Angular

Spherical

0.0

2.0

4.0

6.0

8.0

10.0

0 5 10 15 20 25 30 35

Time (minutes)

NSR

(kg/

kg-h

r)

Spherical

Angular

0.0

2.0

4.0

6.0

8.0

10.0

0 5 10 15 20 25 30 35

Time (minutes)

NSR

(kg/

kg-h

)

Angular

Spherical

Figure 5.4 Comparison of NSR between potash and urea for size ratio 2.0:1.0 when coarse size was 3,675 µm at strain rates (a) 1.0, (b) 0.5 Hz, and (c) 0.25 Hz, with ±SD as error bars

(b)

(a)

(c)

96

5.5 Conclusions

The PSSC-II was capable of operating at different speeds to quantify segregation in the

binary size mixtures of urea and potash, i.e., six size ratios of urea two for each coarse size 3,675

µm, 3,075 µm, and 2,580 µm and nine size ratios of potash three for each coarse size 3,675 µm,

3,075 µm, and 2,580 µm. The operating conditions for the binary size tests were 85 mm bed

depth, 6% strain, and strain rates of 0.25, 0.5, 1.0 Hz. Based on the analysis of results, it was

concluded: 1) for both materials, the NSR of binary mixtures depended on strain rate when

subjected to shear motion. Furthermore, the NSR increased when the strain rate increased from

0.25 Hz to 1.0 Hz; for instance, the NSR increased from 0.95 to 1.70 kg/kg-h, almost 79% for the

size ratio 2.4:1.0 of potash when the strain rate increased by four-fold, 2) the NSR for different

size ratios were affected by strain rate, for instance, at strain rate of 1.0 Hz, the NSR decreased

from 1.70 kg/kg-h for the size ratio 2.4:1.0 to 0.17 kg/kg-h for the size ratio 1.7:1.0, almost 90%

decrease, 3) the NSR was dependent on the size of coarse and fine particles and also on the strain

rates; at the strain rate of 1.0 Hz, the NSR decreased from 1.62 to 1.32 kg/kg-h with increasing

size of fines 1,550 µm vs. 1,850 µm for the size ratio 2.0:1.0, and 4) the NSR was dependent on

the type of material selected and the strain rate; at the strain rate of 1.0 Hz, the NSR of spherical-

shaped urea (0.71 kg/kg-h) was lower than the NSR of angular-shaped potash (1.13 kg/kg-h) at

the end of 30 minutes.

5.6 Key Findings The binary mixtures of urea and potash were tested for percolation segregation of fines at

three strain rates of 0.25, 0.5, and 1.0 Hz and strain of 6% to measure and compare the effect of

size ratio, mixing ratio, coarse and fines size and materials. Again, size ratio was found the most

dominant parameter responsible for segregation. The percolation of fines from the binary

mixtures was not linearly dependent on the strain rate with increase from 0.25 to 1.0 Hz. The

movement of blended material must be restricted to possible minimum to mitigate segregation in

particulate mixtures. The percolation segregation of fines in the binary mixtures was higher for

potash compared with urea at these three strain rates.

97

5.7 References

Bradley, M. S. A. and R. J. Farnish. 2005. Segregation of blended fertilizer during spreading: the effect of differences in ballistic properties. In Proc 554. The International Fertilizer Society, York, UK. pp: 15.

Bridgwater, J. and N. D. Ingram.1971. Rate of spontaneous inter-particle percolation. Transactions of the Institute of Chemical Engineers 49:163-169.

Bridgwater, J. 1976. Fundamental powder mixing mechanism. Powder Technology 15: 215–236. Bridgwater, J. 1999. Segregation mechanisms in condensed granular flow: A summary of some

fundamental experiments. In A. D. Rosato, & D. L. Blackmore (Eds.), IUTAM symposium on segregation in granular flows, Cape May, NJ. Dordrecht: Kluwer Academic Publishers.

Bridle, I. A., M. S. A. Bradley, and A. R. Reed. 2004. Non-segregating blended fertilizer development: A new predictive test for optimising granulometry. In Proc 547. The International Fertilizer Society, York, UK. pp: 27

Cooke, M. H., D. J. Stephens, and J. Bridgwater. 1976. Powder mixing- a literature survey. Powder Technology 15: 1–20.

Cooke, M. H. and J. Bridgwater. 1979. Interparticle percolation: a statistical mechanical interpretation. Industrial Engineering Chemistry Fundamentals 18: 25–27.



Foo, W. S. and Bridgwater, J. 1983. Particle migration. Powder Technology 36: 271-273. Jha, A. K., J. S. Gill, and V. M. Puri. 2007a. Percolation segregation in binary size mixtures of

spherical and angular-shaped particles of different densities. Particulate Science and Technology, An International Journal, In review.

Jha, A. K., H. Yi, and V. M. Puri. 2007b. Percolation segregation and flowability of urea under different relative humidities. KONA (Powder and Particle), In review.

Rosato, A.D. and D.L. Blackmore. 2000. Preface. Eds: Rosato, A.D. and D.L. Blackmore. IUTAM Symposium on Segregation in Granular Flows 11-29. Norwell: Kluwer Academic Publishers.


Scott, A. M. and J. Bridgwater. 1975. Interparticle percolation: A fundamental solids mixing mechanism. Industrial Engineering Chemistry Fundamentals 14(1): 22–27.

Scott, A. M. and J. Bridgwater. 1976. Self-diffusion of spherical particles in a simple shear apparatus. Powder Technology 14: 177–183.




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Vallance, J. W. and S. B. Savage. 2000. Particle segregation in granular flows down chutes. Eds: Rosato, A.D. and D.L. Blackmore. IUTAM Symposium on Segregation in Granular Flows 31-51. Kluwer Academic Publishers. Norwell, USA.

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6. CHAPTER - PERCOLATION SEGREGATION IN BINARY SIZE MIXTURES UNDER DIFFERENT SHEAR AND

INTENSITY OF MOTION

6.1 Abstract Percolation segregation in the binary size mixtures of potash and urea were quantified at

three strains of 2%, 6%, and 10% and two strain rates of 0.25 Hz and 0.5 Hz. In this study to

prepare binary size mixtures, three coarse mean sizes: 3,675 µm, 3,075 µm, and 2,580 µm of

potash and urea were mixed with three fines mean sizes: 2,180 µm, 1,850 µm, and 1,550 µm of

potash and two fines sizes: 2,180 µm, 1,850 µm of urea, respectively. Since the fines size 1,550

µm of urea was not available in sufficient quantity; therefore, it was not included in tests.

Percolation segregation of fines in the binary mixed sample was quantified using the primary

segregation shear cell (PSSC-II). Based on the experimental results, the percent segregated fines

and the normalized segregation rate (NSR) of fines for binary mixtures increased when the strain

rate was increased from 0.25 Hz to 0.5 Hz, where NSR is defined as the amount of fines

percolated from initial fines present in the binary mixture based on total time of PSSC-II

operation (kg/kg-h). The NSR and the percent segregated fines also increased with the increase

in strain from 2% to 10%. The NSR increased when the strain was increased from 2%>6%>10%

for the size ratios 1.7:1.0, 2.0:1.0, and 2.4:1.0 (p<0.05). At the three strains: 2%, 6%, and 10%,

the NSR for potash was higher (0.06, 1.13, 1.40 kg/kg-h) than the NSR for urea (0.17, 0.62, and

0.69 kg/kg-h) except at strain of 2%, for the same size ratio 2.0:1.0 when coarse size was 3,675

µm (p<0.05).

6.2 Introduction Segregation in particulate materials affects the quality of mixtures during material-related

unit operations, such as mixing, conveying, filling, discharging, and compaction. Particulate

materials are processed and manufactured for product manufacturing and development in various

industries such as agriculture, ceramic, construction, food, nutraceutical, metal powder and

metallurgy, and pharmaceutical. Particulate materials, if not handled carefully, segregate due to

differences in physical property such as size and size distribution, shape, density, surface texture,

morphology, contact friction, brittleness, density, chemical affinities, ability to absorb moisture,

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magnetic properties, different time and length scale, and subjected under different mechanical

conditions (Rosato et al., 2002 and Jha et al., 2007a). Segregation can be mitigated, if not

eliminated, by understanding the factors affecting the mechanisms at fundamental level.

Bridgwater and his colleagues were the pioneers in identifying the dominant parameters

responsible for segregation (Bridgwater and Ingram, 1971; Scott and Bridgwater, 1975;

Bridgwater, 1976 and 1999; Cooke et al., 1976; Cooke and Bridgwater, 1979; and Foo and

Bridgwater, 1983). Bridgwater and his colleagues found that the size of particulates is the most

dominant parameter contributing towards segregation. Results were later confirmed by several

researchers (for instance, Rosato et al., 2002; Bridle et al., 2004; Tang and Puri, 2004; Bradley

and Farnish, 2004; and Jha et al., 2007a and b). It is also reported that shape and density have

secondary effect on segregation as compared to size. Effects of shape and density on segregation

in binary mixtures were quantified by Tang and Puri (2007). The cumulative effect of shape and

density with size has not been studied. Percolation segregation always occurs under dynamic

conditions induced by shear and vibration in bulk solids (Vallance and Savage, 2000).

Based on the above literature review, the aim of this research was to study the time-

dependent percolation segregation in binary mixtures of two different materials at three strains of

2%, 6%, and 10% and two strain rates of 0.25 and 0.5 Hz. Strain can be defined as the movement

of shear box in backward-forward directions in horizontal plane. Strain rate can be defined as the

cycles of movement (intensity of to-and-fro movement) of the shear box in unit time. A limited

understanding of time-dependent percolation segregation has been achieved by these researchers

(Duffy and Puri, 2002 and 2003, Tang and Puri, 2005, and Jha et al., 2007a and b). The present

study overcomes the limitations of the work of previous researchers by conducting segregation

experiments for a number of size ratios on well mixed systems of real-world materials. The

specific objectives of this study were to determine the effect of strain and strain rate on: 1) size

ratio and 2) materials used to formulate binary size mixtures.

6.3 Materials and Methods The PSSC-II was used to quantify segregation in the binary mixtures of urea and potash.

A sieve of opening size 2,360 µm was used throughout the experiments after preliminary tests

with different size ratios (binary and multi-size mixtures) to ensure that coarse size particles did

not block the sieve openings, while permitting fines to fall freely through sieve openings.

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Since binary size mixtures are considered to be the building blocks to study multi-size

and continuous mixtures, these binary size mixtures were studied at three strains of 2%, 6%, and

10% and two strain rates of 0.25 and 0.5 Hz. In the present article, nine different binary size

ratios of potash and six different size ratios of urea in different mixing ratios were studied (Table

6.1). The segregation results were analyzed using segregation determining metrics such as the

percent segregated fines, segregation rate (kg/h), and normalized segregation rate (kg/kg-h), the

segregation metrics are further sub-divided under three subheadings effect of: (i) strain and strain

rate, (ii) size ratio, and (iii) material.


Urea and potash were selected for studying percolation segregation due to their extreme

shape and density among the three major raw ingredients: urea, potash, and phosphate, used in

the manufacture of different fertilizer blends. Bed depth of 85 mm (shear box height = 100 mm)

was used to represent percolation of fines within bagged fertilizers in normal orientation, i.e.,

depth direction along gravity, during conveying, handling, and transportation.

Three coarse size ranges (3,675, 3,075, and 2,580 µm) of potash and urea were mixed

with three fine size ranges (2,180, 1,850, and 1,550 µm) of potash and two fines size ranges of

urea (2,180, 1,850 µm) to form binary mixtures (Table 6.1). For potash, the nine resulting binary

mixtures were 2.4:1.0, 2.0:1.0, 1.7:1.0, and 2.0:1.0, 1.7:1.0, 1.4:1.0, and 1.7:1.0, 1.4:1.0, 1.2:1.0,

respectively. For urea, the six resulting binary mixtures were 2.0:1.0, 1.7:1.0 and 1.7:1.0, 1.4:1.0,

and 1.4:1.0, 1.2:1.0, respectively. The 15 binary mixtures have either the same or different

mixing ratios to represent the industrial conditions (Table 6.1).

6.3.2 Test condition and experimental design

Coarse size particles were mixed with fine size particles in a 225-W six-speed bench-top


Bentonville, AR) to mix binary size samples. To randomize the tests, a separate experimental

design was considered for both angular and spherical-shaped materials (Table 6.1). Six

replications were performed for each set of experiments for testing percolation segregation using

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PSSC-II. Of the six replicates within 95% confidence interval, three replicates for each set were

completed using load cells and three replicates were completed by collecting segregated fines in

a pan. Only three replicates included in the graphical representation and the other three will be

used for spatial distribution of fines. The segregated fines mass values were measured and two

segregation determining parameters, segregation rate (SR), and normalized segregation rate

(NSR), were deduced from the fines mass values. The SR was defined as amount of fines

collected in unit time (kg/h), and the NSR was defined as the amount of fines percolated from the

initial fines in a binary mixture for the total time of operation of PSSC-II (kg/kg-h). The SR and

NSR provided similar results; however, when different MRs were used, differing results for SR

and NSR were obtained. Therefore, the two segregation rate metrics were considered whenever

needed. All tests were conducted in an environment-controlled laboratory with average

temperature of 22°C ± 3°C and relative humidity less than 40%.

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Table 6.1 Design of experiment for binary size mixtures for potash and urea* Material Coarse size

(µm) Fine Size (µm) Size

Ratio Mixing Ratio Number

1,400-1,700 (mean = 1,550)

2.4:1.0 50:50

1,700-2,000 (mean = 1,850)

2.0:1.0 37:63

Potash

3,350-4,000 (Mean = 3,675)

2,000-2,360 (mean = 2,180)

1.7:1.0 37:63

3

1,400-1,700 (mean = 1,550)

2.0:1.0 67:33

1,700-2,000 (mean = 1,850)

1.7:1.0 50:50

Potash

2,800-3,350 (mean = 3,075)

2,000-2,360 (mean = 2,180)

1.4:1.0 50:50

3

1,400-1,700 (mean = 1,550)

1.7:1.0 67:33

1,700-2,000 (mean = 1,850)

1.4:1.0 60:40

Potash

2,360-2,800 (mean = 2,580)

2,000-2,360 (mean = 2,180)

1.2:1.0 60:40

3

1,700-2,000 (mean 1,850)

2.0:1.0 37:63

Urea

3,350-4,000 (mean = 3,675) 2,000-2,360

(mean 2,180) 1.7:1.0 37:63

2

1,700-2,000 (mean 1850)

1.7:1.0 50:50

Urea

2,800-3,350

(mean = 3,075) 2,000-2,360 (mean 2,180)

1.4:1.0 50:50

2

1,700-2,000 (mean 1,850)

1.4:1.0 60:40 Urea

2,360-2,800 (mean = 2,580) 2,000-2,360

(mean 2,180 1.2:1.0 60:40

2

Total (six replications) 90×6 =540 * All tests were performed at strains of 2%, 6%, and 10% and strain rates of 0.25 and 0.5 Hz

6.4 Results and Discussion

The mass of percolated fines in the 15 binary mixtures were recorded at the three strains

of 2%, 6%, and 10% and two strain rates of 0.25 and 0.5 Hz. The results are presented in the

categories: percent segregated fines, segregation rate and normalized segregation rate. The

results of segregation rate and normalized segregation rate were similar except different mixing

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ratios for the same size ratio, therefore, results are presented only in two forms percent

segregated fines and normalized segregation rate in this chapter. The results of different mixing

ratios can be found in Jha et al. (2007a). The effect of strain and strain rate on size ratio, and

material (angular vs. spherical) on segregation of fines are discussed in subsequent paragraphs.


As expected, by increasing the strain from 2% to 10%, the percent segregated fines mass

increased with time for all binary mixtures tested. The strain rates of 0.25 and 0.5 Hz had

significant effect on binary mixtures at tested strains of 2%, 6%, and 10% (p<0.05).

6.4.1.1 Strain and strain rate effects Figure 6.1 compares the effect of strains 2%, 6%, and 10% at strain rates of 0.25 and 0.5

Hz for the size ratio 2.4:1.0 of potash. The percent segregated fines mass was compared based on

the data collected upto 30 minutes for binary mixtures using the PSSC-II. Of the total time of the

PSCC-II operation, for the first 10 minutes fines were collected at 30 s interval, thereafter, 120 s

interval due to the slow down in discharge of fines. For the binary size ratio 2.4:1.0, the percent

segregated fines mass was the lowest and the highest at strains of 2% and 10% at both strain

rates of 0.25 and 0.5 Hz, respectively. As expected, the percent segregated fines mass at strain of

6% was in-between strains of 2% and 10%. At the strain of 2% and strain rate of 0.25 Hz, after

15 s, 1.0% of the total initial fines present in the binary mixtures was collected for the size ratio

2.4:1.0. At the end of 30 minutes, the percent segregated fines at these strain and strain rate

combination was 6.5% (Figure 6.1a). At the strain of 2% and strain rate of 0.5 Hz, after 15 s,

1.3% of the total initial fines present in the binary mixtures was collected for the size ratio

2.4:1.0. At the end of 30 minutes, the percent segregated fines was 9.6% (Figure 6.1b). At the

strain of 6% and 0.25 Hz, after 15 s, 2.2% of the total initial fines present in the binary mixtures

was collected for the size ratio 2.4:1.0. At the end of 30 minutes, the percent segregated fines

was 47.5% (Figure 6.1a). At the strain of 6% and strain rate of 0.5 Hz, after 15 s, 3.6% of the

total initial fines present in the binary mixtures was collected for the size ratio 2.4:1.0. At the end

of 30 minutes, the percent segregated fines was 79.6% (Figure 6.1b). At the strain of 10% and

strain rate of 0.25 Hz, after 15 s, 2.9% of the total initial fines present in the binary mixtures was

collected for the size ratio 2.4:1.0. At the end of 30 minutes, the percent segregated fines was

76.6% (Figure 6.1a). At the strain of 10% and strain rate of 0.5 Hz, after 15 s, 4.0% of the total

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initial fines present in the binary mixtures was collected for the size ratio 2.4:1.0. At the end of

30 minutes, the percent segregated fines was 85.8% (Figure 6.1b). The percent segregated fines

mass for binary size ratio 2.4:1.0 at the three strains of 2%, 6%, and 10% and two strain rates of

0.25 and 0.5 Hz was significantly different (p<0.05).

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Figure 6.1 Comparison of strains on size ratio 2.4:1.0 at strain rates (a) 0.25 Hz and (b) 0.5

Hz, with ±SD as error bars

For size ratio 2.4:1.0 at strain rate of 0.25 Hz, when the strain increased by three times

from 2% to 6% the percent segregated fines mass was increased by 7.36 times. When the strain

increased five times from 2% to 10% the percent segregated fines was increased by 11.86 times.

By comparison, the percent segregated fines mass increased only by 1.61 times when the strain

increased from 6% to 10%. For size ratio 2.4:1.0 at strain rate of 0.5 Hz, when the strain

(a)

(b)

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increased by three times from 2% to 6% the percent segregated fines mass was increased by 8.23

times. When the strain increased five times from 2% to 10% the percent segregated fines was

increased by 8.90 times; whereas, the percent segregated fines mass increased only by 1.08 times

when the strain was increased from 6% to 10%. The percent segregated fines mass at the strain

of 2% and strain rates of 0.25 and 0.5 Hz was similar but significantly different (p<0.05) but

differences at these two strain rates increased with the increasing strains at 6% and 10%. Similar

results were found for size ratios 2.0:1.0, and 2.0:1.0, 1.7:1.0, and 1.7:1.0 in combination with

coarse sizes 3,675 µm, 3,075 µm, and 2,580 µm of potash, respectively. Unlike results of binary

mixtures of smaller fines 1,550 µm and 1,850 µm, the percent segregated fines mass size ratio

1.7:1.0, and 1.4:1.0, and 1.2:1.0 with coarse size 3,675 µm, 3,075 µm, and 2,580 µm of potash

were not significantly different (p>0.05). The reason of having minimal or no effect of strain and

strain rate on binary mixtures was due to the large size of fines 2,180 µm used in formulation.

The void space created in the bed of coarse particles at these three strains was not sufficient so

that fines of larger size 2,180 µm can percolate under the shear motion. This observation is in

agreement with the hypothesis with that size of particulate is the dominant variable contributing

towards percolation of fines.

6.4.1.2 Size ratio effect The percent segregated fines mass results for binary size ratios were similar at strain rates

of 0.25 and 0.5 Hz. Therefore, only the percent segregated fine mass for binary size ratios at

strain rate of 0.5 Hz is discussed. Figure 6.2 shows the comparison of percent segregated fines

for three size ratios 2.4:1.0, 2.0:1.0, and 1.7:1.0 when coarse mean size 3,675 µm was used for

angular-shaped particles at the three strains of 2%, 6%, 10% and strain rate of 0.5 Hz. As

expected, the percent segregated fines for size ratio 2.4:1.0 was the highest while it was the

lowest for size ratio of 1.7:1.0. The closeness of size ratio 2.0:1.0 with 2.4:1.0 and 1.7:1.0

depends on strain created in the coarse particles’ bed. At strain of 2%, the percent segregated

fines for size ratio 2.0:1.0 was closer to size ratio 1.7:1.0 (Figure 6.2a); whereas, at strains of 6%

and 10%, the percent segregated fines for size ratio 2.0:1.0 was closer to size ratio 2.4:1.0

(Figures 6.2a and 6.2b), respectively. The percent segregated fines for size ratio 2.0:1.0 increased

with the increase in strain from 2% to 10%, and was closer to size ratio 2.4:1.0 at higher strains

10% vs. 6%. At strain of 2%, after 15 s, the percent segregated fines mass for size ratios 2.4:1.0,

2.0:1.0, and 1.7:1.0 were 1.3%, 0.5%, and 1.2%, respectively. At the end of 30 minutes, the

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segregated fines mass were 9.6%, 2.9%, 5.3% in the same order and were significantly different

(p<0.05) (Figure 6.2a). At strain of 6%, after 15 s, the percent segregated fines mass for size

ratios 2.4:1.0, 2.0:1.0, and 1.7:1.0 were 3.6%, 1.7%, and 0.5%, respectively. At the end of 30

minutes, the percent segregated fines mass were 79.6%, 49.5%, 7.1% in the same order and were

significantly different (p<0.05) (Figure 6.2b). At strain of 10%, after 15 s, the percent segregated

fines mass for size ratios 2.4:1.0, 2.0:1.0, and 1.7:1.0 were 4.0%, 2.4%, and 0.6%, respectively.

At the end of 30 minutes, the segregated fines mass were 85.8%, 69.8%, 8.9% in the same order

and were significantly different (p<0.05) (Figure 6.2c). At the end of 30 minutes at strain of 2%,

the percent segregated fines decreased by 0.30, 0.55, and increased by 1.83 times when size

ratios 2.4:1.0 vs. 2.0:1.0, 2.4:1.0 vs. 1.7:1.0, and 2.0:1.0 vs. 1.7:1.0 were compared. The percent

segregated fines mass for size ratio 2.0:1.0 was lower than the size ratios 2.4:1.0 and 1.7:1.0. The

reason of having lower percent segregated fines is that of small strain. The percolation

segregation is governed by diffusive mechanism instead of convective mechanism at lower strain

of 2% vs. 6% and 10%. A plausible reason is the mechanical interlocking of angular-shaped

potash in binary mixtures at strain of 2%. At strain of 6%, the percent segregated fines decreased

by 0.62, 0.09, and 0.14 times when size ratios 2.4:1.0 vs. 2.0:1.0, 2.4:1.0 vs. 1.7:1.0, and 2.0:1.0

vs. 1.7:1.0 were compared. At strain of 10%, the percent segregated fines decreased by 0.81,

0.10, and 0.13 times when size ratios 2.4:1.0 vs. 2.0:1.0, 2.4:1.0 vs. 1.7:1.0, and 2.0:1.0 vs.

1.7:1.0 were compared. Similar results were obtained for different size ratios when using coarse

sizes 3,075 and 2,580 µm, i.e., percent segregated fines were also significantly different

(p<0.05).

108

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Figure 6.2 Comparison of percent segregated fines for three size ratios of potash when coarse size was 3,675 µm at strain rate of 0.5 Hz under strains of (a) 2%, (b) 6%, and (c)

10%, with ±SD as error bars

(a)

(c)

(b)

109

6.4.1.3 Comparison between angular-shaped potash and spherical-shaped urea Figure 6.3 compares the percent segregated fines of urea (spherical shaped particles) and

potash (angular shaped particles) for size ratio 2.0:1.0 when coarse size 3,675 µm was used. At

strain of 2% and strain rate of 0.5 Hz, after 15 s, the percent segregated fines mass for binary

mixtures prepared using spherical-shaped urea and angular-shaped potash were 1.5% and 0.5%,

respectively. At the end of 30 minutes, the percent segregated fines for urea and potash were

2.8% and 8.3%, respectively. In the first few minutes (<2 minutes), at strain of 6%, the percent

segregated fines for urea and potash were very close 8.9% and 8.0%, respectively of their

respective total fines; however, after 2 minutes, the percentage of fines increased very rapidly

for angular shaped potash in comparison with the spherical shaped urea binary mixtures. At the

end of 30 minutes, the percentage of segregated fines for urea and potash were 45.2% and 59.3%

of their, respective, initial fines mass. The difference in percent segregated fines of urea and

potash were significant (p<0.05). Within the first minute of the PSSC-II operation, at the strain

of 10%, the percent segregated fines for urea and potash were very close 7.3% and 7.0%,

respectively of their respective total fines; however, after 60 s, the percentage of fines increased

very rapidly for angular shaped potash in comparison with the spherical shaped urea binary

mixtures (p<0.05). At the end of 30 minutes, the percentage of segregated fines for urea and

potash were 51.4% and 70.2% of their, respective, initial fines mass. Similar results were

obtained for binary mixtures comprising other size ratios (p<0.05). As hypothesized, more fines

were expected in the case of potash because of angular-shaped particles (porosity of 51%, i.e.,

larger void spaces) and higher particle density compared with spherical shape urea particles

(porosity of 44% i.e., smaller void spaces). At strain of 2%, the segregation of fines was

governed by diffusive mechanism in contrast to segregation of fines at higher strains 6% and

10% where convective mechanism was dominant. When diffusive mechanism was dominant, the

role of density was not as important as in convective mechanism with size and shape. The

percolation segregation in binary mixtures of urea and potash can be explained by the same size

but dissimilar shape and density. In this case, the more percent segregated fines is expected in the

binary mixture of urea compared with potash because of spherical vs. angular shape and higher

particle density of potash vs. urea.

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Figure 6.3 Comparison of percent segregated fines for size ratio 2.0:1.0 of potash and urea when coarse size was 3,675 µm at strain rate of 0.5 Hz under strains of (a) 2%, (b) 6% Hz,

and (c) 10%, with ±SD as error bars

(a)

(b)

(c)

111


The SR and NSR results are similar at strain of 2%, 6%, and 10% and strain rates of 0.25

and 0.5 Hz when comparing results for the same mixing ratio; however, different mixing ratios

for some treatments yielded differing results (Jha et al., 2007a). The mixing ratios for the tested

binary size mixtures were kept constant for testing the segregation potential of fines at the three

mentioned strains and two strain rates. Herein, only the NSR results are presented.

6.4.2.1 Strain and strain rate effect It was hypothesized that larger void space and large intensity of void space creation in the

coarse bed result in larger NSR when other test conditions were the same. This hypothesis was

tested by using binary size mixtures of angular-shaped potash for size ratio 2.4:1.0 when coarse

mean size 3,675 µm was used at the three strains of 2%, 6% and 10% and strain rates of 0.25 and

0.5 Hz (Figure 6.4). At the strain of 2% and strain rate of 0.25 Hz, after 15 s, the NSR was

2.47 kg/kg-h for size ratio 2.4:1.0. The NSR decreased very rapidly in the initial phase and then

decreased linearly with time till data collection was stopped at the end of 30 minutes. At the end

of 30 minutes, the NSR was found to be 0.13 kg/kg-h. At strain of 6% and strain rate of 0.25

Hz, after 15 s, the NSR was 5.35 kg/kg-h for size ratio 2.4:1.0. The NSR decreased very rapidly

in the initial phase and then decreased linearly with time till data collection was stopped at the

end of 30 minutes. At the end of 30 minutes, the NSR was found to be 0.95 kg/kg-h. At the strain

of 10% at strain rate of 0.25 Hz, after 15 s, the NSR was 6.83 kg/kg-h for size ratio 2.4:1.0. The

NSR decreased very rapidly in the initial phase and then decreased linearly with time till data

collection was stopped at the end of 30 minutes. At the end of 30 minutes, the NSR was found to

be 1.53 kg/kg-h.

At strain of 2% and strain rate of 0.5 Hz, after 15 s, the NSR was 3.00 kg/kg-h for size

ratio 2.4:1.0. The NSR decreased very rapidly in the initial phase and then decreased linearly

with time till data collection was stopped at the end of 30 minutes. At the end of 30 minutes, the

NSR was found to be 0.19 kg/kg-h. At strain of 6% and strain rate of 0.5 Hz, after 15 s, the NSR

was 7.39 kg/kg-h for size ratio 2.4:1.0. At the end of 30 minutes, the NSR was found to be 1.59

kg/kg-h. At strain of 10% and strain rate of 0.5 Hz, after 15 s, the NSR was 9.57 kg/kg-h for size

ratio 2.4:1.0. At the end of 30 minutes, the NSR was found to be 1.72 kg/kg-h.

At the end of the data collection for size ratio 2.4:1.0 at strain rate of 0.25 Hz, when the

strain increased by three times from 2% to 6% the NSR was increased by 7.31 times. When the

112

strain increased five times from 2% to 10% the NSR was increased by 11.86 times; whereas, the

NSR increased only by 1.61 times for the increase in strain from 6% to 10%. Similar results were

found for size ratios 2.0:1.0, and 2.0:1.0, 1.7:1.0, and 1.7:1.0 with coarse sizes 3,675 µm, 3,075

µm, and 2,580 µm of potash, respectively. Unlike results of binary mixtures of smaller fines

1,550 µm and 1,850 µm, the percent segregated fines for size ratios 1.7:1.0, and 1.4:1.0, and

1.2:1.0 with coarse size 3,675 µm, 3,075 µm, and 2,580 µm of potash were not significantly

different (p>0.05). The effect of strain rate and strain on tested size ratios shows that the

relationship between NSR and strain and strain rate was not linear.

0.0

2.0

4.0

6.0

8.0

10.0

0 5 10 15 20 25 30 35

Time (minutes)

NSR

(kg/

kg-h

)

Strain 10%

Strain 2%

Strain 6%

0.0

2.0

4.0

6.0

8.0

10.0

0 5 10 15 20 25 30 35

Time (minutes)

NSR

(kg/

kg-h

)

Strain 10%

Strain 6%Strain 2%

Figure 6.4 Comparison of strains on size ratio 2.4:1.0 at strain rates (a) 0.25 Hz and

(b) 0.5 Hz, with ±SD as error bars

(a)

(b)

113

6.4.2.2 Effect of size ratio It was hypothesized that the larger void size and intensity of creation during shear motion

for a bed of binary size mixtures, result in larger normalized segregation rate when the other test

conditions were the same. This hypothesis was tested by using the binary size ratios 2.4:1.0,

2.0:1.0, and 1.7:1.0 at the three strains of 2%, 6%, and 10% and strain rate of 0.25 and 0.5 Hz.

The results for binary mixtures of potash were similar at two strain rates of 0.25 and 0.5 Hz. The

only difference between these two results was the magnitude. Herein, only results of the NSR at

0.5 Hz are discussed. The NSR results for binary size ratios 2.4:1.0, 2.0:1.0, and 1.7:1.0 when

coarse mean size was 3,675 µm at the three strains of 2%, 6%, and 10% and strain rate of 0.5 Hz

are presented in Figure 6.5. At strain of 2%, after 15 s, the NSRs were 3.00, 1.22, and 0.39

kg/kg-h for the size ratios 2.4:1.0, 2.0:1.0, and 1.7:1.0 when the coarse size was 3,675 µm,

respectively. At the end of 30 minutes, the NSRs were 0.19, 0.06, 0.02 kg/kg-h in the same order

(p<0.05) (Figure 6.5a). At strain of 6%, after 15 s, the NSRs were 7.34, 4.25, 1.17 kg/kg-h for

the size ratios 2.4:1.0, 2.0:1.0, and 1.7:1.0 when the coarse size was 3,675 µm, respectively. At

the end of 30 minutes, the NSRs were 1.59, 1.09, 0.12 kg/kg-h in the same order (p<0.05)

(Figure 6.5b). At strain of 10%, after 15 s, the NSRs were 9.57, 5.75, 1.42 kg/kg-h for the size

ratios 2.4:1.0, 2.0:1.0, and 1.7:1.0 when the coarse size was 3,675 µm, respectively. At the end of

30 minutes, the NSRs were 1.72, 1.40, 0.18 kg/kg-h in the same order (p<0.05) (Figure 6.5c).

At strain of 2%, the percent segregated fines decreased by 0.31, 0.10, and 0.10 times

when size ratios 2.4:1.0 vs. 2.0:1.0, 2.4:1.0 vs. 1.7:1.0, and 2.0:1.0 vs. 1.7:1.0 were compared. At

strain of 6%, the percent segregated fines decreased by 0.68, 0.08, and 0.11 times when size

ratios 2.4:1.0 vs. 2.0:1.0, 2.4:1.0 vs. 1.7:1.0, and 2.0:1.0 vs. 1.7:1.0 were compared. At strain of

10%, the percent segregated fines decreased by 0.81, 0.10, and 0.13 times when size ratios

2.4:1.0 vs. 2.0:1.0, 2.4:1.0 vs. 1.7:1.0, and 2.0:1.0 vs. 1.7:1.0 were compared. Similar results

were obtained for different size ratios when using coarse sizes 3,075 and 2,580 µm, i.e., percent

segregated fines were also significantly different (p<0.05).

114

0.0

2.0

4.0

6.0

8.0

10.0

0 5 10 15 20 25 30 35

Time (minutes)

NSR

(kg/

kg-h

)

Size ratio =2.4:1.0Size ratio = 2.0:1.0 Size ratio =1.7:1.0

0.0

2.0

4.0

6.0

8.0

10.0

0 5 10 15 20 25 30 35

Time (minutes)

NSR

(kg/

kg-h

)


Size ratio = 2.0:1.0Size ratio = 1.7:1.0

0.0

2.0

4.0

6.0

8.0

10.0

0 5 10 15 20 25 30 35

Time (minutes)

NSR

(kg/

kg-h

)



Figure 6.5 Comparison of NSR for three size ratios of potash when coarse size was

3,675 µm at strain rate of 0.5 Hz under strains of (a) 2%, (b) 6%, and (c) 10%, with ±SD as error bars

(a)

(b)

(c)

115

6.4.2.3 Comparison between angular and spherical-shaped material Figure 6.6 compares the NSR for urea and potash at the three strains 2%, 6%, and 10%

and strain rate of 0.5 Hz for the size ratio 2.0:1.0. At strain of 2%, after 15 s, the NSR was 1.22

and 3.52 kg/kg-h for the spherical and angular-shaped binary mixtures, respectively. At the end

of 30 minutes, the NSR was 0.17 and 0.06 kg/kg-h for spherical and angular-shaped binary

mixtures, respectively. At strain of 6% and strain rate of 0.5 Hz, after 15 s, the NSR was 8.38

and 4.25 kg/kg-h for spherical and angular binary mixtures, respectively. After 3 minutes, the

NSR values were very close to each other, i.e., 2.39 and 2.35 kg/kg-h. At the end of 30 minutes,

the NSR was 0.62 and 1.13 kg/kg-h for spherical and angular binary-shaped mixtures,

respectively. At strain of 10% and strain rate of 0.5 Hz, after 15 s, the NSR was 8.06 and 5.75

kg/kg-h for spherical and angular binary mixtures, respectively. After first minutes, the NSR

values were very close to each other, i.e., 4.18 and 4.38 kg/kg-h. At the end of 30 minutes, the

NSR was 0.69 and 1.40 kg/kg-h for spherical and angular binary mixtures, respectively. At strain

of 2%, the segregation of fines was governed by diffusive mechanism in contrast to segregation

of fines at higher strains 6% and 10% where convective mechanism was dominant. When

diffusive mechanism was dominant then density effect was not as important as with size and

shape of potash compared with convective mechanism. The percolation segregation in binary

mixtures of urea and potash can be explained by the same size but dissimilar shape attribute. In

this case, the more percent segregated fines is expected in the binary mixture of urea compared

with potash because of spherical vs. angular shape.

116

0.0

2.0

4.0

6.0

8.0

10.0

0 5 10 15 20 25 30 35

Time (minutes)

NSR

(kg/

kg-h

)

UreaPotash

0.0

2.0

4.0

6.0

8.0

10.0

0 5 10 15 20 25 30 35

Time (minutes)

NSR

(kg/

kg-h

)

Urea

Potash

0.0

2.0

4.0

6.0

8.0

10.0

0 5 10 15 20 25 30 35

Time (minutes)

NSR

(kg/

kg-h

)

Urea

Potash

Figure 6.6 Comparison of NSR for size ratio 2.0:1.0 of potash and urea when coarse size

was 3,675 µm at strain rate of 0.5 Hz under strains of (a) 2%, (b) 6%, and (c) 10%, with ±SD as error bars

(a)

(b)

(c)

117

6.5 Conclusions

The PSSC-II was capable of quantifying percolation segregation in the binary mixtures at

different strain and strain rates for two materials potash and urea, i.e., six size ratios of urea two

for each coarse size 3,675 µm, 3,075 µm, and 2,580 µm and nine size ratios of potash three for

each coarse size 3,675 µm, 3,075 µm, and 2,580 µm. The operating conditions for the binary size

tests were 85 mm bed depth, strains of 2%, 6% and 10% and strain rates of 0.25 and 0.5 Hz.

Based on the analysis of results, the following key conclusions were drawn:

1. For size ratio 2.4:1.0 at strain rate of 0.25 Hz , when the strain was increased by

three times from 2% to 6% the NSR was increased by 7.31 times. When the strain

was increased five times from 2% to 10%, the NSR increased by 11.86 times;

whereas, the NSR increased only by 1.61 times for the increase in strain from 6%

to 10%.

2. For size ratio 2.4:1.0 at strain rate of 0.5 Hz, when the strain increased by three

times from 2% to 6%, the NSR increased by 8.23 times. When the strain

increased five times from 2% to 10% the percent segregated fines was increased

by 8.90 times; whereas, the percent segregated fines mass increased only by 1.08

times when the strain was increased from 6% to 10%.

3. At strain of 2%, the percent segregated fines decreased by 0.31, 0.10, and 0.10

times when size ratios 2.4:1.0 vs. 2.0, 2.4:1.0 vs. 1.7:1.0, and 2.0:1.0 vs. 1.7:1.0

were compared. At strain of 6%, the percent segregated fines decreased by 0.68,

0.08, and 0.11 times when size ratios 2.4:1.0 vs. 2.0, 2.4:1.0 vs. 1.7:1.0, and

2.0:1.0 vs. 1.7:1.0 were compared. In addition at strain of 10%, the percent

segregated fines decreased by 0.81, 0.10, and 0.13 times when size ratios 2.4:1.0

vs. 2.0:1.0, 2.4:1.0 vs. 1.7:1.0, and 2.0:1.0 vs. 1.7:1.0 were compared.

4. At strain of 2%, the segregation of fines was governed by the diffusive

mechanism vs. higher strains 6% and 10% where the convective mechanism was

dominant.

6.6 Key Findings Size ratio was found to be the most dominant variable contributing towards segregation

of fines in binary size mixtures at two strain rates of 0.25 and 0.5 Hz and three strains of 2%, 6%,

118

and 10%. The relationships between the NSR and strain rates and strains for size ratios were not

linear. The percolation segregation of fines was less than 10% of material in the binary mixtures

(limit for blend to pass chemical analysis test -10% set by the AOAC standard) at strain of 2%

and strain rates of 0.25 and 0.5 Hz. Therefore, it is recommended to have minimum possible

head space available in the bag to mitigate segregation in association with possible minimum

size ratio.

6.7 References Bradley, M. S. A. and R. J. Farnish. 2005. Segregation of blended fertilizer during spreading: the

effect of differences in ballistic properties. In Proc 554. The International Fertilizer Society, York, UK. pp: 15.

Bridgwater, J. and N. D. Ingram. 1971. Rate of spontaneous inter-particle percolation. Transactions of the Institute of Chemical Engineers 49: 163-169.

Bridgwater, J. 1976. Fundamental powder mixing mechanism. Powder Technology 15: 215-236. Bridgwater, J. 1999. Segregation mechanisms in condensed granular flow: A summary of some

fundamental experiments. In A. D. Rosato, & D. L. Blackmore (Eds.), IUTAM symposium on segregation in granular flows, Cape May, NJ. Dordrecht: Kluwer Academic Publishers.


Cooke, M. H., D. J. Stephens, and J. Bridgwater. 1976. Powder mixing- a literature survey. Powder Technology 15: 1-20.

Cooke, M. H. and J. Bridgwater. 1979. Interparticle percolation: a statistical mechanical interpretation. Industrial and Engineering Chemistry Fundamentals 18: 25-27.


Duffy, S. P. and V. M. Puri. 2003. Development and validation of a constitutive model for size -segregation during percolation. KONA (Powder and Particle) 21: 151-162.

Foo, W. S. and J. Bridgwater. 1983. Particle migration. Powder Technology 36: 271-273. Jha, A. K., J. S. Gill, and V. M. Puri. 2007a. Percolation segregation in binary size mixtures of

spherical and angular-shaped particles of different densities. Particulate Science and Technology, An International Journal (In review).

Jha, A. K., H. Yi, and V. M. Puri. 2007b. Percolation segregation and flowability of urea under different relative humidities, KONA (Powder and Particle) (In review).

Rosato, A. D. and D. L. Blackmore. 2000. Preface. Eds: Rosato, A.D. and D.L. Blackmore. IUTAM Symposium on Segregation in Granular Flows 11-29. Norwell: Kluwer Academic Publishers.


Scott, A. M. and J. Bridgwater. 1975. Interparticle percolation: A fundamental solids mixing mechanism. Industrial and Engineering Chemistry Fundamentals 14: 22-27.

119

Scott, A. M. and J. Bridgwater. 1976. Self-diffusion of spherical particles in a simple shear apparatus. Powder Technology 14: 177-183.

Tang, P. and V. M. Puri. 2004. Methods for minimizing segregation, a review. Particulate Science and Technology, An International Journal 22: 321-338.

Tang, P. and V. M. Puri. 2005. An innovative device for quantification of percolation and sieving segregation patterns – Single component and multiple size fractions. Particulate Science and Technology, An International Journal 23: 335-350.


Vallance, J. W. and S. B. Savage.2000. Particle segregation in granular flows down chutes. Eds: Rosato, A.D. and D.L. Blackmore. IUTAM Symposium on Segregation in Granular Flows 31-51. Kluwer Academic Publishers. Norwell, USA.

120

7. CHAPTER - PERCOLATION SEGREGATION OF MULTI-SIZE AND MULTI-COMPONENT PARTICULATE MATERIALS

7.1 Abstract Percolation of fines in binary, ternary, and quaternary mixtures was quantified at two

strain rates of 0.25 and 0.5 Hz for both urea (spherical-shaped) and potash (angular-shaped).

Three coarse and three fines sizes for potash and three coarse and two fines sizes for urea were

used for preparation of multi-size mixtures. Binary mixture samples were prepared from three

mean coarse sizes with their corresponding three and two fines sizes for potash and urea,

respectively. Ternary mixture samples were prepared from two coarse sizes at a time from the

three available coarse size particles with their corresponding fines one each from three and two

fines sizes available for potash and urea, respectively. Quaternary mixture samples were

prepared from three coarse sizes with their corresponding two fines sizes (1,850 µm, and 1,550

µm) for potash and urea, respectively. Percolation segregation in binary, ternary, and quaternary

samples were quantified using the primary segregation shear cell (PSSC-II). Based on the results,

the percent segregated fines’ mass and the normalized segregation rate (NSR) of fines decreased

with the increase in number of coarse size components for a given fines size (from binary to

quaternary), where NSR is defined as the amount of fines percolated from initial fines present in

the binary mixture based on total time of PSSC-II operation (kg/kg-h). The NSR decreased with

the increase in order of mixtures, i.e., binary>ternary>quaternary at two strain rates of 0.25 Hz

and 0.5Hz (p<0.05). The NSR decreased with the decreasing size ratios in binary, ternary and

quaternary mixtures, for instance (2.4:1.0>2.0:1.0>1.7:1.0-binary),

(2.4:2.0:1.0>2.0:1.7:1.0>1.7:1.4:1.0-ternary), and (2.4:2.0:1.7:1.0>2.0:1.7:1.4:1.0-quaternary)

(p<0.05), respectively. The NSR for the binary, ternary, and quaternary mixtures increased with

increase in strain rate from 0.25 to 0.5 Hz. The NSR for potash vs. urea at strain rate of 0.5 Hz

for the size ratios 2.0:1.0, 2.0:1.7:1.0, and 2.0:1.7:1.4:1.0 in binary, ternary, and quaternary

mixtures was 1.13 vs. 0.49 kg/kg-h, 0.83 kg/kg-h vs. 0.21 kg/kg-h, 0.33 vs. 0.10 kg/kg-h,

respectively (p<0.05).

121

7.2 Introduction

Segregation by the percolation mechanism occurs in particulate materials during

conveying, storage, flow, and mixing. Percolation segregation depends on size, shape, density of

particulate constituents, intensity of movement, and relative humidity (Jha et al., 2007a and b,

and Jha and Puri, 2007). Particulate materials that are handled and processed in industries for

manufacturing products are always multi-component or polydispersed; however, research on

percolation segregation has been mainly confined to binary mixtures (Duffy and Puri, 2002;

Tang and Puri, 2005 and 2007; Jha et al., 2007a and b; and Jha and Puri, 2007). Also segregation

during filling or emptying of hoppers has been investigated for binary and multi-component

mixtures in two-dimensional situations (Shinohara et al., 1972; Hastie and Wypych, 1999;

Shinohara et al., 2001; Shinohara and Golman, 2002; and Gotoh et al., 1994) and a few studies

on three-dimensional involving a limited number of particles (Muzzio et al., 2002). Time-

dependent segregation study in two-dimensions and three-dimensions for limited number of

particles do not adequately represent industrial three-dimensional conditions. The available

knowledge is not sufficient to represent time-dependent processes involving multi-size and/or

multi-component particulate mixtures. Herein, two industrial materials potash and urea were

chosen to represent angular and spherical shapes, respectively, to study their percolation

response.

Based on the literature review, the aim of this research was to study time-dependent

percolation segregation in binary, ternary, and quaternary mixtures of particulates under two

strain rates 0.25 and 0.5 Hz. The present study overcomes the limitations of previous work and

paves the way for studying continuous mixtures involving well-mixed systems of real-world

materials; the procedure of conducting tests represents industrial operational conditions. The

specific objectives of this study were to determine the effect of: 1) multi-size ratio, 2) coarse and

fines sizes, and 3) shape and density in association with size on percolation segregation of urea

and potash at 0.25 and 0.5 Hz and 6% strain with bed depth of 85 mm. The significance of a

selection of strain of 6%, strain rates of 0.25 and 0.5 Hz, and bed depth of 85 mm is given in Jha

et al. (2007a).

122


Percolation segregation in binary mixtures has been studied to determine the effect of

mixing ratio, size ratio, density, shape, and intensity of movements to build a framework for

multi-size mixtures (Jha et al., 2007a, and Jha and Puri, 2007). In this chapter, nine binary, five

ternary, and two quaternary size ratios of potash, six binary, three ternary, and one quaternary

size ratios of urea at two strain rates of 0.25 and 0.5 Hz were studied. The segregation results for

multi-size mixtures were analyzed using the three segregation determining metrics, i.e., percent

segregated fines, segregation rate (SR) in kg/h, and normalized segregation rate (NSR) in kg/kg-

h of potash and urea, where SR is defined as the amount of fines percolated in unit time (kg/h).

In this study, the coarse and fines designation is based on the reference size of 2,360 µm,

i.e., particles having sizes larger than 2,360 µm are referred to as coarse and those below 2,360

µm as fines; this is discussed further in chapter 4. In all, three coarse size ranges (3,350-4,000,

2,800-3,350, and 2,360-2,800 µm) and three fines size ranges (2,000-2,360, 1,700-2,000, and

1,400-1,700 µm) were used to quantify segregation (Table 7.1). However, the size spread of urea

was smaller compared with potash, therefore, fines size in the range 1,400-1,700 µm were not

found in sufficient quantity, as a result, this fines size could not be included in the segregation

study of urea. Ternary and quaternary size mixtures for both urea and potash were prepared from

available coarse and fine size ranges. The size ratio of ternary and quaternary mixtures was

defined as the ratio of mean size of each coarse size ranges to mean size of fine particles. For the

ternary mixtures, two coarse sizes were mixed with one fines size, whereas for the quaternary

mixtures, three coarse sizes were mixed with one fines size (Table 7.2). For example, in ternary

mixtures, two coarse mean sizes (3,675 µm and 3,075 µm) mixed with fines (1,550 µm), resulted

in the size ratio 3,675 µm: 3,075 µm:1,550 µm that was rounded off to the nearest tenth of the

decimal, i.e., 2.4:2.0:1.0. Different mixing ratios (MR) were used for the different size ratios

based on the weight proportion of different size (Tables 7.1 and 7.2) distributions found in low

analysis fertilizer blend sample collected from several blend plants (such as low analysis 10-10-

10) in the Commonwealth of Pennsylvania.

Parameters for operating the PSSC-II, test conditions, and experimental design to study

percolation segregation in multi-size mixtures can be found in Jha et al. (2007a). All tests were

conducted in an environment-controlled laboratory with average temperature of 22°C ± 3°C and

relative humidity less than 40%.

123

Table 7.1 Experimental design for binary size mixtures for potash and urea (Jha and Puri, 2007)*

Material Strain rate (Hz)

Coarse size (µm)

Fines size (µm)

Size ratio Mixing ratio Number

1,550 2.4:1.0 50:50 1,850 2.0:1.0 37:63

Potash

0.25 0.50

3,675

2,180 1.7:1.0 37:63

9

1,550 2.0:1.0 63:37 1,850 1.7:1.0 50:50

Potash

0.25 0.50

3,075

2,180 1.4:1.0 50:50

9

1,550 1.7:1.0 63:37 1,850 1.4:1.0 63:37

Potash

0.25 0.50

2,580

2,180 1.2:1.0 63:37

9

1,850 2.0:1.0 37:63 Urea

0.25 0.50

3,675 2,180 1.7:1.0 37:63

6

1,850 1.7:1.0 50:50 Urea

0.25 0.50

3,075 2,180 1.4:1.0 50:50

6

1,850 1.4:1.0 63:37 Urea

0.25 0.50

2,580 2,180 1.2:1.0 63:37

6


*Strain of 6%

Table 7.2 Experimental design for ternary and quaternary size mixtures for potash and

urea* Material Strain rate

(Hz) Coarse size

(µm) Fines size

(µm) Size ratio Mixing ratio Number

1,550 2.4:2.0:1.0 28:44:28 1,850 2.0:1.7:1.0 22:39:39

Potash 0.25 0.50

3,675+3,075

2,180 1.7:1.4:1.0 22:39-39

6

1,550 2.0:1.7:1.0 33:46:21 Potash 0.25 0.50

3,075+2,580 1,850 1.7:1.4:1.0 29:42:29

4

1,550 2.4:2.0:1.7:1.0 17:28:38:17 Potash 0.25 0.50

3,675+3,075+ 2,580 1,850 2.0:1.7:1.4:1.0 13:25:37:25

4

1,850 2.0:1.7:1.0 22:39:39 Urea 0.25 0.50

3,675+3,075 2,180 1.7:1.4:1.0 22:39-39

4

Urea 0.25 3,075+2,580 1,850 1.7:1.4:1.0 29:42:29 2 Urea 0.25 3,675+3,075 1,850 2.0:1.7:1.4:1.0 13:25:37:25 2 Total (six replications) 22×6 = 132

*Strain of 6%

124


The segregation rate and normalized segregation rate had similar trends, so segregation rate

values are included only in tabular form. The percent segregated fines mass and normalized

segregation rate are further discussed under two subheadings, i.e., the effect of multi-size ratio

and comparison of materials. The results of the percent segregated fines and normalized

segregation rate are compared also at the two strain rates of 0.25 and 0.5 Hz.


As expected, the percent segregated fines mass in multi-size mixtures decreased with

increasing number of coarse size components, i.e., binary>ternary>quaternary. The percent

segregated fines mass values also increased with the increase in the strain rate from 0.25 Hz to

0.5 Hz (Tables 7.3 and 7.4).

125

Table 7.3 Segregation results for binary, ternary, and quaternary mixtures for potash* Coarse Mean Size

(µm) Size ratio Mixing ratio Strain rate

(Hz) Collected fines (g)

Percent fines (%)

Segregation rate (kg/h)

NSR (kg-kg/h)

0.25 234.80 (4.4) 48.9 0.47 (0.01) 0.98 (0.02) 2.4:1.0 50:50 0.50 367.90 (1.8) 76.6 0.74 (0.01) 1.54 (0.03) 0.25 197.70 (7.4) 31.9 0.40 (0.01) 0.64 (0.64) 2.0:1.0 37:63 0.50 280.20 (6.0) 45.2 0.56 (0.01) 0.90 (0.02) 0.25 35.40 (3.4) 5.8 0.07 (0.01) 0.12 (0.01)

3675 1.7:1.0 37:63

0.50 34.40 (1.1) 5.7 0.07 (0.00) 0.11 (0.00) 0.25 139.40(1.6) 37.7 0.28 (0.02) 0.75 (0.06) 2.0:1.0 63:37 0.50 215.90 (4.7) 58.4 0.43 (0.01) 1.17 (0.03) 0.25 119.30 (6.4) 24.9 0.24 (0.01) 0.50 (0.03) 1.7:1.0 50:50 0.50 217.50 (1.7) 45.3 0.44 (0.01) 0.92 (0.02) 0.25 28.80 (1.0) 6.0 0.06 (0.00) 0.12 (0.00)

3075 1.4:1.0 50:50

0.50 38.90 (0.8) 8.1 0.08 (0.00) 0.16 (0.00) 0.25 55.70 (1.0) 18.6 0.14 (0.00) 0.36 (0.01) 1.7:1.0 63:37 0.50 68.20 (1.4) 22.7 0.12 (0.01) 0.40 (0.04) 0.25 40.90 (0.5) 10.7 0.08 (0.00) 0.21 (0.00) 1.4:1.0 63:37 0.50 44.50 (1.8) 11.6 0.09 (0.00) 0.23 (0.01) 0.25 12.90 (1.7) 3.4 0.03 (0.00) 0.07 (0.01)

2580 1.2:1.0 63:37

0.50 12.80 (0.8) 3.4 0.03 (0.00) 0.07 (0.00) 0.25 122.80 (7.2) 45.9 0.25 (0.01) 0.92 (0.05) 2.4:2.0:1.0 28:44:28 0.50 169.90 (3.8) 63.6 0.33 (0.01) 2.00 (0.05) 0.25 110.80 (2.1) 29.9 0.22 (0.00) 0.60 (0.01) 2.0:1.7:1.0 22:39:39 0.50 154.70 (5.7) 41.7 0.31 (0.01) 0.83 (0.03) 0.25 30.20 (7.1) 8.1 0.06 (0.01) 0.16 (0.04)

3675+3075

1.7:1.4:1.0 22:39-39 0.50 40.10 (4.3) 10.8 0.08(0.01) 0.21 (0.02) 0.25 41.50 (3.9) 20.7 0.08 (0.01) 0.42 (0.04) 2.0:1.7:1.0 33:46:21 0.50 56.80 (3.3) 28.4 0.11 (0.01) 0.57 (0.03) 0.25 32.90 (2.1) 12.0 0.07 (0.00) 0.24 (0.02)

3075+2580

1.7:1.4:1.0 29:42:29 0.50 36.70 (1.5) 13.4 0.08 (0.00) 0.27 (0.00) 0.25 37.30 (1.4) 22.4 0.07 (0.00) 0.45 (0.02) 2.4:2.0:1.7:1.0 17:28:38:17 0.50 53.10 (4.3) 31.9 0.106 (0.0) 0.62 (0.06) 0.25 34.50 (1.7) 14.2 0.07 (0.00) 0.27 (0.01)

3675+3075+2580

2.0:1.7:1.4:1.0 13:25:37:25 0.50 41.70 (0.8) 17.2 0.08 (0.01) 0.34 (0.01)

* standard deviation in parenthesis

126

Table 7.4 Segregation results for binary, ternary, and quaternary mixtures for urea* Coarse mean size

(µm) Size ratio Mixing ratio Strain

rate (Hz)Collected fines (g)

Percent fines (%)

Segregation rate (kg/h)

NSR (kg/kg-h)

0.25 81.60 (1.8) 18.1 0.16 (0.00) 0.36 (0.01) 2.0:1.0 37:63 0.50 140.30 (4.0) 31.0 0.28 (0.01) 0.62 (0.02) 0.25 31.18 (1.7) 7.1 0.06 (0.00) 0.14 (0.01)

3,675 1.7:1.0 37:63

0.50 27.30 (2.8) 6.2 0.05 (0.01) 0.12 (0.01) 0.25 27.49 (1.3) 7.8 0.05 (0.00) 0.16 (0.01) 1.7:1.0 50:50 0.50 41.20 (3.7) 11.8 0.08 (0.01) 0.24 (0.02) 0.25 21.90 (2.3) 6.3 0.04 (0.00) 0.13 (0.01)

3,075 1.4:1.0 50:50

0.50 19.76 (5.8) 5.6 0.04 (0.01) 0.11 (0.03) 0.25 9.80 (1.0) 3.5 0.02 (0.00) 0.07 (0.01) 1.4:1.0 63:37 0.50 12.26 (0.7) 4.4 0.02 (0.00) 0.09 (0.01) 0.25 9.91 (0.5) 3.5 0.02 (0.00) 0.07 (0.00)

2,580 1.2:1.0 63:37 0.50 7.02 (0.4) 2.0 0.01 (0.00) 0.05 (0.00) 0.25 24.82 (3.8) 9.2 0.05 (0.01) 0.18 (0.03) 2.0:1.7:1.0

22:39:39

0.50 28.15 (2.8) 10.4 0.06 (0.01) 0.21 (0.02) 0.25 17.85 (2.6) 6.6 0.04 (0.01) 0.13 (0.02)

3,675+3,075

1.7:1.4:1.0 22:39:39 0.50 19.53 (3.2) 7.2 0.04 (0.01) 0.14 (0.02) 0.25 8.81 (1.1) 4.4 0.02 (0.00) 0.09 (0.01) 3,075+2,580 1.7:1.4:1.0 29:42:29 0.50 7.92 (2.1) 3.9 0.00 (0.00) 0.08 (0.02) 0.25 7.48 (0.8) 4.2 0.01 (0.00) 0.08 (0.01) 3,675+3,075+2,580 2.0:1.7:1.4:1.0 13:25:37:25 0.50 8.61 (0.8) 4.9 0.01 (0.00) 0.10 (0.01)

*standard deviation in parenthesis

128

7.4.1.1 Effect of multi-size ratio Figures 7.1 and 7.2 compare the percent segregated fines at strain rates of 0.5 and 0.25

Hz, respectively, for the binary size ratios 2.4:1.0, 2.0:1.0, and 1.7:1.0, ternary size ratios

2.4:2.0:1.0, 2.0:1.7:1.0, and 1.7:1.4:1.0 and quaternary size ratio 2.0:1.7:1.4:1.0 when the coarse

sizes used were 3,675 µm, and 3,675, 3,075 µm, and 3,675, 3,075, 2,580 µm, respectively. All

multi-size mixture tests were run for 30 minutes. Of the total time of 30 minutes, for the first 10

minutes fines were collected at 30 s interval, thereafter at 120 s interval until completion of the

test. In the binary mixtures, the percent segregated fines mass decreased with the deceasing size

ratio 2.4:1.0>2.0:1.0>1.7:1.0. In the ternary and quaternary size mixtures, the percent segregated

fines mass decreased with the increase in the size of fines 1,550 µm>1,850 µm>2,180 µm for the

same coarse size combinations. The percent segregated fines mass decreased with the increase in

the number of size components of coarse particles, i.e., from binary to quaternary at strain rates

of 0.25 and 0.5 Hz.

After 15 s, for the ternary mixtures at the strain rate of 0.5 Hz, the percent segregated

fines mass values were 2.7%, 1.8%, and 0.5% for the size ratios 2.4:2.0:1.0, 2.0:1.7:1.0, and

1.7:1.4:1.0, respectively; whereas, at the end of the data collection, i.e., 30 minutes, the percent

segregated fines mass values were 63.6%, 41.7%, and 10.8% in the same order (p<0.05) (Figure

7.1b). At the end of 30 minutes, substantial increases in the percent segregated fines were

recorded when compared with 15 s. The increase in the higher fines mass recorded for the higher

size ratios 2.4:2.0:1.0, 2.0:1.7:1.0 compared with smaller size ratio 1.7:1.4:1.0 was due to the

dynamic void spaces created in the ternary size that was not sufficient for large fines size 2,180

µm to percolate through void spaces at strain of 6% of the shear box. At strain rate of 0.25 Hz,

after 15 s, the percent segregated fines mass values were 2.3%, 1.3%, and 0.3% for the size ratios

2.4:2.0:1.0, 2.0:1.7:1.0, and 1.7:1.4:1.0, respectively. At the end of 30 minutes, the percent

segregated fines mass values were 45.9%, 29.9%, and 8.1% (p<0.05) in the same order (Figure

7.2b). At the end of 30 minutes, the difference between the percent segregated fines values at

strain rates of 0.25 and 0.5 Hz were 17.7%, 11.8%, and 2.5%, respectively. The difference in the

mass values was observed due to the intensity of void space created in the coarse particles bed.

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Figure 7.1 Comparison of percent segregated fines for multi-size ratios for potash at strain

rate of 0.5 Hz in (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars

(b)

(c)

(a)

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Size ratio = 2.0:1.7:1.4:1.0

Figure 7.2 Comparison of percent segregated fines for multi-size ratios for potash at strain rate of 0.25 Hz in (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error

bars

(c)

(b)

(a)

131

The percent segregated fines mass values decreased with the decreasing size ratios from

2.4:2.0:1.0>2.0:1.7:1.0>1.7:1.4:1.0.

At strain rate of 0.5 Hz, after 15 s, the percent segregated fines mass values were 3.0%

and 1.2% for the quaternary size ratios 2.4:2.0:1.7:1.0 and 2.0:1.7:1.4:1.0, respectively. At the

end of 30 minutes, the percent segregated fines mass values were 31.9% and 17.2% in the same

order (p<0.05) (Figure 7.1c). At strain rate of 0.25Hz, after 15 s, the percent segregated fines

mass values were 2.0% and 1.1% for the quaternary size ratios 2.4:2.0:1.7:1.0 and

2.0:1.7:1.4:1.0, respectively. At the end of 30 minutes, the percent segregated fines mass values

were 22.4% and 14.2% in the same order (p<0.05) (Figure 7.2c). At the end of the 30 minutes,

the differences in the percent segregated fines values collected at the strain rates of 0.25 and 0.5

Hz were 9.5% and 3.0% for the quaternary size ratios 2.4:2.0:1.7:1.0 and 2.0:1.7:1.4:1.0,

respectively.

At strain rate of 0.5 Hz, the percent segregated fines decreased by 13.0% when one more

coarse size 3,675 µm was added to binary mixture comprising smaller size 3,075 µm to make

ternary mixtures. Thereafter one more coarse size 2,580 µm was added to formulate quaternary

mixtures. The percent segregated fines decreased by: (1) 13.0% and 44.7% in ternary and

quaternary compared with binary mixture starting from size ratio 2.4:1.0; (2) 31.7% in the

quaternary mixture compared with ternary size ratio of 2.4:2.0:1.0; (3) 3.5% and 28.0% in the

ternary and quaternary mixtures compared with binary mixture 2.0:1.0, respectively. At strain

rate of 0.25 Hz, the percent segregated fines decreased by: (1) 31.7% in the quaternary mixture

compared with ternary size ratio of 2.4:2.0:1.0; (2) 11.2% and 17.7% in the ternary and

quaternary mixtures compared with binary mixture 2.0:1.0, respectively.

The fines mass in the binary, ternary, quaternary mixtures was in different proportions for

urea and potash (Tables 7.1 and 7.2). For discussion, the binary size (2.4:1.0), ternary

(2.4:2.0:1.0), and quaternary (2.4:2.0:1.7:1.0) mixtures of potash were compared when the same

fines mean size 1,550 µm was used. At strain rate of 0.5 Hz, the percent segregated fines mass

for three proportions of fines mass 33.0%, 50.0%, and 67.0% was compared for binary size ratio

of 2.0:1.0 of potash. It was found that the percent segregated fines mass was the highest and the

lowest for binary mixtures that contained fines proportions of 33.0% and 67.0%. The percent

segregated fines mass that contained the fines proportion of 50.0% was found in-between 33.0

and 67.0% (Jha et al., 2007a). For the binary, ternary, and quaternary mixtures contained fines

132

mass in the proportions of 50.0%, 28.0%, and 17.0%, respectively, the percent segregated fines

mass was 76.6%, 63.6%, and 31.9%, respectively. Based on the above results, the percent

segregated fines mass would have been the highest and the lowest for the binary mixtures

containing fines mass in the proportion of 17.0% and 50.0%. However, the percent segregated

fines mass was 76.6%, 63.6%, and 31.9% of their respective fines mass in the binary, ternary,

and quaternary mixtures, respectively. The decrease in the percent segregated fines mass was

measured because ternary and quaternary mixtures percolation segregation mechanism was

dominated by smaller size coarse particles compared with binary mixtures.

7.4.1.2 Material comparison Figure 7.3 compares the percent segregated fines of urea (spherical-shaped particles) and

potash (angular-shaped particles) at strain rates of 0.25 and 0.5 Hz for binary, ternary, and

quaternary size ratios 2.0:1.0, 2.0:1.7:1.0, and 2.0:1.7:1.4:1.0, respectively, when coarse sizes

used were 3,675 µm, 3,675 and 3,075 µm, and 3,675, 3,075 and 2,580 µm. At strain rates of 0.25

and 0.5 Hz, in the first few minutes, the percent segregated fines mass for binary, ternary,

quaternary mixtures prepared were higher for spherical-shaped urea vs. angular-shaped potash;

however, after initial few minutes, the percent segregated fines mass increased very rapidly for

angular-shaped potash compared with spherical-shaped urea. More fines were expected in the

case of potash because of the angular-shaped particles (porosity of 51%, i.e., larger void spaces)

and higher particle density (2,291 kg/m3 vs. 1,459 kg/m3) compared with the spherical shape

urea particles (porosity of 44%, i.e., smaller void spaces).

At strain rate 0.25 Hz for ternary mixtures, in the first minute (<1 minute), the percent

segregated fines for the same size ratio for urea and potash were 2.9% and 2.9%, respectively,

however, at the end of the test, 30 minutes, the percent segregated fines increased very rapidly

for potash (29.9%) compared with urea (9.2%) (p<0.05). At strain rate 0.5 Hz, in the first minute

(1 minute), the percent segregated fines for urea and potash were 3.6% and 3.7%, respectively,

however, at the end of the test, 30 minutes, the percent segregated fines increased very rapidly

for potash (41.7%) compared with urea (10.4%) (p<0.05) (Figure 7.3b).

Initially, the higher percent segregated fines for urea compared with potash was observed

for all binary, ternary, and quaternary size ratios. This was attributed to size, which was the only

dominant variable but after few minutes the size effect was combined with shape and density

effect. At strain rate of 0.5 Hz, the percent segregation rate decreased by 23.3% and 52.2% for

133

binary mixtures when compared with ternary mixtures for potash and urea, respectively, from

ternary to quaternary, the percent segregated fines decreased by 58.5% and 58.9% for potash and

urea, respectively, whereas for binary mixtures when compared with quaternary mixtures the

percent segregated fines decreased by 70.7% and 80.4% for potash and urea, respectively

(Figures 7.3a, 7.3b, and 7.3c). At strain rate of 0.25 Hz, the percent segregation rate decreased by

8.8% and 45.9% when compared with binary mixtures for ternary mixtures of potash and urea,

respectively, for quaternary mixtures when compared with from ternary to quaternary, the

percent segregated fines decreased by 53.8% and 62.2% for potash and urea, respectively,

whereas when binary mixtures compared with quaternary mixtures the percent segregated fines

decreased by 57.8% and 79.6% for potash and urea, respectively (Figures 7.3a, 7.3b, and 7.3c).

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Figure 7.3 Comparison of percent segregated fines between angular (potash) and spherical

(urea) at strain rates 0.5 Hz and 0.25 Hz for (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars

(c)

(b)

(a)

135


Since the SR and NSR results are similar for binary, ternary, and quaternary mixtures at

strain rates of 0.25, and 0.5 Hz, only the NSR results are discussed.

7.4.2.1 Strain rate effect on size ratio It was hypothesized that increase in the number of coarse size components for a given

fines size results in decrease in normalized segregation rate when the other test conditions were

the same. The hypothesis was tested by using the binary, ternary, and quaternary mixtures at

strain rates of 0.25 and 0.5 Hz (Figures 7.4 and 7.5).

At strain rate of 0.5 Hz and 15 s for ternary mixtures, the NSR was 6.54, 4.43, and 1.23

kg/kg-h for the ternary size ratio 2.4:2.0:1.0, 2.0:1.7:1.0, and 1.7:1.4:1.0 with fines 1,550 µm,

1,850 µm and 2,180 µm, respectively. At the end of 30 minutes, NSR was measured to be 2.00,

0.83, and 0.21 kg/kg-h in the same order (p<0.05) (Figure 7.4b). At strain rate of 0.25 Hz, 15 s,

the NSR was 5.47, 3.12, and 0.80 kg/kg-h for the ternary size ratio 2.4:2.0:1.0, 2.0:1.7:1.0, and

1.7:1.4:1.0 with fines 1,550 µm, 1,850 µm and 2,180 µm, respectively. At the end of 30 minutes,

the NSR was found to be 0.92, 0.60, 0.16 kg/kg-h in the same order (p<0.05) (Figure 7.5b).

At strain rate of 0.5 Hz, the NSR decreased by 13.0% when in binary size mixtures was

added (coarse size 3,675 µm) one more coarse size 3,075 µm to formulate ternary mixtures.

Thereafter one more coarse size 2,580 µm was added to formulate quaternary mixtures. The

NSR decreased by: (1) 13.0% and 44.7% for the ternary and quaternary mixtures when compared

with binary mixture starting from size ratio 2.4:1.0; (2) 31.7% in the quaternary mixture

compared with ternary size ratio of 2.4:2.0:1.0; (3) 3.5% and 28.0% for the ternary and

quaternary mixtures compared with binary mixture 2.0:1.0, respectively. At strain rate of 0.25

Hz, the NSR decreased by: (1) 31.7% for the quaternary mixture compared with ternary size

ratio of 2.4:2.0:1.0; (2) 11.2% and 17.7% for the ternary and quaternary mixtures when

compared with binary mixture 2.0:1.0, respectively.

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Size ratio 2.0:1.7:1.4:1.0

Size ratio 2.4:2.0:1.7:1.0

Figure 7.4 Comparison of NSR between size ratios at strain rate 0.5 Hz for (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars

(a)

(c)

(b)

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Figure 7.5 Comparison of NSR between size ratios at strain rate 0.25 Hz for (a) binary, (b)

ternary, and (c) quaternary mixtures, with ±SD as error bars

(c)

(b)

(a)

138

7.4.2.2 Comparison between angular and spherical-shaped materials Figure 7.6 compares the NSR for urea and potash at two strain rates of 0.25 and 0.5 Hz

for binary, ternary, and quaternary mixtures. For multi-size mixtures, in the first few minutes, the

NSR was higher for urea vs. potash, however, thereafter, the NSR of urea decreased very rapidly

compared with potash.

At strain rate of 0.25 Hz, after 15 s, for ternary mixtures the NSR was 3.12 and 4.38

kg/kg-h for potash and urea, respectively. At 60 s, the NSR values were almost the same i.e.,

1.74 and 1.73 kg/kg-h for potash and urea, respectively. After 60 s, the NSR for potash decreased

rapidly compared with urea. At the end of the test, 30 minutes, the NSR values were 0.60 and

0.18 kg/kg-h for potash and urea (p<0.05). After 15 s, at strain rate 0.5 Hz, the NSR was 4.43

and 4.95 kg/kg-h for potash and urea, respectively. At 45 s, the NSR values were almost the

same i.e., 2.16 and 2.37 kg/kg-h for potash and urea, respectively. After 60 s, the NSR for urea

decreased rapidly compared with potash. At the end of the test, at 30 minutes, the NSR values

were 0.83 and 0.21 kg/kg-h for potash and urea (p<0.05) (Figure 7.6b).

At strain rate of 0.25 Hz, for potash, the NSR increased initially by 3.3% from binary to

ternary mixtures but decreased by 22.1% and 19.6% from ternary to quaternary and binary to

quaternary, respectively (Figure 7.6). At the end of end 30 minutes, the NSR decreased by

13.4%, 53.4%, 59.7% for ternary vs. binary, quaternary vs. ternary, and quaternary vs. binary

mixtures, respectively. For urea, initially the NSR decreased only by 26.3%, 26.1%, and 45.5%

for binary vs. ternary, ternary vs. quaternary, and binary vs. quaternary compared, respectively;

at the end of 30 minutes, those values were 44.4%, 65.7%, and 80.6%, respectively.

At strain rate of 0.5 Hz, for potash, the NSR increased initially by 4.2% from binary to

ternary mixtures but decreased by 33.4% and 30.6% from ternary to quaternary and binary to

quaternary, respectively (Figure 7.6). At the end of end 30 minutes, the NSR decreased by

29.2%, 58.8%, 70.8% for ternary compared with binary, quaternary compared with ternary, and

quaternary compared with binary. For urea, initially the NSR decreased by 40.9%, 33.7%, and

60.9% for binary vs. ternary, ternary vs. quaternary, and binary vs. quaternary compared,

respectively. At the end of 30 minutes, the NSR decreased by 53.1%, 56.5%, and 79.6% for

binary vs. ternary, ternary vs. quaternary, and binary vs. quaternary compared, respectively.

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Figure 7.6 Comparison of NSR between potash and urea at strain rates 0.25 Hz and 0.5 Hz

for (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars

(c)

(b)

(a)

140

7.4.3 Binary, ternary, quaternary, and continuous mixtures It was hypothesized that multi-size mixtures could be used as a representative of

continuous mixtures for studying percolation segregation. Number of coarse and fines needed to

study the percolation segregation in continuous mixtures using multi-size mixtures depend on

mechanical conditions under which mixtures are being handled. This hypothesis was tested using

binary, ternary, quaternary, and continuous mixtures at strain of 6% and strain rate of 0.5 Hz.

The proportion of coarse and fines used to formulate binary, ternary, and quaternary mixtures

was the same as the proportion of coarse and fines sizes used in formulation of 10-10-10 blend.

Figure 7.7 compares the percent segregated fines in binary, ternary, quaternary, and continuous

mixtures. The percent segregated fines in binary size ratio 2.4:1.0 was the highest followed by

ternary, and quaternary size ratios. With the increasing number of intermediate coarse size

component from binary to quaternary mixtures decreases the effective void space in the mixture

resulting in small void space available for fines to percolate. The percent segregated fines of

continuous mixtures (10-10-10) was found to be in-between ternary and quaternary mixtures.

Results could be explained based on the proportion of coarse and fines and void spaces created at

strain of 6% and strain rate of 0.5 Hz. There were three coarse mean sizes: 3,675 µm; 3,075 µm;

and 2,580 µm and four fines mean sizes: 1,290 µm; 1,550 µm; 1,850 µm; and 2,180 µm used for

formulation of continuous mixtures 10-10-10. These coarse and fines sizes were added in the

same proportion as it was found in the size analysis of formulation 10-10-10 collected from

blend plants in the Commonwealth of Pennsylvania.

Figure 7.7 Comparison of NSR among binary, ternary, quaternary, and continuous

mixtures (10-10-10), with ±SD as error bars

0.0

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40.0

60.0

80.0

100.0

0 5 10 15 20 25 30 35

Time (minutes)

Perc

ent s

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d fin

es (%

)

Binary-2.4:1.0

Quaternary-2.4:2.0:1.7:1.0

Ternary-2.4:2.0:1.0

10-10-10

141

7.5 Conclusions

The PSSC-II was capable of quantifying segregation of fines in binary, ternary and

quaternary of both urea and potash, as well as continuous mixtures. The binary, ternary, and

quaternary mixtures were prepared using three different coarse sizes 3,675 µm, 3,075 µm, and

2,580 µm and three different fines 1,550 µm, 1,850 µm, and 2,180 µm. The operating conditions

for the tests were 85 mm bed depth, 6% strain and two strain rates 0.25 Hz and 0.5 Hz.

The following key conclusions were drawn based on binary, ternary, and quaternary size

mixtures results:

1. At strain rate of 0.5 Hz, the percent segregated fines decreased by 13.0%, 31.7%,

44.7% for binary vs. ternary, ternary vs. quaternary, and binary vs. quaternary for

potash. At the strain rate of 0.25 Hz, the percent segregated fines decreased by 11.2%,

31.7%, and 52.8% for binary vs. ternary, ternary vs. quaternary, and binary vs.

quaternary were compared for potash.

2. At strain rate of 0.5 Hz, for potash, at the end of end 30 minutes, the NSR decreased

by 29.2%, 58.8%, 70.8% for binary vs. ternary, ternary vs. quaternary, and binary vs.

quaternary mixtures were compared, respectively. For urea, at the end of 30 minutes,

the NSR decreased by 53.1%, 56.5%, and 79.6% for binary vs. ternary, ternary vs.

quaternary, and binary vs. quaternary were compared, respectively. At strain rate of

0.25 Hz for potash, at the end of end 30 minutes, the NSR decreased by 13.4%,

53.4%, 59.7% for binary vs. ternary, ternary vs. quaternary, and binary vs. quaternary

were compared, respectively. For urea, at the end of 30 minutes, the NSR decreased

by 44.4%, 65.7%, and 80.6% for binary vs. ternary, ternary vs. quaternary, and binary

vs. quaternary were compared, respectively.

3. At strain of 0.5 Hz, the percent segregated fines of continuous mixtures was found to

be in-between ternary and quaternary mixtures.

7.6 Key Findings

The binary, ternary, and quaternary mixtures of urea and potash were tested to determine

the percolation segregation of fines and compared with the segregation potential of fines of

continuous mixtures. The results showed that higher order mixtures were able to represent

percolation of fines in continuous mixtures. The number of coarse sizes needed to represent

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continuous mixtures is dependent on the conditions under which materials are handled. For

example, percolation of fines in continuous mixtures (10-10-10) at strain of 6% and strain rate of

0.5 Hz was predicted by percolation of fines in ternary and quaternary mixtures of potash. The

number of components of higher order mixtures needed to represent continuous mixtures is also

dependent on the material parameters (such as urea and potash).

7.7 References Duffy, S. P. and V. M. Puri. 2002. Primary segregation shear cell for size-segregation analysis of

binary mixtures. KONA (Powder and Particle) 20: 196-207. Gotoh, K., T. Maki, and H. Masuda. 1994. The size segregationof polydispersed particles during

feeding into a vessel. Journal of the Society of Powder Technology, Japan 31: 842– 849. Hastie, D. B. and P. W. Wypych. 1999. Experimental investigation into segregation of bulk

solids during gravity filling of storage bins, in: Proceedings of Reliable Flow of Particulate Solids III, Porsgrunn, pp. 507–518.

Jha, A. K., J. S. Gill, and V. M. Puri. 2007a. Percolation segregation in binary size mixtures of spherical and angular-shaped particles of different densities. Particulate Science and Technology, An International Journal (In review).

Jha, A. K., H. Yi, and V. M. Puri. 2007b. Percolation segregation and flowability of urea under different relative humidities. KONA (Powder and Particle) (In review).

Jha, A. K. and V. M. Puri. 2007. Percolation segregation of binary mixtures under periodic movement. Powder Technology (In review).

Muzzio, F. J., O. S. Sudah, P. E. Arratia, and D. Coffin-Beach. 2002. Mixing of cohesive pharmaceutical formulations in tote (bin) blenders. Drug Development and Industrial Pharmacy 28(8): 1– 7

Shinohara, K., K. Shoji, and T. Tanaka. 1972. Mechanism of size segregation of particles in filling a hopper. Industrial and Engineering Chemistry Process Design and Development 11: 369–376.

Shinohara, K., B. Golman, and T. Nakata. 2001. Size segregation of multicomponent particles during the filling of a hopper. Advanced Powder Technology 12: 33–43.

Shinohara, K. and B. Golman. 2002. Segregation indices of multi-sized particle mixtures during the filling of a two-dimensional hopper. Advanced Powder Technology 13(1): 93–107.


Tang, P. and V. M. Puri. 2007. Segregation quantification of two component particulate mixtures – Effect of particle size, density, shape, and surface texture. Particulate Science and Technology, An International Journal 25(6): 571-588.

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8. CHAPTER - PERCOLATION SEGREGATION OF MULTI-SIZE AND MULTI-COMPONENT PARTICULATE MATERIALS:

UREA AND POTASH AT MULTIPLE STRAIN AND STRAIN RATES

8.1 Abstract Percolation of fines in binary, ternary, and quaternary mixtures was quantified under

different motion conditions using primary segregation shear cell (PSSC-II). Three strains of 2%,

6%, and 10% and two strain rates of 0.25 and 0.5 Hz were used for urea (spherical-shaped) and

potash (angular-shaped). For preparing multi-size mixtures, three coarse and three fines for

potash and three coarse and two fines for urea were used. Ternary samples prepared from two

coarse mean sizes mixed with a fines mean size out of three available fines for potash and two

for urea. Quaternary samples were prepared by mixing three coarse mean sizes with a fines mean

size. Based on the results of binary, ternary, and quaternary mixtures, the percent segregated

fines’ mass and the normalized segregation rate (NSR) of fines decreased with the increasing

number of coarse size components for a given fines size, where NSR is defined as the amount of

fines percolated from initial fines present in the mixtures based on total time of PSSC-II

operation. The NSR decreased with the increasing order of mixtures, i.e.,

binary>ternary>quaternary at two strain rates of 0.25 Hz and 0.5Hz (p<0.05). The NSR increased

with the increase in strain from 2% to 10%. The NSR decreased with decreasing size ratios in

binary, ternary, and quaternary mixtures, for instance (2.4:1.0>2.0:1.0>1.7:1.0-binary),

(2.4:2.0:1.0>2.0:1.7:1.0>1.7:1.4:1.0-ternary), (2.4:2.0:1.7:1.0>2.0:1.7:1.4:1.0-quaternary)

(p<0.05). The NSR for potash vs. urea at strain rate of 0.5 Hz for the size ratios 2.0:1.0,

2.0:1.7:1.0, and 2.0:1.7:1.4:1.0 in binary, ternary, and quaternary mixtures was 1.13 vs. 0.49

kg/kg-h, 0.83 kg/kg-h vs. 0.21 kg/kg-h, 0.33 vs. 0.10 kg/kg-h, respectively (p<0.05).

8.1 Introduction

Particulate materials are handled, stored, processed, and manufactured in various

industries including agriculture, ceramic, cosmetic, electronic, food, and pharmaceutical.

However, particulates are blended to manufacture products but they segregate when subjected to

different motion conditions due to differences in physical and mechanical properties. The

144

parameters responsible for segregation in particulate materials include size and size distribution,

shape, density, surface texture, intensity of movement, displacement, relative humidity

(Rosato et al., 2002; Jha et al., 2007a and b; Jha and Puri, 2007a and b). Percolation is one of the

thirteen mechanisms of segregation identified by researchers (Mosby et al., 1996; Salter, 1998;

and de Silva et al., 2000). Study on percolation segregation is mainly confined to binary mixtures

or limited number of cases for multi-size mixtures (Duffy and Puri, 2002; Tang and Puri, 2005

and 2007; and Jha and Puri, 2007b). Limited understanding has been achieved to illustrate the

segregation in polydispersed material which is common in the industries for manufacturing of

products. Segregation has also been studied for binary and multi-component mixtures during

filling or emptying of hoppers (Shinohara et al., 1972; Hastie and Wypych, 1999; Shinohara et

al., 2001; Shinohara and Golman, 2002; and Gotoh et al., 1994). Time-dependent study of multi-

component mixtures for limited number of cases have been done but not sufficient to represent

industrial conditions where materials are subjected to a variety of motion conditions (Jha and

Puri, 2007a and b).

Based on the literature review, the aim of this research was to study time-dependent

percolation segregation in binary, ternary, and quaternary mixtures of particulates at three strains

of 2%, 6%, and 10% and two strain rates of 0.25 and 0.5 Hz. Herein, potash and urea were taken

as representative of real-world materials based on their angular and spherical shapes. The particle

density was higher for potash compared with urea (Jha et al., 2007a). These two materials were

studied to see the effects of size in combination with shape and density. Nine binary, five

ternary, and two quaternary size ratios of potash and six binary, three ternary, and one quaternary

size ratios of urea were tested. The significance of selection of the operating conditions such as

bed depth, strain, and strain rate can found in Jha et al. (2007a). The specific objectives of this

study were to determine the effect of strain and strain rate on: 1) size ratio, and 2) materials (urea

and potash) on percolation segregation of well mixed samples.

8.2 Materials and Methods Percolation segregation in the binary, ternary, and quaternary size mixtures was studied

to build a frame work to predict segregation in continuous mixtures. The segregation results for

multi-size mixtures were analyzed using three segregation determining metrics, i.e., percent

145

segregated fines, segregation rate (SR), and normalized segregation rate (NSR) of potash and

urea.

In this study, the coarse and fines designation is based on the reference size of 2,360 µm,

i.e., particles having sizes larger than 2,360 µm are referred to as coarse and those below 2,360

µm as fines. In all three coarse size ranges (3,350-4,000, 2,800-3,350, and 2,360-2,800 µm) and

three fines size ranges (2,000-2,360, 1,700-2,000, and 1,400-1,700 µm) were used to quantify

segregation (Table 8.1). However, the size spread of urea was smaller compared with potash,

therefore, fines size in the range 1,400-1,700 µm were not found in sufficient quantity, as a

result, this fines size was not included in the segregation study of urea. Ternary and quaternary

size mixtures for both urea and potash were prepared from available coarse and fine size ranges.

The size ratio of ternary and quaternary mixtures was defined as the ratio of mean size of each

coarse size to mean size of fine particles. For the ternary mixtures, two coarse sizes were mixed

with one fines size, whereas for the quaternary mixtures, three coarse sizes were mixed with one

fines size. For example, in ternary mixtures, two coarse mean sizes (3,675 µm and 3,075 µm)

mixed with fines (1,550 µm), resulted in the size ratio 3,675 µm:3,075 µm:1,550 µm that was

rounded off to the nearest tenth of the decimal, i.e., 2.4:2.0:1.0. Different mixing ratios (MR)

were used for the different size ratios based on the weight proportion of different size (Table 8.1)

distributions found in low analysis fertilizer blend sample collected from several blend plants

(such as low analysis 10-10-10) in the Commonwealth of Pennsylvania.

Parameters for operating the PSSC-II, test conditions, and experimental design to study

percolation segregation in multi-size mixtures can be found in Jha et al. (2007a and b). All tests

were conducted in an environment-controlled laboratory with average temperature of 22°C ±

3°C and relative humidity less than 40%.

146

Table 8.1 Experimental design for binary size mixtures for potash and urea (Jha and Puri, 2007a)*

Material Strain rate (Hz)

Coarse size (µm)

Fine size (µm)

Size ratio Mixing ratio Number

1,550 2.4:1.0 50:50 1,850 2.0:1.0 37:63

Potash

0.25 0.50

3,675

2,180 1.7:1.0 37:63

9

1,550 2.0:1.0 63:37 1,850 1.7:1.0 50:50

Potash

0.25 0.50

3,075

2,180 1.4:1.0 50:50

9

1,550 1.7:1.0 63:37 1,850 1.4:1.0 63:37

Potash

0.25 0.50

2,580

2,180 1.2:1.0 63:37

9

1,850 2.0:1.0 37:63 Urea

0.25 0.50

3,675 2,180 1.7:1.0 37:63

6

1,850 1.7:1.0 50:50 Urea

0.25 0.50

3,075 2,180 1.4:1.0 50:50

6

1,850 1.4:1.0 63:37 Urea

0.25 0.50

2,580 2,180 1.2:1.0 63:37

6


*Strains of 2%, 6%, and 10% at two levels of strain rates 0.25 and 0.5 Hz

Table 8.2 Experimental design for multi-size size mixtures for potash and urea* Material Strain rate

(Hz) Coarse size

(µm) Fine size


1,550 2.4:2.0:1.0 28:44:28 1,850 2.0:1.7:1.0 22:39:39

Potash 0.25 0.50

3,675+3,075

2,180 1.7:1.4:1.0 22:39:39

6

1,550 2.0:1.7:1.0 33:46:21Potash 0.25 0.50

3,075+2,580 1,850 1.7:1.4:1.0 29:42:29

4

1,550 2.4:2.0:1.7:1.0 17:28:38:17 Potash 0.25 0.50

3,675+3,075+ 2,580 1,850 2.0:1.7:1.4:1.0 13:25:37:25

4

1,850 2.4:2.0:1.0 22:39:39 Urea 0.25 0.50

3,675+3,075 2,180 2.0:1.7:1.0 22:39:39

4

Urea 0.25 0.50

3,075+2,580 1,850 2.0:1.7:1.0 29:42:29 2

Urea 0.25 0.50

3,675+3,075+ 2,580

1,850 2.0:1.7:1.4:1.0 13:25:37:25 2


*Strains of 2%, 6%, and 10% at two levels of strain rates 0.25 and 0.5 Hz

147


The segregated fines mass was collected for the tested binary, ternary, quaternary size

ratios of urea and potash. The segregation results were analyzed using the three segregation

determining metrices: the percent segregated fines mass (%), segregation rate (kg/h), normalized

segregation rate (kg/kg-h).

8.4.1 Segregated fines mass The percent segregated fines mass for binary, ternary, and quaternary mixtures were

calculated from the collected segregated fines mass. It was expected that the percent of

segregated fines decreased with the increase in number of size components, i.e., binary>

ternary>quaternary. The percent segregated fines mass for multi-size mixtures also increased

with the increase in strains 2%>6%>10% and strain rate from 0.25 Hz to 0.5 Hz.

8.4.1.1 Effect of strain and strain rate Figures 8.1 and 8.2 compare the effect of strain rates of 0.25 and 0.5 Hz for binary,

ternary, and quaternary mixtures at three different strains of 2%, 6%, and 10%, respectively. The

binary, ternary, and quaternary size ratios 2.4:1.0, 2.4:2.0:1.0, and 2.4:2.0:1.7:1.0 were used

when coarse size were 3,675 µm; 3,675 µm and 3,075 µm; and 3,675 µm, 3,075 µm, and 2,580

µm, respectively. The percent segregated fines mass were compared based on the data collected

upto 30 minutes using the PSSC-II. Of the total time, for the first 10 minutes fines were collected

at 30 s interval, and thereafter, 120 s interval due to the slow down in discharge of fines.

At strain of 2% and strain rate of 0.25 Hz, after 15 s, 1.0% of the total initial fines present

in the binary mixtures was collected for the size ratio 2.4:1.0. At the end of 30 minutes, the

percent segregated fines was 6.5%. For ternary mixtures, after 15 s, 1.1% of the total initial fines

percolated for the size ratio 2.4:2.0:1.0. At the end of 30 minutes, the percent segregated fines

mass was 4.8% of the total fines. For quaternary mixtures, after 15 s, 1.2% of the total initial

fines percolated for the size ratio 2.4:2.0:1.7:1.0. At the end of 30 minutes, the percent

segregated fines mass was 2.8% of the total fines (Figure 8.1a). The percent segregated fines

mass was higher at strain of 6% than at strain of 2% (Figure 8.1b).

At strain of 10% and strain rate of 0.25 Hz, after 15 s, 2.9% of the total initial fines

present in the binary mixtures was collected for the size ratios 2.4:1.0. At the end of 30 minutes,

the percent segregated fines mass was 76.6%. For ternary mixtures, after 15 s, 2.3% of the total

148

initial fines percolated for the size ratio 2.4:2.0:1.0. At the end of 30 minutes, the percent

segregated fines mass was 42.1% of the total fines. For quaternary mixtures, after 15 s, 2.0% of

the total initial fines percolated for the size ratio 2.4:2.0:1.7:1.0. At the end of 30 minutes, the

percent segregated fines mass was 33.9% (Figure 8.1c).

At strain of 2% and strain rate of 0.5 Hz, after 15 s, 1.3% of the total initial fines present

in the binary mixtures was collected for the size ratios 2.4:1.0. At the end of 30 minutes, the

percent segregated fines mass was 9.6%. For ternary mixtures, after 15 s, 1.3% of the total initial

fines percolated for the size ratio 2.4:2.0:1.0. At the end of 30 minutes, the percent segregated

fines mass was 4.8% of the total fines. For quaternary mixtures, after 15 s, 1.0% of the total

initial fines percolated for the size ratio 2.4:2.0:1.7:1.0. At the end of 30 minutes, the percent

segregated fines mass was 3.4% of the total fines (Figure 8.2a). The percent segregated fines

mass was higher at strain of 6% than at strain of 2% (Figure 8.2b).

At strain of 10% and strain rate of 0.5 Hz, after 15 s, 4.0% of the total initial fines

present in the binary mixtures was collected for the size ratios 2.4:1.0. At the end of 30 minutes,

the percent segregated fines mass was 85.8%. For ternary mixtures, after 15 s, 4.2% of the total

initial fines percolated for the size ratio 2.4:2.0:1.0. At the end of 30 minutes, the percent

segregated fines mass was 82.6%. For quaternary mixtures, after 15 s, 3.2% of the total initial

fines percolated for the size ratio 2.4:2.0:1.7:1.0. At the end of 30 minutes, the percent

segregated fines mass was 42.1% (Figure 8.3c).

149

0.0

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40.0

60.0

80.0

100.0

0 5 10 15 20 25 30 35

Time (minutes)

Perc

ent s

egre

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d fin

es (%

)

Size ratio = 2.4:1.0Size ratio = 2.4:2.0:1.7:1.0

Size ratio = 2.4:2.0:1.0

0.0

20.0

40.0

60.0

80.0

100.0

0 5 10 15 20 25 30 35

Time (minutes)

Perc

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)


Size ratio = 2.4:2.0:1.7:1.0

Size ratio = 2.4:2.0:1.0

0.0

20.0

40.0

60.0

80.0

100.0

0 5 10 15 20 25 30 35

Time (minutes)

Perc

ent s

egre

gate

d fin

es (%

)


Size ratio = 2.4:2.0:1.7:1.0

Size ratio = 2.4:2.0:1.0

Figure 8.1 Comparison of binary, ternary, and quaternary size ratio at strain rate of 0.25 Hz and strains (a) 2%, (b) 6%, and (c) 10%, with ±SD as error bars

(a)

(b)

(c)

150

0.0

20.0

40.0

60.0

80.0

100.0

0 5 10 15 20 25 30 35

Time (minutes)

Perc

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)

Size ratio = 2.4:1.0Size ratio = 2.4:2.0:1.0

Size ratio = 2.4:2.0:1.7:1.0

0.0

20.0

40.0

60.0

80.0

100.0

0 5 10 15 20 25 30 35

Time (minutes)

Perc

ent s

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d fin

es (%

)


Size ratio = 2.4:2.0:1.0

Size ratio = 2.4:2.0:1.7:1.0

0.0

20.0

40.0

60.0

80.0

100.0

0 5 10 15 20 25 30 35

Time (minutes)

Perc

ent s

egre

gate

d fin

es (%

)


Size ratio = 2.4:2.0:1.0

Size ratio = 2.4:2.0:1.7:1.0

Figure 8.2 Comparison of binary, ternary, and quaternary size ratio at strain rate of 0.5 Hz

and strains (a) 2%, (b) 6%, and (c) 10%, with ±SD as error bars

(a)

(b)

(c)

151

8.4.1.2 Size ratio effect The results for binary, ternary, and quaternary mixtures were similar at strain rates of

0.25 and 0.5 Hz. Herein, results of binary, ternary, and quaternary mixtures at strain rate of 0.5

are presented. Figures 8.3 through 8.5 compare the percent segregated fines for the binary size

ratios 2.4:1.0, 2.0:1.0, and 1.7:1.0, ternary size ratios 2.4:2.0:1.0, 2.0:1.7:1.0, and 1.7:1.4:1.0 and

quaternary size ratios 2.4:2.0:1.7:1.0 and 2.0:1.7:1.4:1.0, respectively, at strains of 2%, 6%, and

10%, respectively.

At strain of 2%, after 15 s, the percent segregated fines masses in the binary size mixtures

of size ratios 2.4:1.0, 2.0:1.0, and 1.7:1.0 were 1.3%, 0.5%, and 0.2%, respectively. At the end of

30 minutes, the segregated fines masses were 9.6%, 2.8%, 0.9% in the same order and were

significantly different (p<0.05). After 15 s, the percent segregated fines masses in the ternary

size mixtures 2.4:2.0:1.0, 2.0:1.7:1.0 and 1.7:1.4:1.0 were 1.3%, 0.8%, and 0.2%, respectively.

At the end of 30 minutes, the percent segregated fines masses were 4.8%, 4.0% and 1.1%,

respectively and were not significantly different (p>0.05). After 15 s, the percent segregated

fines masses in the quaternary size mixtures 2.4:2.0:1.7:1.0 and 2.0:1.7:1.4:1.0 were 1.0% and

0.6%, respectively. At the end of 30 minutes, the percent segregated fines masses were 3.4% and

2.2% in the same order (Figure 8.3a) and were not different significantly (p>0.05). The percent

segregated fines mass at strain of 6% was higher than the percent segregated fines mass at strain

of 2% (Figure 8.4) (Jha and Puri, 2007a).

At strain of 10%, after 15 s, the percent segregated fines mass for size ratios 2.4:1.0,

2.0:1.0, and 1.7:1.0 were 4.0%, 2.7%, and 0.6%, respectively. At the end of 30 minutes, the

segregated fines mass were 85.8%, 69.8%, 8.9% in the same order and were significantly

different (p<0.05). After 15 s, in the ternary mixtures at the strain rate of 0.5 Hz, the percent

segregated fines mass values were 4.2%, 2.6%, and 0.6% for the size ratios 2.4:2.0:1.0,

2.0:1.7:1.0, and 1.7:1.4:1.0, respectively; whereas after 30 minutes, the percent segregated fines

mass values were 82.6%, 73.1%, and 14.2% in the same order (p<0.05). After 15 s, the percent

segregated fines mass values were 3.2% and 2.0% for the quaternary size ratios 2.4:2.0:1.7:1.0

and 2.0:1.7:1.4:1.0, respectively. At the end of 30 minutes, the percent segregated fines mass

values were 42.1% and 27.6% in the same order (p<0.05) (Figure 8.3c).

The fines mass in the binary, ternary, quaternary mixtures was in different proportions for

urea and potash (Tables 8.1 and 8.2). For discussion, the binary size (2.4:1.0), ternary

152

(2.4:2.0:1.0), and quaternary (2.4:2.0:1.7:1.0) mixtures of potash were compared when the same

fines mean size 1,550 µm was used. At strain rate of 0.5 Hz, the percent segregated fines mass

for three proportions of fines mass 33.0%, 50.0%, and 67.0% was compared for binary size ratio

of 2.0:1.0 of potash. It was found that the percent segregated fines mass was the highest and the

lowest for binary mixtures containing fines proportions of 33.0% and 67.0% (Jha et al., 2007a).

The binary, ternary, and quaternary mixtures contained fines mass in the proportions of 50.0%,

28.0%, and 17.0%, respectively, and the percent segregated fines mass was 76.6%, 45.9%, and

31.9% measures in the same order. Based on the above results, the percent segregated fines mass

would have been the highest and the lowest for the binary mixtures containing fines mass in the

proportion of 17.0% and 50.0%. However, the percent segregated fines mass was 76.6%, 45.9%,

and 31.9% of their respective fines mass in the binary, ternary, and quaternary mixtures,

respectively. The decrease in the percent segregated fines mass was measured because ternary

and quaternary mixtures percolation segregation mechanism was dominated by smaller size

coarse particles compared with binary mixtures. Based on the above results, the increase in the

percent segregated fines for multi-size mixtures followed non-linear trend for strain rates 0.25

and 0.5 Hz.

The percent segregated fines mass also increased with the increase in strain from 2% to

6% to 10%. The increase in percent segregated fines with the increase in strain did not follow the

linear trend. At higher strain of 10%, the intermediate size ratios 2.0:1.0 and 2.0:1.7:1.0 were

close to the higher size ratios 2.4:1.0 and 2.4:2.0:1.0 vs. 1.7:1.0 and 1.7:1.4:1.0, respectively. At

strain of 6%, the intermediate size ratios 2.0:1.0 and 2.0:1.7:1.0 were close to the higher size

ratios 2.4:1.0 and 2.4:2.0:1.0 vs. 1.7:1.0 and 1.7:1.4:1.0, respectively. However, the higher and

intermediate size ratios were close at strains of 6% and 10% compared with lower size ratio,

these two size ratios were closer at strain of 10% compared with strain of 6%. At strain of 2%,

the intermediate size ratios 2.0:1.0 and 2.0:1.7:1.0 were in-between or close to lower size ratios

1.7:1.0 and 1.7:1.4:1.0, respectively. The reason might be at higher strains of 6% and 10%, void

spaces in the coarse particles bed were sufficiently large so that fines sizes 1,550 and 1,850 µm

could percolate easily and show a similar trend. At strain of 2%, the percent segregated fines

mass was not significantly different for ternary and quaternary size ratios and also for urea and

potash for multi-size mixtures (p>0.05). This trend shows that the ternary size mixtures of urea

and potash could be used to characterize the response of continuous mixtures at 2% strain.

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Figure 8.3 Comparison of percent segregated fines for multi-size ratios for potash 2% at strain rate of 0.5 Hz in (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as

error bars

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156

8.4.1.3 Material comparison Figures 8.6 through 8.8 compare the percent segregated fines of urea (spherical-shaped

particles) and potash (angular-shaped particles) at strain rate of 0.5 Hz for binary, ternary, and

quaternary size ratios, respectively. The size ratios in binary 2.0:1.0, ternary 2.0:1.7:1.0, and

quaternary 2.0:1.7:1.4:1.0 mixtures for urea and potash were compared for determining material

effect. At strain rate of 0.5 Hz, in the first few minutes, the percent segregated fines for binary,

ternary, quaternary mixtures prepared were higher for spherical-shaped urea vs. angular-shaped

potash; however, after the initial few minutes, the percent segregated fines mass increased very

rapidly for angular-shaped potash compared with spherical-shaped potash. More fines were

expected in the case of potash because of the angular-shaped particles (porosity of 51%, i.e.,

larger void spaces) and higher particle density compared with the spherical shape urea particles

(porosity of 44%, i.e., smaller void spaces).

At strain of 2%, at the end of 30 minutes, the percent segregated fines for urea and potash

were 2.8% and 8.3%, respectively in binary mixtures (p>0.05). For ternary mixtures, at the end

of the test, 30 minutes, the percent segregated fines increased 4.0% for potash compared with

4.9% for urea (p>0.05). For quaternary mixtures, at the end of the test, 30 minutes, the percent

segregated fines increased 1.7% for potash compared with 2.8% for urea (p>0.05) (Figure 8.6).

The percent segregated fines mass was higher at strain of 6% vs. 2% (Figures 8.6 and 8.7)

At strain of 10%, in the first minutes, the percent segregated fines for urea and potash in

binary mixtures were 7.3% and 7.0%, respectively, however, after 75 s, the percent segregated

fines mass increased by 9.7% for potash compared with 8.8% for urea. At the end of 30 minutes,

the percent segregated fines for urea and potash were 27.6% and 69.8%, respectively. Initially,

the percent segregated fines in ternary mixtures was higher for urea compared with potash. In the

first 15 s, the percent segregated fines for urea and potash were 2.6% and 2.7% in ternary

mixtures, respectively, however, at the end of the test, the percent segregated fines increased

very rapidly for potash (73.1%) compared with urea (24.3%) (p<0.05). In the first 15 s, the

percent segregated fines in quaternary mixtures for the same size ratio for urea and potash 2.0%

and 1.8%, respectively, however, at the end of the test, 30 minutes, the percent segregated fines

increased very rapidly for potash (27.6%) compared with urea (7.5%) (p<0.05) (Figure 8.8).

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Figure 8.6 Comparison of percent segregated fines between potash and urea 2% at strain rate of 0.5 Hz for (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error

bars

(a)

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(c)

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Since the SR and NSR results are similar at strain rates of 0.25 and 0.5 Hz for binary,

ternary and quaternary mixtures, results at strain rate of 0.25 Hz are only discussed in the

following paragraphs.

8.4.2.1 Strain effect It was hypothesized that larger void space and large intensity of void space creation in the

coarse bed result in larger normalized segregation rate for multi-size mixtures when other test

conditions were the same. This hypothesis was tested by using binary, ternary, and quaternary

size mixtures of angular-shaped potash at three strains of 2%, 6% and 10% and strain rate of 0.5

Hz (Figure 8.9).

The NSR decreased very rapidly in the initial phase and then decreased linearly with time

till data collection was stopped at the end of 30 minutes for all binary, ternary, and quaternary

mixtures. At strain of 2% and strain rate of 0.25 Hz, after 15 s, the NSR was 2.47 kg/kg-h for

binary size ratio 2.4:1.0.. At the end of 30 minutes, the NSR was found to be 0.13 kg/kg-h. After

15 s, the NSR was 2.63 kg/kg-h for ternary size ratio 2.4:2.0:1.0. At the end of 30 minutes, the

NSR was found to be 0.10 kg/kg-h. After 15 s, the NSR was 2.84 kg/kg-h for quaternary size

ratio 2.4:2.0:1.7:1.0. At the end of 30 minutes, the NSR was found to be 0.06 kg/kg-h (Figure

8.9a). The binary, ternary, and quaternary mixtures at strain of 6% and strain rate of 0.25 Hz

were not significantly different (p>0.05). The results show that increasing number of

intermediate size components has no significant effect, i.e., binary mixtures can be used as a

representative for multi-size mixtures leading to continuous mixtures. The NSR at strain of 6%

was higher than the NSR at 2% (Figure 8.9b).

At strain of 10% and strain rate of 0.25 Hz, after 15 s, the NSR was 6.83 kg/kg-h for size

ratio 2.4:1.0. At the end of 30 minutes, the NSR was found to be 1.53 kg/kg-h. After 15 s, the

NSR was 5.47 kg/kg-h for ternary size ratio 2.4:2.0:1.0. At the end of 30 minutes, the NSR was

found to be 0.84 kg/kg-h. After 15 s, the NSR was 4.87 kg/kg-h for quaternary size ratio

2.4:2.0:1.7:1.0. At the end of 30 minutes, the NSR was found to be 0.68 kg/kg-h (Figure 8.9c).

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Figure 8.9 Comparison of NSR for binary, ternary, and quaternary size ratios at strain rate of 0.25 Hz and strains (a) 2%, (b) 6%, and (c) 10%, with ±SD as error bars

(b)

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162

8.4.2.2 Size ratio effect It was hypothesized that increasing the number of coarse size components with the given

fines size result in smaller normalized segregation rate when the other test conditions were the

same. This hypothesis was tested by using the binary, ternary, and quaternary mixtures at three

strains 2%, 6%, and 10% and strain rate of 0.25 Hz (Figures 8.10 through 8.12).

At strain of 2% and strain rate of 0.25 Hz, after 15 s, NSR was 2.47, 1.31, 0.33 kg/kg-h

for size ratios 2.4:1.0, 2.0:1.0, and 1.7:1.0. At the end of 30 minutes, NSR was found to be 0.13,

0.08, and 0.01 kg/kg-h in the same order (p<0.05). After 15 s, the NSR was 2.63, 1.59, and 0.80

kg/kg-h for the ternary size ratio 2.4:2.0:1.0, 2.0:1.7:1.0, and 1.7:1.4:1.0 with fines 1,550 µm,

1,850 µm and 2,180 µm, respectively. At the end of 30 minutes, NSR was found to be 0.01, 0.07,

and 0.15 kg/kg-h in the same order (p>0.05). After 15 s, the NSR was 2.84 and 1.49 kg/kg-h for

quaternary size ratios 2.4:2.0:1.7:1.0 and 2.0:1.7:1.4:1.0 with fines 1,550 µm and 1,850 µm,

respectively. At the end of 30 minutes, the NSR was found to be 0.06 and 0.04 kg/kg-h in the

same order (p>0.05) (Figure 8.10). The NSR for multi-size ratios was higher at 6% strain

compared with 2% strain (Figure 8.11).

At strain of 10% and strain rate of 0.25 Hz, after 15 s, NSR was 6.83, 2.91, and 0.86

kg/kg-h for size ratios 2.4:1.0, 2.0:1.0, and 1.7:1.0. At the end of 30 minutes, NSR was found to

be 1.53, 0.95, and 0.16 kg/kg-h in the same order (p<0.05). After 15 s, the NSR was 5.47, 3.12,

and 0.80 kg/kg-h for the ternary size ratio 2.4:2.0:1.0, 2.0:1.7:1.0, and 1.7:1.4:1.0 with fines

1,550 µm, 1,850 µm and 2,180 µm, respectively. At the end of 30 minutes, NSR was found to be

0.84, 0.58, and 0.15 kg/kg-h in the same order (p<0.05). After 15 s, the NSR was 4.87 and 3.56

kg/kg-h for quaternary size ratios 2.4:2.0:1.7:1.0 and 2.0:1.7:1.4:1.0 with fines 1,550 µm and

1,850 µm, respectively. At the end of 30 minutes, the NSR was found to be 0.68 and 0.43 kg/kg-

h in the same order (p<0.05) (Figure 8.12).

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Figure 8.10 Comparison of NSR for multi-size ratios for potash 2% at strain rate of 0.25 Hz in (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars

(a)

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Figure 8.11 Comparison of NSR for multi-size ratios for potash 6% at strain rate of 0.25 Hz in (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars

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Figure 8.12 Comparison of NSR for multi-size ratios for potash 10% at strain rate of 0.25

Hz in (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars

(b)

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8.4.2.3 Comparison between angular and spherical-shaped materials Figures 8.13 through 8.15 compare the NSR for urea and potash at three strains of 2%,

6%, and 10% and strain rate of 0.5 Hz for binary, ternary, and quaternary mixtures. For multi-

size mixtures, in the first few minutes, the NSR was higher for urea vs. potash, however,

thereafter, the NSR of urea decreased very rapidly compared with potash.

At strain of 2% and strain rate of 0.5 Hz, after 15 s, the NSR was 3.52 and 1.22 kg/kg-h

for the spherical and angular-shaped binary mixtures, respectively. At the end of 30 minutes, the

NSR was 0.17 and 0.06 kg/kg-h for spherical and angular-shaped binary mixtures, respectively.

After 15 s, at strain rate 0.5 Hz, the NSR was 2.00 and 3.34 kg/kg-h for potash and urea in

ternary mixtures, respectively. At the end of the test, at 30 minutes, the NSR values were 0.08

and 0.10 kg/kg-h for potash and urea (p>0.05). After 15 s, at strain rate of 0.5 Hz, the NSR was

1.97 and 3.07 kg/kg-h for potash and urea, respectively. At the end of the test, at 30 minutes, the

NSR values were 0.03 and 0.06 kg/kg-h for potash and urea, respectively (p>0.05) (Figure 8.13).

The NSR of urea and potash was higher at strain of 6% compared with strain of 2% (Figure 8.14)

At strain of 10% and strain rate of 0.5 Hz, after 15 s, the NSR was 8.06 and 5.75 kg/kg-h

for spherical and angular binary mixtures, respectively. After 60 s, the NSR values were very

close to each other, i.e., 4.37 and 4.18 kg/kg-h. At the end of 30 minutes, the NSR was 0.55 and

1.40 kg/kg-h for spherical and angular-shaped binary mixtures, respectively (p<0.05). After

15 s, at strain rate of 0.5 Hz for ternary mixtures, the NSR was 6.27 and 6.53 kg/kg-h for potash

and urea, respectively. After 30 s, the NSR values were almost the same i.e., 5.20 and 4.28

kg/kg-h for potash and urea, respectively. At the end of the test, at 30 minutes, the NSR values

were 1.46 and 0.49 kg/kg-h for potash and urea (p<0.05). After 15 s, at strain rate of 0.5 Hz, the

NSR was 4.91 and 4.35 kg/kg-h for potash and urea, respectively. At the end of the test, at 30

minutes, the NSR values were 0.55 and 0.15 kg/kg-h for potash and urea, respectively (p<0.05)

(Figure 8.15).

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Figure 8.13 Comparison of NSR for multi-size ratios for potash 2% at strain rate of 0.5 Hz

in (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars

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Figure 8.14 Comparison of NSR for multi-size ratios for potash 6% at strain rate of 0.5 Hz

in (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars

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Figure 8.15 Comparison of NSR for multi-size ratios for potash 10% at strain rate of 0.5

Hz in (a) binary, (b) ternary, and (c) quaternary mixtures, with ±SD as error bars

(a)

(b)

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8.4.3 Binary, ternary, quaternary, and continuous mixtures It was hypothesized that multi-size mixtures could be used as a representative of

continuous mixtures for studying percolation segregation. Number of coarse and fines needed to

study the percolation segregation in continuous mixtures using multi-size mixtures depend on

mechanical conditions under which mixtures are being handled. This hypothesis was tested using

binary, ternary, quaternary, and continuous mixtures at strains of 2% and 6% and strain rate of

0.5 Hz. Figure 8.16 compares the percent segregated fines in binary, ternary, quaternary, and

continuous mixtures at strain of 6% and strain rate of 0.5 Hz. The percent segregated fines in

binary size ratio 2.4:1.0 was the highest followed by ternary, and quaternary size ratios. With the

increasing number of intermediate coarse size component from binary to quaternary mixtures,

the effective void space decreased, as a result small void space available for fines to percolate.

The percent segregated fines of continuous mixtures (10-10-10) was found to be in-between

ternary and quaternary mixtures. Results could be explained based on the proportion of coarse

and fines and void spaces created at strain of 6% and strain rate of 0.5 Hz. There were three

coarse mean sizes: 3,675 µm; 3,075 µm; and 2,580 µm and four fines mean sizes: 1,290 µm;

1,550 µm; 1,850 µm; 2,180 µm used for formulation of continuous mixtures 10-10-10. These

coarse and fines sizes were added in the same proportion as it was used to formulate 10-10-10

mixtures in blend plants.

Binary, ternary, and quaternary mixtures were compared at strain of 2% and strain rate

of 0.5 Hz (Figure 8.17). The percent segregated fines was found to be the highest for binary

mixture of 2.4:1.0 when compared with ternary 2.4:2.0:1.0 and quaternary 2.4:2.0:1.7:1.0.

Although, the percent segregated fines for ternary mixture was higher than quaternary mixture,

however, ternary and quaternary mixture were not significantly different at strain of 2% and

strain rate 0.5 Hz (p>0.05). The same binary, ternary, and quaternary mixtures was tested at

strains of 2% and 6% and strain rate 0.5 Hz. This result explained that at lower strain of 2%,

ternary and quaternary mixtures were not significantly different (p>0.05) and could be used to

represent segregation in continuous mixtures. Percolation segregation results at strains of 2% and

6% proved that multi-size mixtures could be used as representative for continuous mixtures and

number of coarse and fines size depend on motion conditions under which materials were being

handled.

171

Figure 8.16 Comparison of percent segregated fines among binary, ternary, quaternary, and (10-10-10) mixtures at strain of 6% and strain rate of 0.5 Hz, with ±SD as error bars

0.0

20.0

40.0

60.0

80.0

100.0

0 5 10 15 20 25 30 35

Time (minutes)

Perc

ent s

egre

gate

d fin

es (%

)

Binary-2.4:1.0Quaternary-2.4:2.0:1.7:1.0Ternary-2.4:2.0:1.0

Figure 8.17 Comparison of percent segregated fines among binary, ternary, and

quaternary mixtures at strain of 2% and strain rate of 0.5 Hz, with ±SD as error bars

8.5 Conclusions

The primary segregation shear cell (PSSC-II) was capable of quantifying segregation of

fines in binary, ternary, quaternary mixtures for two materials urea and potash at three strains of

2%, 6%, and 10% and two strain rates of 0.25 and 0.5 Hz.

The following key conclusions were deduced based on the percolation of fines in binary,

ternary, and quaternary mixtures at 10% of strain:

1. At strain rate of 0.5 Hz, the percent segregated fines decreased by 19.9%, 47.1%,

57.7% when binary vs. ternary, ternary vs. quaternary, and binary vs. quaternary

0.0

20.0

40.0

60.0

80.0

100.0

0 5 10 15 20 25 30 35

Time (minutes)

Perc

ent s

egre

gate

d fin

es (%

)

Binary-2.4:1.0

Quaternary-2.4:2.0:1.7:1.0

Ternary-2.4:2.0:1.0

10-10-10

172

were compared for potash. At strain rate of 0.25 Hz, the percent segregated fines

decreased by 11.6%, 46.3%, and 52.8% when binary vs. ternary, ternary vs.

quaternary, and binary vs. quaternary were compared for potash.

2. At strain rate of 0.25 Hz for potash, at the end of end 30 minutes, the NSR

decreased by 13.4%, 53.4%, 59.7% when binary vs. ternary, ternary vs.

quaternary, and binary vs. quaternary were compared, respectively. For urea, at

the end of 30 minutes, the NSR decreased by 44.4%, 65.6%, and 80.6% when

binary vs. ternary, ternary vs. quaternary, and binary vs. quaternary were

compared, respectively. At strain rate of 0.5 Hz, for potash, at the end of end 30

minutes, the NSR decreased by 29.2%, 58.6%, 70.8% when binary vs. ternary,

ternary vs. quaternary, and binary vs. quaternary mixtures were compared,

respectively. For urea, at the end of 30 minutes, the NSR decreased by 53.1%,

56.5%, and 79.6% when binary vs. ternary, ternary vs. quaternary, and binary vs.

quaternary were compared, respectively.

3. Percolation segregation results at strains of 2% and 6% proved that multi-size

mixtures could be used as representative for continuous mixtures; furthermore,

number of coarse and fines size depend on motion conditions under which

materials were being handled.

8.6 Key Findings The binary, ternary, and quaternary mixtures of urea and potash were tested to determine

the percolation segregation of fines. In addition, segregation in thee multi-size mixtures were

compared with the segregation potential of fines in continuous mixtures at three strains of 2%,

6%, and 10% and strain rates of 0.25 and 0.5 Hz. The number of intermediate coarse sizes

needed to represent the continuous mixtures is dependent on the conditions under which

materials were handled. At strain of 2%, the binary mixtures of urea and potash were sufficient

to predict the percolation segregation of fines in the continuous mixtures. The ternary mixtures

of potash but not of urea were sufficient to predict percolation segregation of fines in continuous

mixtures at strain of 6%. The overall results of binary, ternary, and quaternary mixtures showed

at three strain and strain rates that multi-size mixtures results could estimate the segregation of

fines in continuous mixtures of particulates. These results will be able to save time and resources

173

for industry dealing with particulates by reducing number of tests needed to test continuous

mixtures.

8.7 References


Gotoh, K., T. Maki, and H. Masuda. 1994. The size segregation of polydispersed particles during feeding into a vessel. Journal of the Society of Powder Technology, Japan 31: 842– 849.

Hastie, D. B. and P. W. Wypych. 1999. Experimental investigation into segregation of bulk solids during gravity filling of storage bins, in: Proceedings of Reliable Flow of Particulate Solids III, Porsgrunn, pp. 507–518.



Jha, A. K. and V. M. Puri. 2007a. Percolation segregation of binary mixtures under periodic movement. Powder Technology (In review).

Jha, A. K. and V. M. Puri. 2007b. Percolation segregation of multi-component particulate materials (Author review).

Shinohara, K., K. Shoji, and T. Tanaka. 1972. Mechanism of size segregation of particles in filling a hopper. Industrial and Engineering Chemistry Process Design and Development 11: 369–376.

Shinohara, K., B. Golman, and T. Nakata. 2001. Size segregation of multicomponent particles during the filling of a hopper. Advanced Powder Technology 12: 33–43.

Shinohara, K. and B. Golman. 2002. Segregation indices of multi-sized particle mixtures during the filling of a two-dimensional hopper. Advanced Powder Technology 13(1): 93–107.



174

9. CHAPTER - PERCOLATION SEGREGATION AND FLOWABILITY MEASUREMENT OF UREA UNDER

DIFFERENT RELATIVE HUMIDITIES

9.1 Abstract Researchers have documented that size and size distribution of blended fertilizers is the

most dominant physical property contributing towards segregation. Similarly, it is known that

flowability is also affected by the size and size distribution and moisture content of blended

fertilizers. Therefore, segregation and flowability of binary size mixtures were studied at three

different equilibrium relative humidity conditions (40%, 50%, and 60%). Binary size mixtures

were prepared by using coarse and fines size urea of size ratio 2.0:1.0 and 1.7:1.0 mixed in

weight proportions 33:67 and 50:50, respectively. Percolation segregation was quantified using

the Primary Segregation Shear Cell (PSSC-II). Based on experimental results using the PSSC-II,

the segregated fines mass, normalized segregation rate (NSR), and segregation rate (SR) of fines

for binary urea mixtures were higher at equilibrium relative humidity of 40% vs. 50% and 60%.

The NSR is defined as the amount of fines percolated from the total initial fines in the binary

mixture based on the total time of PSSC-II operation (kg/kg-h). For size ratios 2.0:1.0 and

1.7:1.0, only 2.8% and 7.0% decrease in NSRs were recorded for increase in equilibrium relative

humidity by 10 points (from 40% to 50%), respectively, whereas 36.0% and 45.0% decrease in

NSRs were recorded for increase in equilibrium relative humidity by 20 points (from 40% to

60%), respectively (p<0.5). Additionally, flowability of binary size mixtures was quantified

using the Cubical Triaxial Tester (CTT). For size ratios 2.0:1.0 and 1.7:1.0, angle of internal

friction increased from 31.3° to 35.9° to 39.0° and 27.4° to 32.0° to 36.0° when relative humidity

increased from 40% to 50% to 60%, respectively. The angle of internal friction values were

significantly different (p<0.05) but cohesion values, at different relative humidity conditions

were not significantly different (p>0.05). Based on experimental results, relative humidity, if

implemented carefully, could be used as a tool to mitigate segregation in fertilizers.

175

9.2 Introduction

Particulate materials are handled in several industries such as agriculture, ceramic,

construction, food, nutraceutical, pharmaceutical, power, and powder metallurgy. The physical

and mechanical properties’ difference during handling, mixing, conveying, and storage causes an

unwanted phenomenon known as segregation. Segregation is defined as “demixing” or reverse

mixing (Popplewell et al., 1989; and Rollins et al., 1995). Segregation causes uneven quality of

fertilizers and tablets, fluctuating packet weights, low mechanical strength of compacts and

abrasives, poor refractory materials, and low rates of contact and reaction (Shinohara, 1997). For

example, different size granules in blended fertilizers separate from one another during

conveying, transportation, and storage causing uneven distribution of fertilizer in the field that

leads to localized over- and under-supply. For blended materials, the uniformity of blend is

highly dependent on physical attributes, such as, density, particle size and size distribution,

shape, hardness, surface texture, and moisture content.

Several researchers have reported that size of granular materials is the most important

parameter responsible for segregation (Tang and Puri, 2004; Bridle et al., 2004; and Bradley and

Farnish, 2005). However, size segregation in conjunction with other physical parameters has

greater detrimental effect than segregation by size alone. In addition, flowability of the blend is

dependent on physical and mechanical properties of the constituents. Flowability of hygroscopic

granular material is one of the key mechanical properties for mixing and segregation. High

flowability of material has positive and negative effects: for mixing, high flowability is essential,

whereas for segregation high flowability is detrimental. In the literature, relative humidity has

been documented to reduce flowability and hence is expected to lower segregation. However,

systematic and quantative study correlating segregation with flowability of hygroscopic blended

fertilizers could not be found in the literature. Therefore, percolation segregation and flowability

were studied under different equilibrium relative humidities, with the objective to evaluate the

use of relative humidity for mitigating segregation while maintaining flowability at acceptable

level of blended fertilizers.

To know the flow properties at different equilibrium relative humidity conditions,

quantifying their flowability is very important. Herein, a low pressure (<100 kPa) cubical triaxial

tester (CTT) developed by Kamath and Puri (1997) was used to measure flowability using the

Mohr-Coulomb model. The flexible-boundary of CTT allows unrestrained deformations in the

176

samples and minimizes die-wall friction effect. The low pressure CTT is capable of measuring

the three-dimensional response of cohesionless and cohesive particulate materials (Li and Puri,

1996).

The Mohr-Coulomb model, which states that the effective shear strength, increases with

effective normal stress, σ, on the failure plane, is the most commonly used yield criterion in bulk

solids flow theory. It can be represented by equation (9.1).

φστ tan+= c (9.1)

where, c, is the cohesion of the material, and ,φ is the angle of internal friction.

For both of the parameters, and φ , lower values indicate higher flowability and higher

flowability leads to higher segregation (Duffy and Puri, 1997). Therefore, the specific objectives

of the study were: 1) to quantify the percolation segregation under three equilibrium relative

humidity conditions, and 2) to evaluate flowability of binary size mixtures for the same three

equilibrium relative humidity conditions.


9.3.1 Test material selection, preparation, and parameter determination

Urea is a readily available and the most expensive constituent of dry blended fertilizers,

which was selected for studying segregation and flowability at three equilibrium relative

humidity conditions, i.e., 40%, 50%, and 60%, for two size ratios with differing mixing ratios

(Table 5.1). The shape of urea particles was round with sphericity of 0.97 (SD = 0.02). For this

study, different size ranges of urea were obtained using US standard sieves of (2)1/4 series. The

three equilibrium relative humidities (ERHs) were selected based on long-term weather data of

University Park, PA. All the samples were equilibrated at test ERHs by placing the material in

microprocessor controlled humidity chamber (Model 9000L, VWR international, Sheldon

Manufacturing Inc, Cornelius, Oregon) for 48 hours spread in a single layer on sieves. Samples

were placed on sieves to allow air to circulate through sieve perforations all around the urea

granules. All tests were performed after mixing coarse and fine urea granules to form binary size

mixtures using lowest speed setting of a six-speed bench-top 225-W mixer (Model-106772N,

Type-M27, General Electric, Marketed by Wal-Mart Stores Inc., Bentonville, AR). Size ratios

2.0:1.0 and 1.7:1.0 of coarse and fines were mixed in the proportions 33:67 and 50:50,

,τ

c

177

respectively, by weight. These two different mixing proportions were selected based on size

distributions of 10-10-10 fertilizer blend formulations. For flowability quantification, the binary

size mixtures were tested at two confining pressures of 3.5 kPa and 7.0 kPa based on pressure in

fertilizer bins under static storage conditions. All tests for segregation and flowability were

conducted in the environment-controlled laboratory with average temperature of 22°C ± 3°C and

relative humidity less than 40%. On an average, each test lasted for 40 minutes, which is

expected to have minimal influence on urea granules’ moisture content.

Table 9.1 Binary size mixtures of urea used for both segregation and flowability studies Coarse size 3,350-4,000 (dmean = 3,675 µm) and 2,800-3,350 (dmean = 3,075 µm)

Fine size 1,700-2,000 (dmean = 1,850 µm)

Size ratio Coarse: Fine

3,675:1,850 = 2.0:1.0*, mixing ratio = 33:67

3,075:1,850 = 1.7:1.0*, mixing ratio = 50:50

Equilibrium relative humidity

40%, 50%, and 60%

* Rounded up

9.3.2 Segregation

For segregation study, three parameters including material bed depth, particle bed strain,

and strain rate were selected for operating PSSC-II as shown in Table 9.2 (Tang and Puri, 2005).

The bed depth of 85 mm in the shear box was used to represent the bag depth of 22.7 kg blended

bagged fertilizers. The formulation 10-10-10 was selected for test parameter determination

because of the high demand (inexpensive) and its higher susceptibility to segregation under

handling and operating conditions. The higher amount of fillers in the low analysis (10-10-10

and others) bags is the primary reason for large head space that leads to non-uniformity. The

strain of 6% and strain rate of 0.5 Hz were selected to capture the motion of conveyors and front

end loaders when conveying bags (Vursavus and Ozguven, 2004). Binary size mixtures were

prepared using two coarse sizes and one fines size, which resulted in size ratios 2.0:1.0 and

1.7:1.0. Size ratio of binary mixtures is defined as the ratio of mean size of coarse to fine

particles. The purpose of binary size selection was to lay the foundation for studying segregation

potential of fines in multi-size mixtures leading to multi-size/component and continuous size

178

mixtures. For each treatment (Table 9.2), segregated fines mass was collected using the eight

load cells (range ±0.001 g) installed at eight different locations and recorded using LabView

(Version 6.0, National Instruments, Austin, TX). Based on published results (Duffy and Puri,

2002; and Tang and Puri, 2005), and preliminary testing with fertilizer blends, five replications

were deemed sufficient for experimental data to be within the 95% confidence interval.

In this study, eight sampling points distributed in two rows (4 load cells in a row) were

configured (Figure 9.1). The rationale for locations of the load cell was to collect maximum

percolated fines. For ease of reference, these load cells are identified as BR (back right), FR

(front right), BCR (back center right), FCR (front center right), BCL (back center left), FCL

(front center left), BL (back left), and FL (front left) as shown in Figure 9.1(b). Sieve number 8

(opening size = 2,360 µm) was used throughout the tests so that the percolating fines could exit

while coarse particles did not block sieve openings.

Table 9.2 Experimental design for segregation testing of binary size mixtures of urea Parameter Number Size ratios 2:0:1.0 (mixing ratio-33:67) and 1.7:1.0 (mixing ratio-50:50)

2

Equilibrium relative humidities (40%, 50% and 60%) 3 Strain rate (0.5 Hz) 1 Strain (6%) 1 Bed depth (85 mm) 1 Replications (5 per treatment) 5 Number of tests 30

179

Figure 9.1 Collection pan for fines showing eight load cell locations, (a) top view of shear

box and eight load cell positions for data collection, (b) top view of collection pan (all dimensions in mm)

9.3.3 Flowability

The flexible-boundary CTT developed by Kamath and Puri (1997) was used for testing

the flowability of binary size mixtures (Tables 9.1 and 9.3). The cubical triaxial tester uses two

individual pressure controllers (Proportion-Air Inc. QB1TFEE015), which can apply pressures

from 0 to 100 kPa with ± 0.2% of accuracy over the entire range. Individual pressure controllers

regulate horizontal and vertical pressures independently using software developed with LabView

(Version 6.0, National Instruments, Austin, TX) by Kandala and Puri (2000). The flowability

parameters were measured using the conventional triaxial compression (CTC) test. The CTC test

begins with hydrostatic compression at pressure σc, or confining pressure. While this confining

pressure is kept constant in horizontal directions, the pressure in the vertical direction (i.e.,

gravity directions) was increased until the sample failed. The failure stress was denoted as σf.

These pressures (σc and σf) are the principal stresses that were plotted on the normal stress versus

shear stress diagram to produce corresponding Mohr circles. Based on published results (Li and

Puri, 1996; and Kandala and Puri, 2000), three replications were performed for each combination

for testing flow behavior of samples using the CTT. A complete block design was selected for

(b)

(a)

180

data analysis. One set of experiments was performed on binary size mixtures of urea equilibrated

at relative humidity values of 40%, 50%, and 60%. All the three data sets were analyzed

separately and compared for determining flow properties corresponding to three different ERHs. Table 9.3 Experimental design for flowability testing of binary size mixtures of urea Parameter Number

Size ratios 2.0:1.0 (mixing ratio – 33:67) and 1.7:1.0(mixing ratio – 50:50)

2

Confining pressures (3.5 kPa and 7.0 kPa) 2

Equilibrium relative humidities (40%, 50%, and 60%) 3

Replications (three per treatment) 3

Number of tests 36

From the common tangent line of two Mohr circles, the angle of internal friction (φ) and

the cohesion (c) of samples were determined. Before filling the cavity (50 mm x 50 mm x 50

mm), a low inflating pressure of 5 kPa was applied to ensure that membranes were in contact all

around to prevent fertilizer from exiting or squeezing out. Then, well mixed binary size sample

was placed into the cavity in three steps. In the first step, cavity was one-third filled and top

surface was leveled off with a soft nylon brush; this was repeated for the next third and the final-

one third. The amount of test material in the cavity was 59 g ±1 g. After placing the sample into

the cavity, a confining pressure was applied using a compressed air source. Subsequently, the

pressure in the vertical direction was increased at 100 Pa/s until failure. The very low rate of

pressure increase of 100 Pa/s was selected so that 1) particles have sufficient time for

rearrangement, and 2) time-dependent effects are minimized.


9.4.1 Physical properties determination

The characterization of physical properties of binary size mixtures such as bulk density,

particle density, shape, and size of the test materials is essential before testing because of

inherent variability of bulk solids (Table 9.4). The flow and segregation responses of bulk solids

vary with variation in their physical properties.

181

Table 9.4 Physical property of binary size mixtures of urea (sphericity = 0.97*) at three different equilibrium relative humidity conditions

Size ratio

Mixing ratio

Equilibrium relative humidity (%)

Particle density** (kg/m3)

Bulk density** (kg/m3)

Porosity***

40 1,456 (2) 726 (2) 50 50 1,458 (3) 743 (3) 49

2.0:1.0

33:67

60 1,461 (5) 744 (4) 49 40 1,455 (2) 727 (1) 50 50 1,458 (3) 732 (1) 50 1.7:1.0 50:50 60 1,461 (3) 733 (0) 50

* Based on three principal dimensions (Mohsenin, 1986) ** Measured values - Quantachrome multipyconometer (Model MVP-2) with ultra pure He– five replicates *** Calculated values

In Table 9.4, for size ratios 2.0:1.0 and 1.7:1.0, both particle density (PD) and bulk

density (BD) increased with increase in RH from 40% to 60%. With increase in RH by 20%

points (i.e., 40% to 60%), PD increased by 0.3% and 0.4%, respectively, whereas for increase in

RH by 10% points (40% to 50%), PD increased by 0.1% and 0.1%, respectively. The small

increase in PD with increase in equilibrium relative humidity was obtained because of surface air

pores were filled by water (p>0.05). The same trend was observed for bulk density for both the

size ratios 2.0:1.0 and 1.7:1.0 (p>0.05). No measurable change in porosity was noted when RH

increased from 40% to 60%, which is beyond the detection capability of the multipyconometer

used in this study.

9.4.2 Percolation Segregation

The test results of two binary size mixtures (2.0:1.0 and 1.7:1.0), conditioned at three

different ERHs (40%, 50% and 60%) in terms of measured mass of segregated fines (g) are

summarized in Table 9.5. Figures 9.2 and 9.3 show typical profiles of cumulative fines mass

collected by the eight load cells in real-time for size ratios 2.0:1.0 and 1.7:1.0, respectively.

Similar profiles were obtained at other ERHs. Both of these figures show that most of the

segregated fines were collected at the two ends, which is in agreement with the results reported

for glass beads by Duffy and Puri (2002) and glass beads and mash feed by Tang and Puri

(2005). Since the time evaluation of segregated fines was recorded using the PSSC-II, two rate

metrics: segregation rate (kg/h) and normalized segregation rate (kg/kg-h) are introduced.

Herein, segregation rate is defined as the mass of fines segregated from the binary size mixture

182

of urea per unit total time of PSSC-II operation; whereas, NSR is defined as the ratio of collected

fines mass to total mass of fines mixed with coarse divided by total time of PSSC-II operation.

Table 9.5 Segregated fines, mean segregation rate and mean NSR for binary size mixtures urea

Size ratio (Mixing ratio)

ERH (%)

Average time for

discharge (minutes)

Segregated fines (g)

Average segregation rate (kg/h)

NSR (kg/kg-h)

40 10.4 (0.1) 87.74 (1.2) 0.51 (0.01) 1.12 (0.02) 50 10.4 (0.1) 85.69 (1.6) 0.49 (0.01) 1.09 (0.02) 2.0:1.0

(33:37) 60 10.2 (0.2) 56.21 (1.5) 0.33 (0.01) 0.73 (0.02) 40 11.5 (0.0) 41.03 (1.2) 0.21 (0.01) 0.61 (0.02) 50 11.4 (0.1) 38.40 (1.8) 0.20 (0.01) 0.58 (0.03) 1.7:1.0

(50:50) 60 11.4 (0.2) 22.99 (1.3) 0.12 (0.01) 0.34 (0.02) *Standard deviation values in parenthesis

In Table 9.5, for size ratio 2.0:1.0, when RH increased by 20% points (40% to 60%) and

10% points (40% to 50%), segregated fines decreased by 36.0% and 2.3%, respectively. For size

ratio 1.7:1.0, when RH increased by 20% points (40% to 60%) and 10 points (40% to 50%)

segregated fines decreased by 44.0% and 6.4%, respectively. The results suggest that relative

humidity could be used as an effective tool to mitigate segregation.

183

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0 3 6 9 12 15Time (minutes)

Col

lect

ed fi

nes

mas

s (g

)

BRFRFCRBCBL

FCFLBCL

Figure 9.2 Typical segregated fines mass of binary size urea mixture for size ratio 2.0:1.0 equilibrated at 50% relative humidity environment with bed depth of 85 mm. The curves

are for different load cell locations shown in Figure 9.1.

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0 3 6 9 12 15Time (minutes)

Col

lect

ed fi

nes

mas

s (g

)

BRFR

BLFLFCR

FCLBCR

BCL

Figure 9.3 Typical segregated fines mass of binary size urea mixture for size ratio 1.7:1.0 equilibrated at 50% relative humidity environment with bed depth of 85 mm. The curves

are for different load cell locations shown in Figure 9.1.

184

Figures 9.4 shows typical profiles of segregated fines mass of binary mixture for size

ratio 2.0:1.0 and 1.7:1.0, respectively, collected by the eight load cells configured four each in

two rows (Figure 9.1). The measured mass values are for binary mixtures of urea that were

equilibrated at 50% relative humidity. Both of these figures show that fines masses collected by

the eight load cells increased with time. Fines mass collected for size ratio 2.0:1.0 was higher

compared with size ratio 1.7:1.0. Results confirmed that higher size ratio has higher segregation

potential. Fines masses collected by eight load cells were different for both of these size ratios.

For size ratio 2.0:1.0 (Figure 9.4), fines mass collected by eight load cells were more uniform

compared with mass collected for size ratio 1.7:1.0.

Figure 9.4 shows iso-mass contours for segregated fines for size ratios 2.0 (Figure 9.4a)

and 1.7 (Figure 9.4b) at the end of 10 minutes, which is the expected time duration of motion

conditions for bagged fertilizer to experience between filling and transportation. Even though

iso-mass contours are shown at the end of 10 minutes, these can be analyzed at any time from 0

to 10 minutes in the interval of 1 s. At the end of 10 minutes, the fines were collected more at

both ends of the shear box such as BL, FL, BR and FR compared to the center zone such as BCL

and FCL (p>0.05). Load cells in the center received less fines compared to other load cells

because of diffusive percolation mechanism. This result is in agreement with previous results

obtained for size ratio less than 4:1 (Duffy and Puri, 2002).

Figure 9.4 Typical distributed fines mass of binary size urea mixtures for (a) size ratio 2.0:1.0 and for (b) size ratio 1.7:1.0 equilibrated at 50% relative humidity; x and y axes dimensions denote the opening size available at the bottom of the shear box for fines to

percolate

(a) (b)

185

9.4.3 Normalized segregation rate (NSR)

For size ratio 2.0:1.0, NSR decreased from 1.12 kg/kg-h to 1.09 kg/kg-h to 0.73 kg/kg-h

when urea binary size mixtures equilibrated relative humidity increased from 40% to 50% to

60%. Similarly, for size ratio 1.7:1.0, NSR decreased from 0.62 kg/kg-h to 0.58 kg/kg-h to

0.34 kg/kg-h when urea binary size mixtures’ equilibrated relative humidity increased from 40%

to 50% to 60%. Figure 9.5 shows a typical profile of NSR at 40% RH of binary mixture for size

ratio 2.0:1.0. The NSR declined rapidly in the first few minutes (<3 minutes) of PSSC-II

operation followed by an asymptotic approach to a linear decline. The rapid initial decline can be

attributed to availability of fines with low coordination number, which increases with time, i.e.,

fine becomes more constrained. Similar profiles were obtained for other ERHs (50% and 60%)

and for size ratio 1.7:1.0. The NSR profiles could be used to predict the amount of segregation in

the mixture under given operating condition in real-time.

0.0

2.0

4.0

6.0

8.0

10.0

0 5 10 15 20 25 30 35

Time (minutes)

NSR

(kg/

kg-h

)

Figure 9.5 Segregation rate at 40% ERH for size ratio 2.0:1.0, with ±SD as error bars

9.4.4 Distribution of segregation rate Distribution of segregation rate (DSR) metric was used to evaluate the spatial distribution

of segregation rate (SR) corresponding to the eight load cell locations. Figures 9.6 and 9.7 show

typical SR of percolated fines along the eight load cells at 50% RH for the size ratios 2.0:1.0 and

186

1.7:1.0, respectively. Results were in agreement with the NSR result, i.e., NSR decreased with

increasing relative humidity. Figure 9.6, size ratio 2.0:1.0, shows that SR was higher at both ends

of the shear box compared with the center region and decreased with time, i.e., 60 s (Figure 9.6a)

to 120 s (Figure 9.6b) to 180 s (Figure 9.6c) (p>0.05). At 60 s, SR was higher in the center and

right of the shear box because of initial percolated fines present initially in the bottom of the

mixture. Figure 9.7 shows, size ratio 1.7:1.0, fines mass were collected more at both ends of the

shear box such as BL, FL, BR and FR compared to the center zone such as BCL and FCL

(p>0.05) and SR decreased with time, i.e., 60 s (Figure 9.7a), 120 s (Figure 9.7b), and 180 s

(Figure 10.7c). For both size ratios 2.0:1.0 and 1.7:1.0, load cells in the center received less fines

compared to other load cells because of diffusive percolation mechanism. This result is in

agreement with previous results obtained for size ratio less than 4:1 (Duffy and Puri, 2002).

187

Figure 9.6 Typical distributed segregation rate of fines mass of binary urea mixtures at, (a) 60 s, (b) 120 s, and (c) 180 s for size ratio 2.0:1.0 at 50% RH; x and y axes denotes the open size available at the bottom of the shear box for fines to percolate

Figure 9.7 Typical distributed segregation rate of fines mass of binary urea mixtures at, (a) 60 s, (b) 120 s, and (c) 180 s for size ratio 1.7:1.0 at 50% RH; x and y axes denotes the open size available at the bottom of the shear box for fines to percolate

(a) (b)

(a) (b) (c)

(c)

192

9.4.5 Flowability

For determining flowability parameters, conventional triaxial compression (CTC) tests

using the CTT were performed on binary size mixtures of urea (Tables 9.1 and 9.3) conditioned

at three different equilibrium relative humidity conditions (40%, 50%, and 60%).

From the CTC tests, failure stress of binary mixtures was determined. Figure 9.8

illustrates the failure stress values of well mixed binary size urea mixtures. For size ratio 2.0:1.0

at confining pressure σc = 3.5 kPa, failure stress increased from 12.2 kPa to 15.5 kPa to 16.2 kPa

when ERH increased from 40% to 50% to 60%. At relatively higher confining pressure σc = 7

kPa, failure stress increased from 23.5 kPa to 29.3 kPa to 32.0 kPa for increase in ERH from

40% to 50% to 60%, respectively. For size ratio 1.7:1.0 at confining stress (σc = 3.5 kPa), failure

stress increased from 11.2 kPa to 14.5 kPa when ERH increased from 40% to 50% and plateaued

thereafter; whereas, failure stress increased from 22.7 kPa to 28.0 kPa for increase in ERH from

40% to 60% at higher confining pressure σc = 7 kPa. A plausible explanation for the minimal to

no effect of ERHs for size ratio of 1.7:1.0 at lower confining pressure (σc = 3.5 kPa) was a result

of more tightly packed samples, i.e., 3.5 kPa of confining pressure was not sufficient to induce

rearrangement of particles.

0.0

10.0

20.0

30.0

40.0

30 40 50 60 70


Shea

r stre

ss (k

Pa) Size ratio 2.0:1.0, σc= 7.0 kPa

1.7:1.0, 7.0 kPa

2.0:1.0, 3.5 kPa

1.7:1.0, 3.5 kPa

Figure 9.8 Failure stress difference for binary mixtures of size ratios of 2.0:1.0 and 1.7:1.0

and confining pressures of 3.5 and 7.0 kPa

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The results presented in this chapter demonstrated that segregation and flowability

decreased with the increase in relative humidity, as expected. Higher size ratio and equilibrium

relative humidity tend to induce higher failure stress, which implies tighter packing of the

samples. For both of the size ratios 2.0:1.0 and 1.7:1.0, particle density values increased with the

increase in equilibrium relative humidity.

The flowability determining parameters, i.e., angle of internal friction and cohesion are

summarized in Table 9.6. For size ratio 2.0:1.0, the angle of internal friction increased from

31.3° to 35.9° to 39.0° for increases in ERH from 40% to 50% to 60%, respectively. For size

ratio of 1.7:1.0, angle of internal friction increased from 26.8° to 36.0° when relative humidity

increased from 40% to 60%. In all cases, size ratio of 2.0:1.0 showed higher angle of internal

friction than size ratio of 1.7:1.0 suggesting that size ratio of 2.0:1.0 mixture has lower

flowability.

Table 9.6 Flowability parameters for binary size mixtures at three equilibrium relative humidities*

Size ratio (Mixing ratio)


Angle of internal friction (φ) Cohesion (c, kPa)

40 31.3° (1.2) 0.3 (0.2) 50 35.9° (1.7) 0.5 (0.3)

2.0:1.0 (33:67) 60 39.0° (2.3) 0.3 (0.4)

40 27.4° (1.9) 0.5 (0.4) 50 32.0° (3.4) 0.9 (0.9)

1.7:1.0 (50:50) 60 36.0° (0.0) 0.3 (0.0)

* Standard deviation values in parenthesis

For both size ratios of 2.0:1.0 and 1.7:1.0, cohesion values remained constant and were not

significantly different (p>0.05). Negligible cohesion values were consistent with visual

observations.

Results showed that flowability of particles decreased with increase in angle of internal

friction while cohesion remains insignificant. The lower flowability for size ratio of 2.0:1.0

compared to size ratio of 1.7:1.0 is because of the mixing and size ratios’ differences; large size

ratio had more fines compared to coarse (mixing ratio 33:67) and mixture’s response was

governed by the quantity of fines. For larger size, more pore spaces were available in the coarse

particle bed vs. small size ratio. Furthermore, flowability parameters result also confirmed the

194

segregation results. PSSC-II results also demonstrated that segregation in binary size of urea

mixtures decreased with increasing ERHs from 40% to 60%. Results of flowability and

segregation for binary size urea mixtures were in agreement with the results published by Duffy

and Puri (1997) for food powders.

9.5 Conclusions Percolation segregation of binary size mixtures of urea by blending fines (1,700-2,000

µm) with coarse (3,350-4,000 µm and 2,800-3,350 µm) equilibrated at three relative humidity

conditions (40%, 50%, and 60%) was measured using PSSC-II. All tests were conducted at bed

depth of 85 mm, strain of 6%, and strain rate of 0.5 Hz. Results showed that the PSSC-II is

capable of quantifying segregation of binary size mixtures. For quantification of segregation,

four metrics; 1) segregated fines mass, 2) segregation rate, 3) normalized segregation rate, and 4)

distribution segregation rate of fines were used. The following conclusions were drawn from this

study.

1. Size ratio 2.0:1.0

1. Segregated fines mass values decreased from 87.74 g to 85.69 g to 56.21 g when

ERHs increased from 40% to 50% to 60%, respectively. Only 2.0% of decrease in

collected fines mass was recorded for increase in ERH by 10 points (from 40% to

50%), whereas 36.0% decrease in fines mass was recorded for increase in ERH by 20

points (from 40% to 60%).

2. NSR decreased from 1.12 kg/h to 1.09 kg/h to 0.73 kg/h when ERHs increased from

40% to 50% to 60%, respectively. Only 2.8% decrease in SR was recorded for

increase in ERH by 10 points (from 40% to 50%), whereas 36.0% decrease in SR was

recorded for increase in ERH by 20 points (from 40% to 60%).

2. Size ratio 1.7:1.0

1. Segregated fines mass values decreased from 41.03 g to 38.40 g to 22.99 g when

ERH increased from 40% to 50% to 60%, respectively. Only 6.0% of decrease in

collected fines mass was recorded for increase in ERH by 10 points (from 40% to

50%), whereas 43.0% decrease in mass was recorded for increase in ERH by 20

points (from 40% to 60%).

195

2. NSR decreased from 0.61 kg/kg-h to 0.58 kg/kg-h to 0.34 kg/kg-h when relative

humidity increased from 40% to 50% to 60%, respectively. Only 7.0% decrease in

NSR recorded for increase in ERH by 10 points (from 40% to 50%), whereas 45.0%

decrease in NSR was recorded for increase in ERH by 20 points (from 40% to 60%).

With the two different mixtures of fines (1,700-2,000 µm) and coarse (3,350-4,000 µm and

2,800-3,350 µm) at three different ERHs (40%, 50% and 60%), conventional triaxial

compression tests were performed to evaluate flowability using the CTT. From those results, the

following conclusions were drawn:

1. For size ratio 2.0:1.0, angle of internal friction increased from 31.3° to 35.9° to 39.0°

when ERH increased from 40% to 50% to 60%, respectively.

2. For size ratio 1.7:1.0, angle of internal friction increased from 27.4° to 32.0° to 36.0°

when ERH increased from 40% to 50% to 60%, respectively.

3. The measured negligible cohesion values were not significantly different (p>0.05) for

both size ratios 2.0:1.0 and 1.7:1.0 at all three ERHs.

In conclusion, addition of moisture could be used as an effective management approach to

mitigate segregation in granular materials by marginally reducing their flowability by addition of

moisture. Flowability should not be lowered below a critical value, otherwise flow issues may

arise.

9.6 Key Findings The binary mixtures of urea were tested for quantifying segregation and flowability when

exposed to three equilibrium relative humidity conditions (40%, 50%, and 60%). The

segregation and flowability decreased with the increase in relative humidity from 40% to 60%.

The higher ERH 60% was below the critical relative humidity for urea so that urea material did

not form aggregate due to the presence of moisture. When hygroscopic materials are exposed to

equilibrium relative higher than their respective critical relative humidity then flow issues will

arise instead of segregation.

196

9.7 References

Bradley, M. S. A. and R. J. Farnish. 2005. Segregation of blended fertilizer during spreading: the effect of differences in ballistic properties. In Proc 554. The International Fertilizer Society. York, UK. pp: 15.

Bridle, I. A., M. S. A. Bradley, and A. R. Reed. 2004. Non-segregating blended fertilizer development: A new predictive test for optimising granulometry. In Proc 547. The International Fertilizer Society. York, UK. pp: 27.

Duffy, S. P. and V. M. Puri. 1997. Evaluation of computer controlled dynamic yield locus tester (DYLT). Powder Technology 101: 257-265.


Li, F. and V. M. Puri. 1996. Measurement of anisotropic behavior of dry cohesive and cohesioless powders using a cubical triaxial tester. Powder Technology 89: 197-207.

Kamath, S. and V. M. Puri. 1997. Measurement of powder flow constitutive model parameters using cubical triaxial tester. Power Technology 90: 59-90.

Kandala, R. N. and V. M. Puri. 2000. Measurement of cohesion and angle of internal friction using cubical triaxial tester and comparison with computer controlled shear cell. Particulate Science and Technology, An International Journal 18(2): 71-88.

Jenike, A.W. 1960. A preliminary study of segregation. Bulletin of the University of Utah, Bulletin Number 107 of the Utah Engineering Experimental Station. Salt Lake City, UT



Shinohara, K. 1997. Segregation of particles. Ed.: Gotoh, K.H. Masuda, and K. Higashitani. Powder Technology Handbook (2nd Ed.). Marcel Dekker Inc. New York. USA.

Tang, P. 2004. Percolation and sieving segregation patterns-quantification, mechanistic theory, model development and validation, and application. Ph.D. Diss. The Pennsylvania State University, University Park, PA.

Tang, P. and V. M. Puri. 2004. Methods for minimizing segregation, a review. Particulate Science and Technology, An International Journal 22(4): 321-338.



197

10. CHAPTER - SOLID FERTILIZER SAMPLING AND COMPARISON OF SINGLE TUBE TRIERS OF 12.7 mm AND

19.1 mm OPENING WIDTHS

10.1 Abstract Solid fertilizers, from different locations in three blend plants, were sampled to determine

chemical analysis, size guide number (SGN), and uniformity index (UI) of raw ingredients and

blends. Five different types of triers were used to sample fertilizers from five different locations,

i.e., rail car or truck, bins, front-end-loader, stream sampling, and 10-10-10 bags. The

formulation 10-10-10 was sampled from bags using 12.7 and 19.1 mm triers by a two-person

team of Pennsylvania Department of Agriculture (PDA) inspectors at three blend plants in

Pennsylvania. An innovative time-sequence procedure for sampling of bags was devised and

implemented. For this, bags in each lot (i.e., batch) were separated into four sublots, i.e., each

sublot corresponded to one quarter of the batch from all three blend plants and for all 10-10-10

bagged fertilizers sampled. Size analysis of ingredients from the three blend plants showed that

there was a large spread in SGNs and UIs, with appreciable variability from plant-to-plant.

The SGN of 19.1 mm width trier was either higher or the same compared with samples collected

using 12.7 mm trier. No substantial differences between SGNs and UIs for these two triers were

found, except for 10-10-10 (bags from the second quarter) from BP1 where all SGNs and UIs

were within 7 and 2, respectively. Eleven out of the twelve samples from bagged fertilizers using

12.7 mm vs. 19.1 mm had the same outcomes, i.e., only one sample from BP3 10-10-10 (bags

from the third quarter) using 12.7 mm vs. 19.1 mm had a conflicting outcome – the sample

obtained using 19.1 mm width trier (SGN=259, UI=47) passed, whereas the sample with 12.7

mm trier (SGN=256, UI=47) failed the chemical analysis. Therefore, further study is needed to

recommend the best trier to collect representative samples from fertilizer bags.

10.2 Introduction

The sampling instruments and procedures used for solid fertilizer are somewhat biased

for determining both physical and chemical properties of these materials (Baker et al., 1967).

The first comprehensive study of solid fertilizer sampling using different trier widths was

completed by Baker et al. (1967). Thereafter, a trier opening width of 12.7 mm was used as the

198

Association of Analytical Chemists (AOAC) standard for sampling bagged fertilizer. Caine and

Hancock (1998) reported that most fertilizer materials have shown an increase in particle size

since Baker et al.’s study performed in 1966. It has been reported in the literature that a sampling

trier with a 12.7 mm opening width secured an excess of particles larger than 20 mesh (SGN =

87) and triers having larger diameter produced less sampler bias compared with 12.7 mm

diameter of the same design (Fiskell et al., 1958 and Fiskell and Chew, 1957). Sauchelli (1960)

reported that a standard single tube trier opening width of 12.7 mm secured more particles

smaller than 14 mesh (SGN=140) and less particles larger than 6 mesh (SGN = 335) compared

with 22.2 mm opening width of an Archer tube. An excess of fine particles secured by a smaller

opening width trier was also reported by Gehrke et al. (1967).

Caine and Hancock (1998) considered Baker et al.’s study as the framework for their

study for finding a suitable trier for solid fertilizer sampling. The findings of Caine and Hancock

(1998) formed the basis for adoption of the most recent recommendation by the Association of

American Plant Food Control Officials (AAPFCO) and AOAC of using a 19.1 mm opening trier

for securing samples from bagged fertilizers that are representative of the blend. However, even

when a fertilizer is correctly formulated to produce a desired analysis, samples collected using

recommended procedures often fail the chemical analysis test. For example, the tolerance limit

for primary raw ingredients (N-P-K) in the Commonwealth of Pennsylvania is 10%. In addition,

if the total commercial value (TCV) of the fertilizer is below the tolerance limit (97% for

Commonwealth of Pennsylvania), the blenders are penalized by state regulatory agency (TFI,

1996).

The study of Caine and Hancock had not included the sampling of raw materials and how

the composition of the blended material in storage bins varies before filling the bags. Based on

the literature review and initial visits to the three fertilizer blending plants in Pennsylvania in

Spring of 2006, an experiment was designed to study sampling of fertilizers from three fertilizer

blending plants in Spring 2007. The objective of the study was to compare 12.7 mm and

19.1 mm trier for collecting samples from blended bagged fertilizer. The hypothesis of this study

was that the triers of opening widths 12.7 mm and 19.1 mm collect similar sample from fertilizer

bags.

199


Three fertilizer blend plants were selected in the Commonwealth of Pennsylvania based

on their blend production capacity (Table 10.1). Solid fertilizer samples were collected from the

three fertilizer blend plants in the months of April and May 2007. During the visits, samples

were collected throughout the plant, i.e., delivery truck/railcar, materials in bins, front end

loaders, blender outlet, storage and discharge (to fill bags). The capacity of the material

locations (except storage bins and track/rail car), from where the samples were collected, is given

in Table 10.1. Finally, samples were collected from bagged blended fertilizers using 12.7 and

19.1 mm triers. It has been documented that a low analysis fertilizer blend such as 10-10-10 is

one of the most popular among farmers and very susceptible to segregation. Therefore, a 10-10-

10 blend with dry solids fertilizers was selected for detailed analysis from the three blend plants.

Although the experimental design for data collection was similar to that of Caine and Hancock

(1998); however, it was more comprehensive than Caine and Hancock study, i.e., the samples

were obtained from start of the process (sampling truck/railcar) to filled bags vs. filled bags only

in Caine and Hancock study.

Table 10.1 Capacity of material locations at three blending plants Material amount BP1 BP2 BP3

Front end loader* (kg) 453.60 453.60 453.60

Mixer (kg) 1814.40 7257.60 3628.80

Bag (kg) 22.68 22.68 33.29

*Estimated weight

The raw ingredients used for manufacturing of 10-10-10 by BP1, BP2, and BP3 are given

in Table 10.2; where BP1, BP2, and BP3 designate blend plant 1, 2, and 3, respectively. Urea

and potash were the only common raw ingredients among the three blend plants for the

production of 10-10-10. Raw ingredients were handled following normal operating procedures in

each blend plant. In order to prepare a well mixed 10-10-10 blend, the mixer was usually

operated for 4-5 minutes, following the manufacturers' recommendations after loading the raw

ingredients.

200

Table 10.2 Blending formula for 10-10-10 at three different blend plants (kg) Plant Urea Potash DAP MAP Ammonium

Sulfate Filler Batch

Capacity BP1 118.0 317.5 - 362.9 426.4 589.7 1,814.5 BP2 1,106.8 1,215.7 762.1 725.8 - 3,447.4 7,257.8 BP3 480.8 616.9 798.3 - - 1,732.8 3,628.8

The particle size analysis was performed using US standard sieves of (2)1/4 series starting

from number 4 to 16. Also, chemical analysis was performed based on the AOAC standards

through Pennsylvania Department of Agriculture (PDA).

10.3.1 Trier specification

Five different triers were used for collecting samples from different locations: Missouri D

Tube, 990.6 mm Double Tube, Stream Sampling Cup, single tube 12.7 mm, and AOAC single

tube 19.1 mm. The specifications of these five triers are given in Table 10.3 and schematics of

the AOAC single tube, 990.6 mm Double Tube (B), Missouri D Tube (A), and Sampling Cup

(C) are shown in Figure 10.1(a), (b), and (c). Missouri D Tube, 990.6 mm Double Tube, and

stream Sampling Cup were used for sample collection from the raw materials in storage bins,

front end loader, and mixer outlet, respectively (TFI, 1996). Figure 10.1(d) and 10.1(e) show the

sampling of a stream using the Stream Sampling Cup and the front end loader using the 990.6

mm Double Tube trier. The AOAC single tube 12.7 and 19.1 mm were used for sampling only

the bagged fertilizer. The four triers (Double Tube, Missouri D Tube, sampling cup, and 19.1

mm width trier) were used by one PDA inspectors and one trier (12.7 mm width) by second PDA

inspector so that sampling results could be compared for human error through analysis of size

distributions of blend 10-10-10 (TFI, 1996).

Table 10.3 Specifications of the five triers used for collecting samples of dry solid fertilizer ingredients and from bagged 10-10-10 blends

Sampler Specifications Compartment Openings Trier/Sample Cup Length

(mm) OD

(mm) ID

(mm) Number Width (mm)

Length (mm)

Missouri D Tube (A*) 1244.6 31.5 25.4 1 - 1092.2 990.6 mm Double Tube (B*) - - - 6 - - Stream Cup (C*) 254.0 - 101.6 1 19.1 - Single Tube (D*) 927.1 22.3 18.7 1 12.7 812.8 AOAC Single Tube (E*) 952.5 25.4 22.3 1 19.1 800.1 *Identification letter

201

10.3.2 Sampling procedures and preparation

With the given resources, a separate experiment was not designed but followed the

experimental design of Caine and Hancock (1998) for studying 12.7 mm and 19.1 mm opening

widths triers. The 10-10-10 blended formulation in the prepared batch was discharged and

collected in 22.68 kg bags in BP1 and BP2 plants and 36.29 kg bags in BP3 plant. For collecting

samples from the bags, an innovative time-sequence procedure for sampling the bags was

devised and implemented. For this, the bags in each lot (i.e., batch) were separated into four

sublots, i.e., each sublot corresponded to one quarter of the batch in the lot. For example, the

total blended lot size at BP1 was 1814.5 kg, i.e., the number of 22.68 kg bags filled was 80

(=1,814.5 kg/22.68 kg). The total number of bags was divided into four sublots each comprising

20 bags. The 20 bags filled in each quarter were stored separately to determine the variation in

the chemical composition, SGN, and UI during the filling of well-mixed samples in bags. In this

article, the bags filled with 10-10-10 in the first, second, third, and fourth quarters are designated

as 10-10-10(1), 10-10-10(2), 10-10-10(3), and 10-10-10(4), respectively, which were sampled

using 12.7 and 19.1 mm triers (TFI, 1996). A similar procedure was followed at plants BP2 and

BP3. The bags were sampled using the single tube triers of opening width 12.7 and 19.1 mm

from the same hole by the first and then the second PDA inspector following the sequence given

in Table 10.4. The sequence of sampling resulted in each trier being used once for each of the ten

bags. Sampled portions from each trier were collected in separate containers. The raw

ingredients and blended samples obtained from triers were first sub-divided into two halves

using a riffler for: (1) size analysis and (2) chemical analysis and retention by the manufacturer

at the blend facility. Fist half was kept for size analysis using US standard sieve in the Powder

Mechanics Lab at Penn State. The second half was further sub-divided into two halves using the

same riffler, one portion was for chemical analysis and one portion was for the manufacturer to

retain for further analysis, if desired. The chemical analysis was performed through PDA for

determination of total nitrogen, available phosphate, and/or soluble potash in raw ingredients and

the 10-10-10 blend samples. The particle size analysis was done using the US standard sieve

numbers 5 (4.00 mm), 6 (3.35 mm), 7 (2.80 mm), 8 (2.36 mm), 10 (2.00 mm), 12 (1.70 mm), 14

(1.40 mm), and 16 (1.20 mm). The sieve numbers below 16 were not used because the weight

proportion of these size fractions was less than 0.1%.

202

Table 10.4 Sequence of the use of two triers for securing samples from 22.68 kg and 33.29 bags using the same hole*

Bag Number 1 2 3 4 5 6 7 8 9 10 D E D E D E D E D E Trier Sequence** E D E D E D E D E D

*Material condition: Free flowing **D = 12.7 mm trier, E = AOAC 19.1 mm trier

203

Figure 10.1 Schematic of different triers: (a) single and double tube, (b) Missouri D tube, (c) sampling cup, (d) stream sample with sampling cup, and (e) sampling front end loader

(TFI, 1996)

(a) (b)

(c)

(d)

(e)

204


For the three plants BP1, BP2, and BP3, the chemical analysis, SGN and UI results for

the raw ingredients and the 10-10-10 formulation sampled using the five triers are summarized in

Tables 10.5, 10.6, and 10.7, respectively. The results are presented and discussed in the

following sections.

10.4.1 Size distribution of raw ingredient and 10-10-10 blend

Raw materials used in manufacturing of 10-10-10 blend were sieved for particle size

analysis. A typical particle size distribution of urea and 10-10-10 blend from BP1 is shown in

Figures 10.2 and 10.3, respectively. Figures 10.2a, 10.2b, and 10.2c show the percent cumulative

mass of three repeated samples of urea collected from bins and Figure 10.2d shows the percent

cumulative mass of urea samples from front end loaders. Minor variation in size distribution was

observed in samples between front end loaders and bins for all raw ingredients and three blend

plants. Samples from front end loaders received more fines compared to bins. Particle size

distributions of samples from bins and front end loaders did not show any definite trend. These

results are consistent with the results reported by Baker et al. in 1967.

From BP1, the highest mass proportion was found on sieve size 2.36 mm for all the raw

ingredients from bins and front end loaders, i.e., potash, urea, ammonium sulfate, MAP, and

filler. The collected mass of urea and potash on sieve sizes was 2.80 mm, 3.35 mm, and 2.00 mm

in this order followed the sieve size 2.36 mm. similar trends were found for other three raw

ingredients ammonium sulfate, MAP, and filler, except order of mass collection on sieve sizes

3.35 and 2.00 mm was reversed. Size distribution of filler was succinct compared to other raw

ingredients but more fines were collected from ammonium sulfate. The size distributions from

samples collected from four quarters followed the similar trend as raw materials. Difference in

size distribution of raw ingredients was sufficient to cause segregation in blend. Results of 10-

10-10 blends in Table 10.5 confirmed the segregation in blends while mixing and handling.

For BP2, the mass proportions of raw ingredients urea, potash (pink), and DAP were the

highest on sieve size 2.80 mm followed by sieve sizes 2.36 mm and 3.35 mm in this order.

Particle size of urea and potash (pink) was also large and very small amount of fines were

collected. Whereas the mass proportion of potash (white), MAP, and filler was the highest on

sieve size 2.36 mm followed by sieve sizes 2.80 mm and 3.35 mm in this order. Fines

205

proportions were higher in the later three compared to three raw ingredients discussed early. The

higher proportion of large size particles for urea, potash (pink), and DAP resulted in higher SGN

and UI. Small proportion of large size and high proportion of fines in potash (white), MAP, and

filler resulted in smaller SGN and UI. Particle size distribution results of samples from four

quarters of 10-10-10 blend showed similar trend as raw ingredients. However, samples form first

and second quarters received more fines smaller than size 1.70 mm compared to third and fourth

quarters. Large proportion of fines in first and second quarters showed the presence of large

amount of smaller size MAP, filler, and potash (white). The difference in SGN and UI between

these two groups of raw ingredients was sufficient to segregate. Here percolation segregation

was observed in the 10-10-10 blend (Table 10.6). Initially more fines were collected in samples

resulted in deficiency of higher size raw ingredients leading to chemically deficient samples.

Later four samples passed the chemical analysis test because of size matching among raw

ingredients after percolation of fines in early stage.

In case of BP3, the mass collected for potash was the highest on sieve size 3.35 mm

followed by sieve sizes 2.80 mm and 2.36 mm in this order resulted in very high SGN. Unlike

potash, mass collected for urea, DAP, and filler was the highest on sieve size 2.36 mm followed

by sieve sizes 2.80 mm, 2.00 mm, and 1.70 mm in this order. Size distributions of three raw

ingredients were large compared to potash. Size distribution results showed that more fines were

found in filler compared to other raw ingredients. Difference in SGN and UI were very large

between potash and other raw ingredients made blend more susceptible to segregation. Large

difference in SGN and higher proportion of fines in filler resulted in segregation of blend leading

to deficient 10-10-10 blend in N-P-K for first two quarters and a sample in third quarter. Size

distribution results of samples of 10-10-10 blend showed similar results as raw ingredients urea,

DAP, and filler. Little higher SGN of samples from blend compared to urea, DAP, and filler

showed presence of higher SGN potash. Samples from first and second quarters contained more

fines compared to third and fourth quarters, except a sample from third quarter (Table 10.7).

Comparing chemical and size analyses result of four quarters confirmed the segregation in blend.

The segregation in blend might have happened in mixer, holding bin, or in bag.

206

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Figure 10.2 Typical size distribution of urea samples from bin of SGN (a) 270, (b) 271, (c) 271, and front end loader (d) 266

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Figure 10.3 Typical size distribution of 10-10-10 (a) 1, (b) 2, (c) 3, and (d) 4 quarters, broken line 12.7 (252-1, 256-2, 251-3, and 246-4) and solid line 19.1 (252-1, 268-2, 252-3,

249-4)

(b) (a)

(c) (d)

(b) (a)

(c) (d)

207

10.4.2 Blend Plant 1 (BP1)

From Table 10.5, the average SGNs of the three samples from bins for potash,

ammonium sulfate, MAP, urea, and filler were 278, 248, 262, 271, and 238, respectively;

whereas, the SGNs of the samples collected from the front end loader bucket for the same

materials were 275 (-1.0% of the raw ingredient SGN in storage), 248 (0%), 275 (+5.0%), 266 (-

1.8%), and 230 (-3.4%), respectively. In the manufacturing of 10-10-10 blend, more than 50% of

materials (ammonium sulfate and filler) had relatively small SGNs between 230 and 249. The

SGN of potash was different from the other raw ingredients. However, all the samples collected

from 10 out of 20 bags filled during the four different quarters using triers 19.1 and 12.7 mm

passed the chemical analysis test; even though, the filler and ammonium sulfate, with smaller

SGNs, had strong influence in determining the SGN of 10-10-10 formulation. The high

proportion (>50%) of small SGN materials influenced the SGN of 10-10-10 blend (SGN = 257

in the stream cut sample of the blend). For samples from the bagged fertilizer collected using

19.1 and 12.7 mm triers, the SGN is either the same or higher for the 19.1 mm trier, i.e., these

results are in partial agreement with the study of Caine and Hancock (1998) which concluded

that the larger width trier collected more larger particles. However, the samples collected from

10-10-10(1) blend using the 12.7 mm trier had more potash (10.30% vs 9.97% for the19.1 trier),

which had the largest SGN among all the five raw ingredients This observation is counter to the

hypothesis that a smaller width trier biases the samples toward greater amount of fines; i.e., in

partial disagreement with the Caine and Hancock (1998) conclusion.

208

Table 10.5 Size and chemical analyses of different materials at various sampling locations for blend plant BP1

Material Sampling Location

Trier SGN UI Chemical Analysis N-P-K

Pass/Fail

Bin A 281 275 278

44 41 45

0.00-0.00-61.19 0.00-0.00-61.15 0.00-0.00-60.72

Pass Pass Pass

Potash

Front end loader

B 275 38 0.00-0.00-60.85 Pass

Bin A 247 249 249

41 46 40

21.10-0.00-0.00 21.10-0.00-0.00 20.70-0.00-0.00

Pass Pass Pass

Ammonium Sulfate

Front end loader

B 248 44 21.0-0.00-0.00 Pass

Bin A 265 252 269

46 41 47

10.96-52.36-0.00 10.80-52.35-0.00 11.00-52.38-0.00

Pass Pass Pass

MAP

Front end loader

B 275 50 10.80-52.37-0.00 Pass

Bin A 270 271 271

38 42 36

46.40-0.00-0.00 46.70-0.00-0.00 46.80-0.00-0.00

Pass Pass Pass

Urea

Front end loader

B 266

43 46.30-0.00-0.00 Pass

Bin A 242 241 232

42 38 48

Not tested

- - -

Filler

Front end loader

B 230 51 Not tested -

10-10-10 Stream cut C 257 42 9.76-10.22-9.90 Pass 10-10-10(1)

Bags (10 out of 20)

E D

252 252

41 42

9.61-9.83-9.97 9.48-9.90-10.30

Pass Pass

10-10-10(2) Bags (10 out of 20)

D E

256 268

41 48

9.50-9.93-10.53 9.93-9.98-10.50

Pass Pass

10-10-10(3) Bags (10 out of 20)

E D

252 251

41 42

10.10-10.09-9.91 9.70-10.09-9.84

Pass Pass

10-10-10(4) Bags (10 out of 20)

D E

246 249

43 43

9.80-9.92-9.74 9.26-10.25-10.48

Pass Pass

209


The average SGN of samples from the bins for potash (pink), potash (white), DAP,

MAP, urea, and filler were 292, 259, 293, 278, 300 and 249, respectively; whereas, the SGN of

samples collected from front end loaders for the same materials were 289 (-1.0% of storage

SGN), 261 (+0.8%), 271 (-7.5%), 266 (-4.3%), 271 (-9.7%), and 237 (-4.8%), respectively

(Table 10.6). In the manufacturing of the 10-10-10 blend, about 50% of materials (potash white

and filler) have SGN between 237 and 263. The SGNs of potash (pink), urea, and DAP were

higher than the other raw ingredients. Samples were collected from 10 out of 80 bags filled per

quarter for each of the four quarters of the batch. Of the total of eight 10-10-10 samples from the

bags the samples from the first two quarters failed while the samples from the last two quarters

passed the chemical analysis regardless of which trier was used to collect the sample (Table

10.6). It seems that small SGN materials, i.e., the filler and potash white, had a strong influence

in determining the SGN of 10-10-10 formulation (SGN = 263 in the stream cut sample of the

blend). In the first four 10-10-10(quarters 1 and 2) samples, the SGNs were in the upper 240s or

lower 250s. But in the next four samples of 10-10-10(quarters 3 and 4), the SGNs were larger

than 257. The samples in the first and second quarters failed chemical analysis test because of

size segregation due to large size distribution of raw ingredients. The SGN was either the same

or higher for 19.1 vs. 12.7 mm trier. Samples collected from 10-10-10(1 and 2) blend using these

two triers 19.1 and 12.7 mm collected more potash or urea. The urea and potash (pink) had

higher SGN compared with other raw ingredients used in the formulation of 10-10-10; similar to

the observation for BP1. The average SGN and UI of 10-10-10(1 and 2) samples that failed the

chemical analysis were 249 and 44, respectively, compared with 10-10-10(3 and 4) samples that

passed were 258 and 43, respectively. Even though the UI value of samples from quarters 3 and

4 dropped by 2.3% (not a good trend), the increase in SGN of the samples from quarters 3 and 4

by +3.6% was sufficient for the samples to pass the chemical analysis tests. The chemical

analysis results show that samples were deficient due to lower percentage of urea and potash and

these two raw ingredients had higher SGNs compared with other raw ingredients.

210



Trier SGN UI Chemical Analysis N-P-K

Pass/Fail

Bin A 293 292 292

53 53 52

0.00-0.00-61.99 0.00-0.00-61.31 0.00-0.00-60.82

Pass Pass Pass

Potash (pink)

Front end loader

B 289 47 0.00-0.00-60.20 Pass

Bin A 252 263 262

41 41 41

0.00-0.00-61.99 0.00-0.00-62.72 0.00-0.00-62.97

Pass Pass Pass

Potash (white)

Front end loader

B 261 38 0.00-0.00-61.96 Pass

Bin A 290 293 297

46 54 52

18.20-46.13-0.00 18.30-46.44-0.00 18.30-46.44-0.00

Pass Pass Pass

DAP

Front end loader

B 271 42 18.40-46.40-0.00 Pass

Bin A 279 277 277

51 47 47

10.90-52.22-0.00 10.85-51.82-0.00 10-90-52.35-0.00

Pass Pass Pass

MAP

Front end loader

B 266 48 10.80-51.28-0.00 Pass

Bin A 300 301 299

55 55 51

47.20-0.00-0.00 46.70-0.00-0.00

46.80-0-0

Pass Pass Pass

Urea

Front end loader

B 271 42 47.20-0.00-0.00 Pass

Bin A 246 251 251

50 47 47

Not tested - - -

Filler

Front end loader

B 237 46 Not tested -

10-10-10 Stream cut C 263 45 9.71-10.00-11.00 Pass 10-10-10(1) Bags (10 out

of 80) E D

248 248

43 42

9.16-8.72-9.12 10.00-8.93-8.89

Fail Fail

10-10-10(2) Bags (10 out of 80)

D E

246 253

44 46

7.99-9.47-11.08 7.56-8.83-11.11

Fail Fail

10-10-10(3) Bags (10 out of 80)

E D

257 257

45 46

9.28-10.30-10.95 11.10-9.59-11.08

Pass Pass

10-10-10(4) Bags (10 out of 80)

D E

257 261

40 42

11.30-10.64-8.54 12.10-10.23-9.89

Pass Pass

211


The average SGN of samples from bins for potash, DAP, urea, and filler were 298, 250,

246, and 250, respectively; whereas, the SGNs of samples collected from front end loaders for

the same materials were 330 (+10.7% of the SGN in the storage bin), 258 (+3.2%), 243 (+1.2%),

and 269 (+7.6%), respectively (Table 10.7). In the manufacturing of 10-10-10 blend, more than

80% of materials (urea, DAP and filler) have SGN equal to or below 250. Despite the low SGN

of the three raw ingredients compared with potash, the SGN of 10-10-10 blend for the four

quarters was either 255 or more.

212



Trier SGN UI Chemical Analysis

Pass/Fail

Bin A 297 303 294

50 49 49

0.00-0.00-60.74 0.00-0.00-60.87 0.00-0.00-61.28

Pass Pass Pass

Potash

Front end loader

B 330 54 0.00-0.00-60.43 Pass

Bin A 253 250 248

52 52 47

18.30-45.74-0.00 18.22-46.29-0.00 18.20-46.31-0.00

Pass Pass Pass

DAP

Front end loader

B 258 258

61 49

18.06-45.90-0.00 18.06-46.15-0.00

Pass

Bin A 247 246 246

57 57 57

46.70-0.00-0.00 46.80-0.00-0.00 47.20-0.00-0.00

Pass Pass Pass

Urea

Front end loader

B 243 58 46.15-0.00-0.00 Pass

Filler Bin A 249 253 247

45 45 44

Not tested - - -

Front end loader

B 276 262

61 47

Not tested -

10-10-10 Stream cut C 264 45 9.77-10.18-10.20 Pass 10-10-10(1) Bags (10 out

of 25) E D

257 255

45 45

8.74-9.57-8.64 9.68-10.00-8.26

Fail Fail

10-10-10(2) Bag (10 out of 25)

D E

262 262

47 47

9.28-9.32-9.48 9.36-9.22-9.70

Fail Fail

10-10-10(3) Bag (10 out of 25)

E D

259 256

47 47

10.31-10.00-9.00 8.72-8.92-7.84

Pass Fail

10-10-10(4) Bag (10 out of 25)

D E

259 263

46 47

10.63-10.25-9.21 11.07-10.26-9.33

Pass Pass

10.4.5 Theoretical and experimentally measured SGN and UI

Table 10.8 summarizes the theoretical and Tables 10.5, 10.6, and 10.7 experimentally

measured SGNs and UIs based on samples collected from front end loader and the best

representative samples from bins used for manufacturing fertilizer blends, of the 10-10-10 blend

formulations from BP1, BP2, and BP3, respectively. In determining the size-match of the raw

ingredients, the SGN and UI values from the front end loader are the most representative as these

were actually used to prepare the 10-10-10 blend; therefore, those SGNs and UIs are used. Also,

213

for BP2, 7,257.8 kg of 10-10-10 blended formulation was batch-mixed, which required more

than one bucket load of each of the five raw ingredients (Table 10.1); however, only the first

bucket load of the front end loader was sampled due to time and resource constraints. Based on

the TFI guidelines, for proper size matching both the SGNs and UIs of the ingredients are

recommended to be within the theoretical range SGN± 10% and UI± 10% of the 10-10-10 blend

formulation. For BP1, this implied that both SGN and UI of the raw ingredients must be within

228 to 278 and 41 to 51, respectively, to be properly size-matched. From Table 10.5, only the UI

of potash (38) was outside the range; therefore, one out of the five ingredients was not size-

matched. Similarly, for BP2, both SGN and UI of the raw ingredients must be within 229 to 281

and 40 to 50, respectively. Therefore, from Table 10.6, the SGN of potash (pink) 289 and UI of

potash (white) 38 are outside the range; i.e., two out of the six ingredients were not size-matched.

Finally, for BP3 based on SGN of 277 and UI of 59 (Table 10.7), both SGN and UI of the raw

ingredients must be within 249 to 305 and 53 to 65, respectively. From Table 10.7, the SGN of

potash (330) and urea (243) and UI of DAP (49) and filler in the second load (47) are outside the

range; therefore, four out of the five ingredients were not size-matched.

The largest difference in SGN values for the 10-10-10 blend samples obtained using 12.7

vs. 19.1mm trier for BP1, BP2, and BP3, were 12, 7, and 4, respectively; whereas, the largest

difference in UI values for BP1, BP2, and BP3 were 7, 2, and 1, respectively. A closer analysis

of the data showed that the largest differences in SGN and UI occurred for the same sample 10-

10-10(2) for BP1. Except for this sample, all SGNs and UIs of 12.7 vs. 19.1 mm trier samples

were within 7 and 2, respectively; these represent small differences. Caine and Hancock (1998)

reported the largest SGN difference of 12 for five different blends when using 12.7 vs. 19.1mm

trier. Therefore, the differences in the SGN values measured in this study are similar to those

reported by Caine and Hancock (1998).

Table 10.8 Theoretical SGN and UI based on samples from bin, front end loader, and

stream sampling at BP1, BP2, and BP3 Bin Front end loader Stream sampling SGN (BP1) 254 253 257 UI (BP1) 43 46 42 SGN (BP2) 269 255 263 UI (BP2) 49 45 45 SGN (BP3) 258 270 264 UI (BP3) 48 59 45

214

From Tables 10.8 and 10.6 for BP2, the samples collected from bags using 19.1 and 12.7

mm width triers failed when the SGN of 10-10-10 samples was lower than any one of the

theoretical SGN at three different locations. For BP2, the minimum theoretical SGN was

calculated at the front end loader 255, the samples collected from bags failed when SGN of blend

was lower than 255. From Tables 10.8 and 10.7 for BP3, the minimum theoretical SGN of 258

was found at the bin location. The 10-10-10 samples collected from bags failed when SGN was

below 258. There was no such observation for BP1 (Tables 10.8 and 10.5). A plausible reason

might be the lower particle size of fertilizers.

For BP1, the overall range of SGNs and UIs of the ingredients were from 230 to 281 and

36 to 51, respectively; for BP2 the ranges were from 237 to 301 and 38 to 55, respectively; and

for BP3 the ranges were from 243 to 330 and 44 to 61, respectively. In general, these represent

large spreads in SGN and UI of raw ingredients, with appreciable variability from plant-to-plant.

10.5 Summary of observations The following concluding observations can be made based on chemical and size analyses

of samples obtained from the three blend plants.

1) Ingredient samples:

Size analysis of ingredients from the three blend plants showed that there was a large

spread in SGNs and UIs, with appreciable variability from plant-to-plant.

One out of five ingredients in BP1, two out of six ingredients in BP2, and five out of

six ingredients in BP3 were not size-matched.

2) 10-10-10 blend samples using 12.7 and 19.1 mms triers:

From all three blend plants and for all 10-10-10 bagged fertilizers sampled, the

average SGN of samples was 257 when using 19.1 mm width trier compared with

254 (-1.2% compared with SGN=257) when using 12.7 mm width trier; the

corresponding UIs were 45 and 44 (-2.2%), respectively.

While the SGN of 19.1 mm width trier was larger than the 12.7 mm width trier, there

were no substantial differences between the SGNs and UIs of the two different width

triers, i.e., except for 10-10-10(2) from BP1, all SGNs and UIs were within 7 and 2,

respectively.

215

Eleven out of the twelve samples from bagged fertilizers using 12.7 mm vs. 19.1 mm

had the same outcomes, i.e., only one sample from BP3 10-10-10(3) using 12.7 mm

vs. 19.1 mm had a conflicting outcome – the sample obtained using 19.1 mm width

trier (SGN=259, UI=47) passed, whereas, the sample with 12.7 mm trier (SGN=256,

UI=47) failed the chemical analysis.

The mass collected by 12.7 mm trier was higher than the mass collected by 19.1 mm

trier.

The percent mass collected by 19.1 mm and 12.7 mm triers was the highest for sieve

number 8.

Caine and Hancock (1998) reported the largest SGN difference of 12 for five

different blends when using 12.7 mm vs. 19.1 mm trier for sampling. Therefore, the

differences in the SGN values measured in this study are similar to those reported by

Caine and Hancock.

From the analyses of 10-10-10 samples in each of the four quarters, segregation

during discharge of the blend from the storage bin was observed.

Overall, only minor differences were observed between the chemical and size

analyses of samples from bagged fertilizers obtained using the 19.1 mm vs. 12.7 mm

width triers.

10.6 Key Findings Solid fertilizers from different locations in three blend plants were sampled to determine

chemical analysis, SGN, and UI of raw ingredients and blend formulation 10-10-10. Five

different triers were used to sample fertilizers from different locations, i.e., rail car or truck,

front-end-loader, stream sampling, and 10-10-10 bags. The formulation 10-10-10 was sampled

from bags using 12.7 and 19.1 mm triers. Size analysis of ingredients and 10-10-10 from three

blend plants showed that there were variations in SGNs and UIs from plant-to-plant and from

sample-to-sample. The SGN and UI of samples collected using 19.1 mm trier was either the

same or higher compared with 12.7 mm trier samples. Only minor differences were found

between samples collected from these two single tube triers; whether these minor differences

were significant or not, more detailed experimentation needs to be done.

216

10.7 References


Caine, D. and M. R. Hancock. 1998. Effect of slot width in bagged fertilizer sampling. General referee report, fertilizers and agricultural liming materials: Journal of AOAC International 89(1): 211.

Fiskell, J. G. A. and V. Chew. 1957. Sieve analysis of some fertilizer mixtures. Journal of Association of Official Agricultural Chemists 40(3): 936-948.

Fiskell, J. G. and W. H. Kelly, J. M. Myers, R. C. Crooks, R. Dixon, and J. J. Taylor. 1958. Variability in individual core analysis of samples of a 10-10-10 and 8-0-8 fertilizer drawn by several sampling devices. Journal of Association of Official Agricultural Chemists 41(3): 640-649.


Kane, P. F. 2005. Fertilizers, Chapter 2, section 2.1.01 – AOAC Official Method 929.01 Sampling of Solids Fertilizers. AOAC International, March.

Sauchelli, V. and A. J. Duncan. 1960. An experiment in the sampling and analysis of bagged fertilizer. Journal of Association of Official Agricultural Chemists 43(4): 831-904.

TFI. 1996. Bulk Blend Quality Control Manual. Published by The Fertilizer Institute, Washington, D.C.

217

11. CHAPTER – VIBRATION-INDUCED SIZE SEGREGATION IN BAGGED FERTILIZER

11.1 Abstract Percolation of fines in bagged blended fertilizers of continuous size distributions was

investigated at two frequencies 5 and 7 Hz. Ferilizer bags were subjected to 5 and 7 Hz

frequencies using an industrial vibration table. The samples from bags were collected using two

single tube triers of opening width 12.7 mm and 19.1 mm following the AOAC procedure for

sample collection from bagged fertilizers. The same bag was used for sample collection at

frequencies 5 and 7 Hz. At the frequency of 5 Hz, the samples were collected at time 0, 15, and

30 minutes, whereas at the frequency of 7 Hz the samples were collected at the time 15 and 30

minutes followed by 5 Hz frequency test. For triers 12.7 mm and 19.1 mm, the percent mass

retained on the sieve number 8 (opening width = 2.36 mm) was the highest. The sieve numbers 7

(2.80 mm) and 10 (2.00 mm) followed the sieve number 8 (2.36 mm) in retaining the percent

mass in this order. The SGN of fertilizer samples collected by 19.1 mm trier was 251, 233, and

225 at time 0, 15, and 30 minutes, respectively. For the same trier, the UI of samples was 39, 42,

and 40 at time 0, 15, and 30 minutes, respectively. The SGN of fertilizer samples collected by

12.7 mm trier was 235, 236, and 229 at time 0, 15, and 30 minutes, respectively. For the same

trier, the UI of samples was 42, 43, and 40 at time 0, 15, and 30 minutes, respectively. The SGN

of fertilizer decreased with time, except at 15 minutes for 12.7 mm trier, whereas UI first

increased and then decreased with time at the frequency of 5 Hz. The particles size distribution

were not significantly affected at the frequency of 5 Hz (p>0.05). The SGN of fertilizer samples

collected by 19.1 mm trier was 239 and 267 at time 15 and 30 minutes, respectively. For the

same trier, the UI of samples was 42 and 48 at time 15 and 30 minutes, respectively. The SGN of

fertilizer samples collected by 12.7 mm trier was 233 and 267 at time 15 and 30 minutes,

respectively. For the same trier, the UI of samples was 43 and 47 at time 15 and 30 minutes,

respectively. The SGN and UI increased with time at frequency of 7 Hz. The proportion of fines

decreased with time in the fertilizer bags and results are consistent with the literature that

vibration induced percolation segregation when physical property of particulate was different.

The SGN and UI of samples collected by 12.7 mm and 19.1 mm triers were not significantly

different (p>0.05).

218

11.2 Introduction

Segregation is a ubiquitous phenomenon in bulk solids and responsible for making

uniform mixture spatially non-uniform when bulk solids are subjected to motion. Its occurrence

during various unit operations such as handling, flow, mixing, and storage is of utmost concern

to industries involved in processing and manufacturing of particulates for making products.

Particulate materials related unit operations are performed in many industries such as agriculture,

chemical, cosmetic, electronic, energy, fertilizer, food, mining, and materials. During these unit

operations, segregation occurs leading to economic loss (Carson et al., 1986 and Bates, 1997). It

has been reported also that segregation in particulates is of a great concern to geologist dealing

with geophysical flows (for instance, Davies, 1988; Savage and Hutter, 1991; Savage, 1992;

McElwaine and Nishimura, 2000). Blended fertilizer in bags and in bulk segregate when

subjected to different motion conditions leading to non-uniform mixture causing economic loss

to blenders and end users (Jha et al., 2007; Bradley and Farnish, 2005; and Bridle et al., 2004).

To minimize segregation, if not eliminated, its understanding at fundamental level is essential.

Researchers have been involved for decades in identifying parameters and mechanisms

responsible for segregation. It has been reported that size and size distributions, shape,

morphology, contact friction, elasticity, brittleness, density, chemical affinities, ability to absorb

moisture, and magnetic properties, extent of movement, intensity of movement are responsible

for segregation in particulate materials (Rosato et al., 2002).

To date, thirteen segregation mechanisms have been identified for processing and

manufacturing of granular solids, i.e., trajectory, air current, rolling, sieving and sifting, impact,

embedding, angle of repose, push-way, displacement or floating, percolation, fluidization,

agglomeration, and, concentration driven displacement (Mosby et al., 1996; Salter, 1998; de

Silva et al., 2000). The most important fact about segregation is, it occurs only under dynamic

conditions (Vallance and Savage, 2000). Within this breadth, segregation also occurs when

energy imparted in the form of shear (Lun et al., 1984; Savage, 1991 and 1992; Rosato and Kim,

1994; Karion and Hunt, 2000; Duffy and Puri, 2002; Tang and Puri, 2005; and Jha et al., 2007a),

gravity (Fowler, 1960 and 1961; Campbell, 1990; and Walton, 1991), and vibration, (Williams

and Shields, 1967; Ahmad and Smalley, 1973; Fauve et al., 1989; Laroche et al., 1989; Clement

and Rajchenbach, 1991; Brennen et al., 1993; Hunt et al., 1994; Lan and Rosato, 1997; Yang,

2006; Ellenberger et al., 2006).

219

Based on the above literature review and the need of segregation study in the fertilizer

industry, an experiment was designed to study the effect of vibration frequency on size

distribution of blended fertilizer at a particular location. The scope of this article is limited to

segregation of bagged blended fertilizer. An industrial vibrator (Model no. 899548 Vibrating

Table with Motor B3-1000-1A-4, Cougar Industries, Peru, IL) was used to study the effect of

vibration on bagged blended fertilizer. Frequency and amplitude were dependent for the

industrial vibrator, i.e., change in frequency adjusted amplitude accordingly and vice-versa . The

objectives of the study were: 1) to sample blended fertilizer bags, 2) to perform size analysis of

blends from three different plants, 3) to determine size distributions at frequencies 5 and 7 Hz,

and 4) to measure size distribution at different times.


It is well documented that low analysis fertilizer blends such as the 10-10-10 formulation

are most susceptible towards segregation under different operating conditions. The formulation

10-10-10 represents the minimum chemical analysis of 10% nitrogen, 10% available phosphate,

and 10% soluble potash in this order. Therefore, the formulation 10-10-10 prepared with dry

solid fertilizers was selected for study and bags were collected from three blending plants in the

Commonwealth of Pennsylvania. The blend plants were designated as BP1, BP2, and BP3 for

anonymity. The raw ingredients used by blending plants BP1, BP2, and BP3 were different. The

22.68 kg bags from BP1 contain urea, potash, MAP, ammonium sulfate, and filler, the 22.68 kg

bags from BP2 contains urea, potash, DAP, MAP, and filler, and the 33.29 kg bags from BP3

contains urea, potash, DAP, and filler.


An industrial vibrator was used to study the effect of vibration on the size distributions of

bagged fertilizer (Figures 11.1 and 11.2). Theoretically, motor can vibrate the vibration table

from 0 to 60 Hz. In this vibrator, frequency and amplitude were dependent, i.e., either frequency

or amplitude can be controlled for the desired output. Initial calibration using empty table and

22.68 kg bags showed that the actual frequency was one-half of the set frequency, for example

for the set frequency of 10 Hz actual frequency was 5 Hz (Figure 11.3).

220

Figure 11.1 Vibrating table with bag placed on vibration plate

221

Figu

re 1

1.2

Sche

mat

ic o

f vib

ratin

g ta

ble

(sou

rce:

Cou

gar

Indu

stri

es In

c.)

222

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0

Controller frequency setting (Hz)

Mea

sure

d fre

quen

cy (H

z)

Empty Table

22.68 kg bags on table

Figure 11.3 Preliminary calibration using empty table and 22.68 kg bag on table

The bags of 22.68 and 33.29 kgs, one at a time, were placed on vibration table. Five bags

of 10-10-10 were tested from three blending plants. The number of bags was decided based on

the actual sample collection from bags for chemical analysis test, five replications were

performed for each set of experiments for testing size segregation using industrial vibrator. A

complete block design was selected for data analysis (Table 11.1). A blend plant was considered

as a block of experiment. Within each block, all treatments (replicate = 1 × 5 = 5) were randomly

assigned. Two vibration frequencies 5 and 7 Hz were chosen for study to have consistent result

with the PSSC-II results under different intensity of motion conditions. Preliminary tests showed

that vibrator can not work effectively below frequency of 5 Hz. The lowest effective frequency

of 5 Hz and the other frequency of 7 Hz were chosen. The 7 Hz was chosen so that bags did not

displace (i.e., move) on the vibration plate during test. The PSSC-II was operated for data

collection during shear tests using fertilizer upto 30 minutes. The data were collected three times

at 0, 15, and 30 minutes for a particular set of frequency to represent industrial conditions and

also efficient use of time and resources. At the frequency of 5 Hz, samples were collected at 0,

15, and 30 minutes of vibration followed by sample collection after 15 and 30 minutes at the

frequency of 7 Hz without replacing bags. Ideally, the tests could be conducted at each of these

two frequencies for individual bag. The bags were not in sufficient numbers due to resource and

cost constraints; therefore, the same bags were used at frequencies of 5 Hz and 7 Hz.

223

Table 11.1 Design of experiment for vibration of 10-10-10 bags Parameter Number

Number of blend plants – BP1, BP2, and BP3 3

Frequency (5 Hz and 7 Hz) 2

Time (minutes) – 0, 15, and 30 3

Samplers – 12.7 and 19.1 mm width opening 2

Replications 5

Total 180

11.3.2 Sampling procedures and preparation

Two different samplers were used for collecting samples from bags: single tube 12.7 mm,

and AOAC single tube 19.1 mm. The specifications of these two samplers are given in Table

11.2 and schematics of the AOAC single tube sampler is given in Figure 11.4.

Table 11.2 Specifications of the triers used for collecting samples from bagged fertilizer Sampler Specifications

Compartment Openings Trier/Sample Cup Length (mm)

OD (mm)

ID (mm) Number Width

(mm) Length (mm)

Single Tube 927.1 22.3 18.7 1 12.7 812.8 AOAC Single Tube 952.5 25.4 22.3 1 19.1 800.1

*Identification letter

The 10-10-10 formulation blended in a given batch was discharged and collected in 22.68

kg bags in BP1 and BP2 plants and 33.29 kg bags in BP3 plant. Per the AOAC standard, five

blended fertilizer bags were randomly sampled. The bags were sampled from the same hole

using the two triers of opening width 12.7 mm and 19.1 mm. The particle size analysis of

samples was done using the US standard sieve numbers 5 (opening width = 4.00 mm), 6 (3.35

mm), 7 (2.80 mm), 8 (2.36 mm), 10 (2.00 mm), 12 (1.70 mm), 14 (1.40 mm), 16 (1.20 mm), and

pan. The sieve numbers below 16 were not used because the weight proportion was less than

0.1%. Sequence of use of two triers 12.7 and 19.1 mm used for sample collection is given in

Table 11.3.

224

Table 11.3 Sequence of the use of two triers for securing samples from 22.68 kg and 33.29 kg bags using the same hole*

Frequency 5 Hz Frequency 7 Hz Time (min) 0 15 30 15 30

19.1 mm 12.7 mm 19.1 mm 12.7 mm 19.1 mm Sampler Sequence** 12.7 mm 19.1 mm 12.7 mm 19.1 mm 12.7 mm

*Material condition: Free flowing

Figure 11.4 Schematic of AOAC single tube sampler (trier) (TFI, 1996)


11.4.1 Comparison of samples from three blend plants

Figure 11.5 illustrates a typical percent cumulative mass of samples from 10-10-10

formulation bags obtained from BP1, BP2, and BP3. The samples collected from bags of plant

BP1, BP2, and BP3 using 19.1 mm trier had the highest mass retained on sieve number 8

(opening width = 2.36 mm) followed by sieve numbers 7 (2.80 mm) and 10 (2.00 mm) in this

order. The percent mass of samples for BP1, BP2, and BP3 retained on sieve number 8 (2.36

mm) was 26%, 31% and 31%, respectively. The sample from plant BP1 contained 15% of mass

retained on top two sieve numbers 5 (4.00 mm) and 6 (3.35 mm), whereas the bottom sieve

number 16 (1.20 mm) and pan contained only 3%. For BP2, the percent cumulative mass of

samples contained 6% of mass retained on top two sieve numbers 5 (4.00 mm) and 6 (3.35 mm),

whereas the bottom sieve number 16 (1.20 mm) and pan contained 5%. For BP3, the percent

cumulative mass of samples retained on top two sieve numbers 5 (4.00 mm) and 6 (3.35 mm)

whereas the bottom sieve number 16 (1.20 mm) and pan contained 3%. The samples collected

from bags of plant BP1, BP2, and BP3 using 12.7 mm trier had the highest mass retained on

sieve number 8 (2.36 mm) followed by sieve numbers 7 (2.80 mm) and 10 (2.00 mm) in this

order. The percent mass of samples from BP1, BP2, and BP3 retained on sieve number 8 (2.36

mm) was 26%, 29% and 32%, respectively. The sample from plant BP1 contained 15% of mass


635 mm long

225

number 16 and pan contained only 3%. For BP2, the percent cumulative mass of samples

contained 6% of mass retained on top two sieve numbers 5 (4.00 mm) and 6 (3.35 mm), whereas

the bottom sieve number 16 (1.20 mm) and pan contained 4%. For BP3, the percent cumulative

mass of samples retained on top two sieves was 9%, whereas the bottom two sieve number 16

and pan contained 1%. The SGN of fertilizer samples collected by 19.1 mm trier was 251, 233,

and 225 at time 0, 15, and 30 minutes, respectively. For the same trier, the UI of samples was 39,

42, and 40 at time 0, 15, and 30 minutes, respectively. The SGN of fertilizer samples collected

by 12.7 mm trier was 235, 236, and 229 at time 0, 15, and 30 minutes, respectively. For the same

trier, the UI of samples was 42, 43, and 40 at time 0, 15, and 30 minutes, respectively. The SGN

of fertilizer decreased with time, except at 15 minutes for 12.7 mm trier, whereas UI first

increased and then decreased with time at the frequency of 5 Hz. The SGN and UI of samples

collected using 12.7 and 19.1 mm triers at different time 0, 15, and 30 minutes did not follow any

definite trend so that 12.7 mm and 19.1 mm triers could not be compared. The present trend was

found because particles size distributions was not significantly affected at the frequency of 5 Hz

(p>0.05). The SGN of fertilizer samples collected by 19.1 mm trier was 239 and 267 at time 15

and 30 minutes, respectively. For the same trier, the UI of samples was 42 and 48 at time 15 and

30 minutes, respectively. The SGN of fertilizer samples collected by 12.7 mm trier was 233 and

267 at time 15 and 30 minutes, respectively. For the same trier, the UI of samples was 43 and 47

at time 15, and 30 minutes, respectively. The SGN and UI increased with time at the frequency

of 7 Hz. The proportion of fines decreased with time in the fertilizer bags and results are

consistent with the literature that vibration induced percolation segregation when physical

property of particulate was different (Rosato et al., 2002).

0.0

20.0

40.0

60.0

80.0

100.0

120.0

1000 10000

Diameter, microns

Perc

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umm

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ive

mas

s (%

)

BP1BP2BP3

0.0

20.0

40.0

60.0

80.0

100.0

120.0

1000 10000

Diameter, microns

Perc

ent c

umm

ulat

ive

mas

s (%

)

BP1BP2BP3

Figure 11.5 Typical size distribution profiles of samples from blend plants BP1, BP2, and

BP3 for (a) 19.1 mm and (b) 12.7 mm

(a) (b)

226

11.4.2 Size distribution of fertilizers from three blend plants

Figure 11.6 illustrates a typical percent cumulative mass of samples from bags contained

formulation 10-10-10 at frequency 5 Hz and time 0 minutes. At the start of the test, the samples

collected from bags of plant BP1 using triers 19.1 mm and 12.7 mm had the highest mass

retained on sieve number 8 (2.36 mm) followed by sieve numbers 7 (opening width = 2.80 mm)

and 10 (2.00 mm) in this order. The percent cumulative mass of samples collected using 19.1

mm and 12.7 mm retained on sieve number 8 (opening width = 2.36 mm) was 28% and 28%,

respectively. The sample from plant BP1 contained 15% of mass retained on top two sieve

numbers 5 (4.00 mm) and 6 (3.35 mm), whereas the bottom sieve number 16 (1.20 mm) and pan

contained only 3%. After 15 minutes, the samples collected from bags of plant BP1 using triers

19.1 mm and 12.7 mm had the highest mass retained on sieve number 8 (2.36 mm) followed by

sieve numbers 7 (2.80 mm) and 10 (2.00 mm) in this order. The percent cumulative mass of

samples collected using 19.1 mm and 12.7 mm retained on sieve number 8 was 28% and 28%,

respectively. The sample from plant BP1 contained 18% and 17% of mass retained on top two

sieve numbers 5 (4.00 mm) and 6 (3.35 mm), whereas the bottom sieve number 16 (1.20 mm)

and pan contained only 2% for both. After 30 minutes, the samples collected from bags of plant

BP1 using triers 19.1 mm and 12.7 mm had the highest mass retained on sieve number 8 (2.36

mm) followed by sieve numbers 7 (2.80 mm) and 10 (2.00 mm) in this order. The percent

cumulative mass of samples collected using 19.1 mm and 12.7 mm retained on sieve number 8

(2.36 mm) was 26% and 24%, respectively. The sample from plant BP1 contained 18% and 18%

of mass retained on top two sieve numbers 5 (4.00 mm) and 6 (3.35 mm), whereas the bottom

sieve number 16 (1.20 mm) and pan secured only 2% for both. The sample secured by 12.7 mm

trier had 7% of mass, whereas 5% for 19.1 mm trier on sieve number 14 (1.40 mm).

227

0

20

40

60

80

100

120

1000 10000

Diameter, microns

Perc

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mas

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)19.1 mm12.7 mm

0

20

40

60

80

100

120

1000 10000

Diameter, microns

Perc

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)

19.1 mm12.7 mm

0

20

40

60

80

100

120

1000 10000

Diameter, microns

Perc

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)

19.1 mm12.7 mm

Figure 11.6 Typical size distribution profiles of samples from blend plants at frequency 5

Hz (a) 0 (b) 15, (c) 30 minutes

11.4.3 Comparison of size distribution at 7 Hz frequency

Figure 11.7 illustrates a typical percent cumulative mass of samples from bags contained

formulation 10-10-10 at frequency 7 Hz. At the start of the test, the samples collected from bags

of plant BP1 using triers 19.1 mm and 12.7 mm had the highest mass retained on sieve number 8

followed by sieve numbers 7 (2.80 mm) and 10 (2.00 mm) in this order. The percent cumulative

mass of samples collected using 19.1 mm and 12.7 mm retained on sieve number 8 (opening

width = 2.36 mm) was 28% and 27%, respectively. The sample from plant BP1 contained 16%

of mass retained on top two sieve numbers 5 (4.00 mm) and 6 (3.35 mm), whereas the bottom

sieve number 16 and pan contained only 1%. After 30 minutes, the samples collected from bags

of plant BP1 using triers 19.1 mm and 12.7 mm had the highest mass retained on sieve number 8

(2.36 mm) followed by sieve number 7 (2.80 mm) and 10 (2.00 mm) in this order. The percent

cumulative mass of samples collected using 19.1 mm and 12.7 mm retained on sieve number 8

(2.36 mm) was 27% and 27%, respectively. The sample from plant BP1 contained 17% of mass


number 16 (1.20 mm) and pan contained only 1% for both triers.

(a) (b)

(c)

228

0

20

40

60

80

100

120

1000 10000

Diameter, microns

Perc

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)

19.1 mm12.7 mm

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)

19.1 mm12.7 mm

Figure 11.7 Typical size distribution profiles of samples from blend plants at frequency 7 Hz (a) 15 and (b) 30 minutes

11.5 Key Findings The following key findings were drawn based on chemical and size analyses of samples obtained

from the three blend plants:

1) Size analysis of bagged fertilizer showed that there was influence of frequency on

size distributions from plant-to-plant.

2) At higher frequency 7 Hz, triers of opening widths 12.7 mm and 19.1 mm

received larger and smaller size particles compared with at frequency 5 Hz.

3) The particle size distributions changed at a location with respect to time when

subjected to vibration frequency 7 Hz.

4) The SGN and UI of samples collected by 12.7 mm and 19.1 mm did not have

definite trend at frequency of 5 Hz.

5) The SGN and UI of samples collected by 12.7 mm and 19.1 mm increased with

time at frequency of 7 Hz.

11.6 References Ahmad, K. and I. J. Smalley. 1973. Observation of particle segregation in vibrated

granular systems. Powder Technology 8: 69–75. Bates, L. 1997. User guide to segregation. British Materials Handling Board: UK. Bradley, M. S. A. and R. J. Farnish. 2005. Segregation of blended fertilizer during spreading: the

effect of differences in ballistic properties. In Proc 554. The International Fertilizer Society, York, UK. pp: 15.

Brennen, C. E., S. Ghosh, and C. Wassgren. 1993. Vertical oscillation of a bed of granular material. In C. Thornton (Ed.), Powders and grains, Birmingham, England. Rotterdam: Balkema.

(a) (b)

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Campbell, C. 1990. Rapid granular flows. Annual Review of Fluid Mechanics 22: 57-92. Carson, J., T. Royal, and D. J. Goodwill. 1986. Understanding and eliminating particle

segregation problems. Bulk Solids Handling 6(1): 139–144. Clement, E., L. Vanel, J. Rajchenbach, and J. Duran. 1996. Pattern formation in a vibrated

granular later. Physical Review E, 53(3): 2972–2975. Davies, T. R. H. 1988. Debris flow surges - a laboratory investigation (pp. 1–122). Mitteilung

Number 96 der Versuchsanstalk fur Wasserbau, Hydrologie, und Glaziology an des ETH. de Silva, S., A. Dyroy, and G. G. Enstad. 2000. Segregation mechanisms and their quantification

using segregation testers. Eds: Rosato, A. D. and D. L. Blackmore. IUTAM Symposium on Segregation in Granular Flows 11-29. Norwell: Kluwer Academic Publishers.



Ellenberger, J., C. O. Vandu, and R. Krishna. 2006. Vibration-induced granular segregation in a pseudo-2D column: The (reverse) Brazil nut effect. Powder Technology 164: 168-173.

Fowler, R. T. 1960. A study of the variables affecting segregation of granular solids by discharge from bins and hoppers, Part 1: Segregation of granular material of different sizes. Australian Journal of Chemical Engineers, December.

Fowler, R. T. 1961. A study of the variables affecting segregation of granular solids by discharge fro bins and hoppers, Part 2: Segregation of a mixture of different specific gravity. Australian Journal of Chemical Engineers, August.

Hunt, M. L., S. Hsiau, and K. T. Hong. 1994. Particle mixing and volumetric expansion in a vibrated granular bed. Journal of Fluids Engineering 116: 785-791.



Jha, A. K. and V. M. Puri. 2007a. Percolation segregation of binary mixtures under periodic movement. Powder Technology (In review).

Jha, A. K. and V. M. Puri. 2007b. Percolation segregation of multi-component particulate materials (Author review).

Karion, A. and M. L. Hunt. 2000. Wall stresses in granular couette flow of mono-sized particles and binary mixtures. Powder Technology 109:145–163.

Lan, Y. and A. D. Rosato. 1997. Convection related phenomena in vibrated granular beds. Physics of Fluids 9(12): 3615–3624.

Laroche, C., S. Douady, and S. Fauve. 1989. Convective flow of granular masses under vertical vibrations. Journal de Physique (France) 50: 699–706.

Lun, C. K. K., S. B. Savage, D. J. Jeffrey, and N. Chepurniy. 1984. Kinetic theories for granular flow: Inelastic particles in couette flow and slightly inelastic particles in a general flow field. Journal of Fluid Mechanics 140: 223-256.

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McElwaine, J. and K. Nishimura. 2000. Size segregation in snow avalanches: Observations and experiments. In A. D. Rosato, & D. L. Blackmore (Eds.), IUTAM Symposium on Segregation in Granular Flows, Cape May, NJ (pp. 81–88). Dordrecht: Kluwer Academic Publishers.

Rosato, A. D. and H. J. Kim. 1994. Particle dynamics calculations of wall stresses and slip velocities for granular Couette flow of smooth inelastic spheres. Continuum Mechanics and Thermodynamics 6(1): 1–20.


Savage, S. B. 1991. Numerical simulations of Couette flow of granular materials: Spatio- temporal coherence and 1/f noise. In J. Dodds, & D. Bideau (Eds.). Physics of Granular Media (pp. 343–362). New York: Nova Scientific Publishers.

Savage, S. B. 1992. Flows of granular materials with applications to geophysical problems. IUTAM International Summer School on Mechanics, Udine, Italy. International Centre of Mechanical Sciences (CISM).

Savage, S. B. and K. Hutter. 1991. The dynamics of avalanches of granular materials from initiation to runout. Part 1: Theory. Acta Mechanica 86(1): 201-223.

Tang, P. and V. M. Puri. 2004. Methods for minimizing segregation, a review. Particulate Science and Technology, An International Journal 22(4): 321-338.

Tang, P. and V. M. Puri. 2005. An innovative device for quantification of percolation and sieving segregation patterns – Single component and multi size fractions. Particulate Science and Technology, An International Journal 23(4): 335-350.

Tang, P. and V. M. Puri. 2007. Segregation quantification of two component particulate mixtures – Effect of particle size, density, shape, and surface texture. Particulate Science and Technology, An International Journal 25(6): 571-588.

Walton, O. R. 1991. Numerical simulation of inclined chute flows of monodisperse, inelastic, frictional sphere. In H. H. Shen, M. Satake, M. Mehrabadi, C. S. Chang, & C. S. Campbell (Eds.), Advances in micromechanics of granular materials, Potsdam, NY (pp. 453–461). Amsterdam: Elsevier.

Williams, J. C. and G. Shields. 1967. The segregation of granules in a vibrated bed. Powder Technology 1: 134-142.

Yang, S. C. 2006. Density effect on mixing and segregation processes in a vibrated binary granular mixture. Powder Technology 164: 65–74.

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12. CHAPTER - CONTINUUM THEORY BASED SIZE-SEGREGATION MODEL DEVELOPMENT AND VALIDATION

12.1 Abstract Segregation negatively impacts the product quality in industries during storage, mixing,

handling, and flow of particulate materials. Size segregation induced by percolation mechanism

is widely observed in industries during the aforementioned unit operations. To quantify size-

segregation in binary mixtures of potash and urea, a continuum theory based convective and

diffusive model was developed and validated. Percolation of fines in terms of segregated mass

data upto 30 minutes of the PSSC-II operation under different operating conditions was used to

determine the model parameters and validation. Herein, for model development, two binary size

ratios for each of the three coarse sizes 3,675 µm, 3,075 µm, and 2,580 µm of potash used were

2.4:1.0 and 1.7:1.0, 2.0:1.0 and 1.4:1, and 1.7:1.0 and 1.2:1.0, respectively. In addition, two

binary size ratios for each of the three coarse sizes 3,675 µm, 3,075 µm, and 2,580 of urea were

2.0:1.0, 1.7:1.0 and 1.7:1.0, 1.4:1.0, and 1.4:1.0 1.2:1.0, respectively. Binary size ratios of potash

were tested at three strains of 2%, 6%, and 10% and two strain rates of 0.25 and 0.5 Hz. Binary

size ratios of urea were tested at three strains of 2%, 6%, and 10% and two strain rates of 0.25

and 1.0 Hz. For validation, size ratio 2.0:1.0 for potash and urea at strain of 6% and strain rate of

0.5 Hz was used. The modeled segregated mass was calculated for a set of convective, diffusive,

and resistance parameters, the set of parameters which had the least root mean square mean

(RMSE) value with respect to measured data were chosen as model parameters. The intermediate

model parameters for a given set of operating conditions were calculated using linear

interpolation and used for model validation.

The results showed that the convective and diffusive modeled segregated mass was

within the 95% confidence interval of the measured segregated mass for size ratios 2.4:1.0 and

1.7:1.0 at strains of 6% and 10%. Although, the modeled data for size ratio 1.7:1.0 was within

the 95% confidence interval of the measured data, however, modeled data was under-predicted.

The modeled data for urea over-predicted initially and thereafter under-predicted at strain rates

of 0.25 and 1.0 Hz and strains of 2%, 6%, and 10%. For size ratio 2.0:1.0 of potash, at strain of

6% and strain rate of 0.5 Hz, the segregated mass from actual modeled data (7.3 g) and from

linear interpolation (45.2 g) was higher than the segregated mass from experiment (but within

232

95% CI). The segregated mass, for size ratio 2.0:1.0 at strain of 10% and strain rate of 0.5 Hz,

from actual modeled data (8.4 g) and from linear interpolation (24.5 g) was higher than the

segregated mass from experiment (but not within 95% CI). For size ratio 2.0:1.0 of urea, at strain

of 6% and strain rate of 0.5 Hz, the segregated mass from actual modeled data (2.3 g) and from

linear interpolation (15.4 g) was higher than the segregated mass from experiment. This is a

limitation of continuum theory-based segregation model (but within 95% CI). To overcome this

limitation of continuum segregation model, a hybrid model which can combine the principles of

continuum and discrete element theories would be able to model the segregation of fines for

smaller size ratio. This can be critical to powder manufactures that could use the information for

different size ratio and operating conditions to determine optimum physical and mechanical

conditions.

12.2 Introduction Segregation in particulate materials is an unwanted phenomenon that occurs during

processing steps such as handling, storage, flow, and mixing. Particulate materials are processed

in bulk for product manufacturing in many industries including agriculture, cosmetic, food, metal

and metallurgy, nutraceutical, and pharmaceutical. Dissimilarity in particulates leads to

segregation that is mainly caused due to difference in physical, and mechanical properties

(Rosato et. al., 2002). Although segregation is governed by several properties, however studying

all parameters simultaneously is not feasible due to the lack of knowledge of their interactions.

Therefore, dominant variables should be identified and additional variables included in

subsequent studies. Toward this end, the dominant parameters were identified and their effect

studied on segregation. Bridgwater and his co-workers were the pioneers in identifying the

dominant mechanisms of segregation (Bridgwater et al., 1978 and Bridgwater 1994). In practice,

segregation has been measured using coefficient, mechanism, and model (Rosato and

Blackmore, 2000). Of the three measurement methods, coefficient of segregation is the most

commonly used to determine the extent of segregation. Although most common, it is capable of

describing the extent of segregation only under a particular set of operating conditions. The

second approach is to study the mechanism of segregation. To date, thirteen segregation

mechanisms have been identified based on different operating conditions, i.e., trajectory, air

current, rolling, sieving and sifting, impact, embedding, angle of repose, push-way, displacement

233

or floating, percolation, fluidization, agglomeration, and concentration driven displacement

(Mosby et al., 1996; Salter, 1998; de Silva et al., 2000). A particular theory can not be developed

for including all the segregation mechanisms. The third approach is to model the segregation

process for a specific mechanism so that the results are applicable under different operating

conditions. However, most studies conducted to date have been for time-independent model

using ideal materials (glass beads) or real-world materials (commonly used in industries), few

models were also developed for time-dependent process using ideal and real world materials

(Duffy and Puri, 2002, and Tang and Puri, 2007). Tang and Puri, and Duffy and Puri used point

feed and a layer of feed of fines in the coarse particle bed, respectively. In this chapter, a

particular mechanism was identified known as percolation segregation for modeling, which is by

far the most common in industrial conditions.

Segregation in particulates can be modeled by three approaches: continuum models,

kinetic theory models, and discrete models (Moakher et al., 2000). Each modeling approach has

advantages and disadvantages, continuum models consider the conservation principles of mass,

momentum, and energy but neglect the discrete nature of particles; kinematic models consider

the principle of interacting grains and colliding molecules in a dense gas but it is limited to the

surface of an agitated granular mass; and discrete models consider the constituent grains to be

distinct and apply the prescribed rules but limited to relatively small systems (Khakhar et al.,

2001). Khakhar et al. (2001) found that continuum models are capable of predicting segregation

in large real-world systems.

Based on the literature review, a continuum theory based convective and diffusive model

was developed and validated for well-mixed binary size real-world materials. As needed in the

continuum based model, the material parameters were measured under specific loading

conditions. Percolation segregation is observed under shear, vibration, and gravity (Tang and

Puri, 2004). Percolation segregation is defined as the migration of fine particles through a bed of

coarse particles during shear and vibration motion when subjected to dynamic conditions

(Vallance and Savage, 2000). To meet the needs of industry, a size-segregation mathematical

model in association with shape and density based on the convective and diffusive formulation

for percolation is presented and validated. The primary segregation shear cell (PSSC-II) was

used to measure the amount of percolated fines from well-mixed binary mixtures.

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The PSSC-II has five main components (Tang, 2004): shear box, measurement system,

sieve system, drive system, and main frame. The shear box moved forward-backward-forward

along x-axis (Figure 12.1) and fines mass percolated in the negative z-direction (gravity

direction). Different size cams could be used to produce different strains in the shear box and

motor switch could be adjusted for different intensity of movements or strain rate. A sieve of

opening size 2,360 µm was used throughout the experiments after preliminary tests with

different size ratios in binary and multi-component mixtures to ensure that coarse size particles

did not block the sieve openings while allowing fines to exit freely (Jha et al., 2007).

Binary size mixture is considered to be the foundation of multi-size and continuous

mixture study. Therefore, convective and diffusive model is presented for binary mixture. In this

chapter, nine different binary size ratios of potash and six different size ratios of urea in different

mixing ratios were used in modeling studies.

Figure 12.1 Primary segregation shear cell (PSSC-II)

12.3.1 Test material selection and parameter determination Urea and potash were selected for studying percolation segregation due to their extreme

shape and density among the three major raw ingredients: urea, potash, and phosphate, used in

the manufacture of different fertilizer blends. For segregation study, three parameters including

Main frame

Drive system Shear box

System system

Measurement system

Z

X

Stationary size Moving side

235

material bed depth, particle bed strain, and strain rate were selected for operating PSSC-II based

on published results (Tang and Puri, 2005). Bed depth of 85 mm (shear box height = 100 mm)

was used to represent percolation of fines within bagged fertilizers in normal orientation, i.e.,

depth direction along gravity, during conveying, handling, and transportation. The selected strain

of 2%, 6%, and 10% and strain rates of 0.25, 0.5, and 1.0 Hz represent the unfilled bag volume

(≤ 15%) and intensity of motion, respectively, experienced by the blend in the bag during

processing operations (<10 Hz) (Vursavus and Ozguven, 2004).

Different coarse and fine size ranges of the test material were obtained using US standard

sieve of (2)1/4 series. Potash and urea were received from local fertilizer blend plant facilities.

Three size ranges (3,350-4,000; 2,800-3,350; and 2,360-2,800 µm) were designated as coarse

and while three size ranges (2,000-2,360; 1,700-2,000; and 1,400-1,700 µm) were designated as

fines in the present study (Table 12.1). Since size spread of urea was small compared with

potash, fines size range 1,400-1,700 µm were not found in sufficient quantity, therefore, this

fines size was not included in the segregation study of urea. Size ratio of binary mixture was

defined as the ratio of mean size of coarse particles to mean size of fine particles. For model

development using potash, two size ratios for each coarse sizes 3,675 µm, 3,075 µm, and 2,580

µm were used: 2.4:1.0, 1.7:1.0; 2.0:1.0, 1.4:1.0; and 1.7:1.0, 1.2:1.0, respectively, (Table 12.1).

For urea, two size ratios for coarse size 3,675 µm, 3,075 µm, and 2,580 µm were used: 2.0:1.0,

1.7:1.0; 1.7:1.0, 1.4:1.0; and 1.4:1.0, 1.2:1.0, respectively (Table 12.1). For validation of

convective and diffusive model, the size ratio 2.0:1.0 of potash was used at strains of 2%, 6%,

and 10% and two strain rates of 0.25 and 0.5 Hz. For urea, two size ratios for coarse size 3,675

µm, 3,075 µm, and 2,580 µm used were 2.0:1.0, 1.7:1.0; 1.7:1.0, 1.4:1.0; and 1.4:1.0, 1.2:1.0,

respectively at strains of 2%, 6%, and 10% and strain rate of 0.5 Hz (Table 12.2). Different

mixing ratios (MR) were used for different size ratios based on weight proportion of different

size (Table 12.1) distributions found in low analysis such as 10-10-10 fertilizer samples collected

from Commonwealth of Pennsylvania blend plants.

12.3.2 Test condition and experimental design Coarse size particles were mixed with fines size particles in a 225-W six-speed bench-top



236

binary size samples. Mixed binary sizes were placed in shear box of the PSSC-II very gently

with a scoop to avoid segregation. From statistical analysis of data, a separate experimental

design was considered for both angular and spherical-shaped materials including dissimilar

amount of fines (Table 12.1). Based on published results (Duffy and Puri, 2002; Duffy and Puri,

2003; and Tang and Puri, 2005), and preliminary testing with fertilizer blends, six replications

were done for each set of experiments for testing percolation segregation using PSSC-II. A

complete block design was selected for data analysis. A set of coarse particles was considered as

a block of experiment. Within each block, all treatments (replicate = 1 × 6 = 6) were randomly

assigned. Of the six replicates, three replicates for each set were completed using load cells and

three replicates were completed by collecting segregated fines in a pan. However, only three

replications were included for the model development and validation because of limited capacity

of load cells (<3.5 g), i.e., load cells were not able to collect data effectively upto 30 minutes

with desired accuracy for all the size ratios (Tables 12.1 and 12.2). All tests were conducted in

the environment-controlled laboratory with average temperature of 22°C ± 3°C and relative

humidity less than 40%.

Table 12.1 Experimental design for binary size mixtures for potash and urea* Material Strain rate

(Hz) Coarse size

(µm) Fines size


1,550 2.4:1.0 50:50 Potash 0.25 0.50

3,675 2,180 1.7:1.0 37:63

4

1,550 2.0:1.0 67:33 Potash 0.25 0.50

3,075 2,180 1.4:1.0 50:50

4

1,550 1.7:1.0 67:33 Potash 0.25 0.50

2,580 2,180 1.2:1.0 60:40

4

1,850 2.0:1.0 37:63 Urea 0.25 1.00

3,675 2,180 1.7:1.0 37:63

4

1,850 2.0:1.0 50:50 Urea 0.25 1.00

3,075

2,180 1.7:1.0 50:50

4

1,850 2.0:1.0 60:40 Urea 0.25 1.00

2,580

2,180 2.0:1.0 60:40

4

Total (three replications) 24×3×3 = 216

*At strains of 2%, 6%, and 10%

237

Table 12.2 Validation schedule for binary size mixtures for potash and urea* Material Strain Rate

(Hz) Coarse size

(µm) Fines Size


Potash 0.25 0.50

3,675 1,850

2.0:1.0

37:63 2

Potash 0.25 0.50

3,075 1,850

1.7:1.0

50:50 2

Potash 0.25 0.50

2,580 1,850

1.4:1.0

63:37 2

1,850 2.0:1.0 37:63 Urea 0.25 1.00

3,675 2,180 1.7:1.0 37:63

2

1,850 2.0:1.0 50:50 Urea 0.25 1.00

3,075

2,180 1.7:1.0 50:50

2

1,850 2.0:1.0 60:40 Urea 0.25 1.00

2,580

2,180 2.0:1.0 60:40

2

Total (three replications) 12×3×3 = 108

*At strains of 2%, 6%, and 10%

12.3.3 Convective and diffusive model development Binary mixtures of different size ratios of urea and potash were filled in the shear box

upto 85 mm (the height of the shear box is 100 mm) (Figure 12.2). Based on size of coarse and

fine particles, the bed of binary mixture was divided into twelve slabs, i.e., 11 interfaces and two

faces (1 to 13 levels) (Figure 12.3). Mass balance of fines along the three principal directions is

given in Figure 12.4.

238

Figure 12.2 Schematic of the shear box

Figure 12.3 Binary mixtures in shear box showing 12 equal size layers for model

development

100 mm

76 mm 150 mm

Y

X

Z

85 mm

239

Figure 12.4 Three dimensional mass balances

Mass flux along y-direction (face 1 and 2)

1212

1212

vvvmmm fff

∆−=

∆−=

yvmvmvmmvvm

yvm

tm fffffff

∆

−∆∆+∆−∆−=

∆

∆=

∆

∆ 11121212112111121212 )( (12.1)

Mass flux along x-direction (face 3 and 4)

3434

3434

vvv

mmm fff

∆−=

∆−=

xvmvmvmmvvm

xvm

tm fyffffff

∆

−∆∆+∆−∆−=

∆

∆=

∆

∆ 333434334333343434 )( (12.2)

Mass flux along z-direction (face 5 and 6)

5656

5656

vvv

mmm fff

∆−=

∆−=

zvmvmvmmvvm

zvm

tm fffffff

∆

−∆∆+∆−∆−=

∆

∆=

∆

∆ 55565656556555565656 )( (12.3)

where,

=kfm fines mass in binary mixtures entering at face k,

=∆ fklm accumulation of fines between faces k and l,

=kv velocity of fines at face k,

66 , vm f

22 , vm f

55 , vm f

33 , vm f

11 , vm f 44 , vm f

X

Y

Z gravity

240

=∆ klv change in velocity of fines between face k and l,

k = 1, 3, 5, and

l = 2, 4, 6

The main driving force acting on binary mixtures in the shear box was gravity. Based on the

nature of driving forces, the following two assumptions were made:

1) 5v is average characteristic velocity and constant along z-direction, with this

assumption, change in velocity of fines along gravity (z-direction) is zero, i.e.,

zv

m f ∆∆

− 565 = 0

2) based on the direction of percolation of fines in the shear box, there is negligible

concentration and velocity gradients along x and y directions compared with z-

direction, i.e., 0, 3434

1212 =

∆∆

∆∆∆

∆y

mv

xmv and 0, 3412 =

∆∆

∆∆

yv

xv , respectively.

With the above assumptions, mass fluxes along x and y-directions are 012 =∆

∆

tm f

and 034 =∆

∆

tm f , respectively

Mass flux along z-direction from equation (12.3)

zmv

tm ff

∆

∆−=

∆

∆ 56556 = velocity driving force or convective (de-mixing) component (12.4)

zvm ff

∆

∆∆ 5656 = is second order and can be neglected

Concentration gradient within binary mixture is present. Then from Fick’s second law of

diffusion, when concentration within a diffusion volume changes with time

Concentration gradient along z-direction = 256

2

5656

zm

Dt

m ff

∂

∂=

∂

∂ (12.5)

The above equation (12.5) can be proved with the Fick’s first law and the mass balance

Fick’s first law

⎟⎟⎠

⎞⎜⎜⎝

⎛∂

∂+

∂

∂+

∂

∂−= k

zm

jy

mi

xm

DJ fff 561234

where, i, j, k are unit vectors along the three principal directions x, y, and z, respectively

241

From Fick’s first law and mass balance

Mass rate in = Mass rate out

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛∂

∂+

∂

∂+

∂

∂−⎟⎟

⎠

⎞⎜⎜⎝

⎛∂∂

+∂∂

+∂∂

−=∂

∂k

zm

jy

mi

xm

Dkz

jy

ixt

m ffff 561234.

⎟⎟⎠

⎞⎜⎜⎝

⎛

∂

∂+

∂

∂+

∂

∂=

∂

∂256

2

212

2

234

2

zm

ym

xm

Dt

m ffff

since x and y diffusion was assumed to be negligible:

⎟⎟⎠

⎞⎜⎜⎝

⎛

∂

∂=

∂

∂256

2

5656

zm

Dt

m ff

Combining the above two equations (12.4) and (12.5)

256

2

556

556

zm

Dz

mv

tm fff

∂

∂+

∂

∂−=

∂

∂ (12.6)

=5D coefficient of diffusivity

256

2

5 zm

D f

∂

∂= diffusive component or mixing component

From now on, ,, 565

56

zm

vz

mv

tm

tm ffff

∂

∂−=

∂

∂−

∂

∂=

∂

∂and 2

2

256

2

5 zm

Dzm

D ff

∂

∂=

∂

∂

The binary mixture in the shear box is filled upto the height of 85 mm, applying this condition to

differential equation (12.6) yields

2

2

zm

Dz

mv

tm fff

∂

∂+

∂

∂−=

∂

∂ 850 =≤≤ hz (12.7)

Here, v and D are the fundamental material parameters and represent the convective or

demixing and diffusive or mixing components, respectively. The units of v and D are mm/min

(dimension, L/T) and mm2/min (dimension, L2/T), respectively. The equation (12.7) was derived

from the well known mass conservation law and Fick’s law of diffusion. Further boundary

conditions were developed based on set-up conditions and physics of the problem and resistance

was introduced for the first time based on physics of the problem.

To model the percolation segregation of binary mixtures, the differential equation (12.7)

needs to be solved to determine the material parameters. The mass of fines in the shear box

decreased with time. Due to the inverse nature of the problem, the finite difference formulation

242

was the chosen method and used to solve the differential equation. The above differential

equation is of second order, two boundary conditions are needed to solve the equation in addition

to the initial condition. The following initial condition and two boundary conditions are used in

order to solve the differential equation.

However, the mixed binary mixtures were poured into the shear box using spatula very

gently to avoid segregation, although minor segregation was evident in the shear box. It is

assumed that fines mass in the shear box was uniformly distributed in the coarse particles bed.

With this assumption, the following equation (12.8) can be deduced

00 )0,( ff mtzm == , 850 ≤≤ z (12.8)

There is a screen of opening size 2,360 µm at the bottom of the shear box, the

preliminary experiments showed that there is no mass accumulation on the screen but some

resistance was offered by screen bottom. The resistance “R” was included in the boundary

condition at the screen bottom given in equation (12.9). Although top surface of binary mixture

was convex during the test but it was assumed that the top surface remains flat (mound angle

≤5°) during the tests as a simplification. With the help of above two conditions, two boundary

conditions were formulated as given in equations (12.9) and (12.10).

( )1

1=

=

=⎟⎟⎠

⎞⎜⎜⎝

⎛∂

∂zf

z

f mz

mR 850 ≤≤ z , Resistance offered by screen (12.9)

0=∂

∂

zm f 850 ≤≤ z , No mass flux out of free surface (12.10)

There are two general methods: implicit and explicit, to solve time-dependent differential

equation using the finite difference method. These two approaches have advantages and

disadvantages. Furthermore, there are three formulations, i.e., backward, forward, and central

difference. The forward and backward difference methods result in lower accuracy. Therefore,

for the same effort, the third option, the central difference method is discussed below for explicit

and implicit methods along z-direction.

For explicit method,

211

1 2z

mmmC

tmm j

fij

fij

fij

fij

fi

∆

+−=

∆

− +−+

(12.11)

243

For implicit method,

2

11

111

1 2z

mmmC

tmm j

fij

fij

fij

fij

fi

∆

+−=

∆

− ++

++−

+

(12.12)

where,

i, represent grid points (Figure 12.4) = 1, 2, 3, 4, 5…….N-1 and

j, represents time values = 0, 1, 2, 3, 4 …, j = 0 corresponds to t = 0

Advantages and disadvantages of using explicit and implicit method are summarized below:

(1) Explicit method is computationally simple but the time step needs to be very small in

order to attain reasonable accuracy.

(2) The main drawback of having more than one unknown coefficient in any equation is the

value of dependent variable at any grid point that cannot be obtained directly, i.e., one

has to generate a system of equations for each time step separately by varying i to obtain

a unique solution. This process needs to be repeated until the final time value is reached.

This makes implicit method computationally intensive.

Crank and Nicolson (1947) proposed, and used, a method that reduces the number of calculations

and results in a difference form that is valid (i.e., convergent and stable) for all finite values. For

the most stable result, Crank-Nicolson scheme takes average of explicit and implicit methods.

⎟⎟⎠

⎞⎜⎜⎝

⎛

∆

+−+

⎟⎟⎠

⎞⎜⎜⎝

⎛

∆

+−=

∆

− +−+

+++

−+

211

2

11

111

1 2212

21

zmmm

zmmm

tmm j

fij

fij

fij

fij

fij

fij

fij

fi (12.13)

For one dimensional part or time-dependent part

⎟⎟⎠

⎞⎜⎜⎝

⎛

∆

−+

⎟⎟⎠

⎞⎜⎜⎝

⎛

∆

−=

∆

− +−+

++

−+

zmm

zmm

tmm j

fij

fij

fij

fij

fij

fi 111

11

11

21

21 (12.14)

Combining equations (12.13) and (12.14),

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

∆

+−

+∆

+−

+⎟⎟⎠

⎞⎜⎜⎝

⎛

∆

−+

∆

−=

∆

−

+−

++

++−

+−+

++

−+

211

2

11

111

111

11

11

2

2

21

21

zmmm

zmmm

zmm

zmm

tmm

jfi

jfi

jfi

jfi

jfi

jfi

jfi

jfi

jfi

jfi

jfi

jfi

……………………………………………………………………………………………... (12.15)

244

In this particular case,

v = convective velocity

D = coefficient of diffusion

Subscripts,

i = number of interface = 1, 2, ….., 13

j = number of time steps = 0, 1, 2, ….., 25

t∆ = time steps = 0.5 min

z∆ = layer thickness = 85 mm/12 = 7.08 mm

Applying all the above information in equation (12.5) leads to:

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

∆

+−

+∆

+−

+⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

∆

−+

∆

−−=

∆

−

+−

+

+

++

−

+−

+

+

+

−

+

211

2

11

111

111

11

11

2

2

22

zmmm

zmmm

Dzmm

zmmv

tmm

jif

jif

jif

jif

jif

jif

jif

jif

jif

jif

jif

jif

………………………………………………………………………………………………(12.16)

Rearranging equation (12.16),

( ) ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+−

++−

∆∆

+−+−∆∆

−=−+−

+

+

++

−

+−

+

+

+

−

+

jif

jif

jif

jif

jif

jifj

ifj

ifj

ifj

ifj

ifj

ifmmm

mmm

ztDmmmm

ztvmm

11

11

111

2111

11

11

2

2

22

………………………………………………………………………………………………(12.17)

Consider

ztv

∆∆

=2

µ , a dimensionless parameter

22 ztD

∆∆

=δ , a dimensionless parameter

The physical interpretations of µ and δ are mass-balance and concentration-gradient

related parameters that represents the fraction of material leaving a given location. Solving for

implicit and explicit parameters after incorporating µ andδ . Rearranging equation (12.17) leads

to

( ) ⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

+−+

+−+−+−−=−

−+

+

−

++

+

−

+

−

++

)2(

)2()()()(2

11

11

111

11

111

jif

jif

jif

jif

jif

jifj

ifjif

jif

jif

jif

jif

mmm

mmmmmmmmm δµ (12.18)

245

The final form of equation (12.18) is given in equation (12.19) jif

jif

jif

jif

jif

jif mmmmmm

1111

111

)22()()22()(+−

+

+

++

−+−−++=−++++− δδµδµδδµδµ

…………...………………………………………………………………………………….(12.19)

Implicit part = explicit part

Form of individual equation for grid points 1 to 13 at first time step:

For i = 1 and j = 0, where j = 0 corresponds to time = 0 and j = 1, time = ∆t 02

01

00

12

11

10

)22()()22()( ffffff mmmmmm δδµδµδδµδµ +−−++=−++++−

For i = 2 and j = 0 03

02

01

13

12

11


For i = 3 and j = 0 04

03

02

14

13

12


Similarly for i = 4, 5, 6, 7, 8, 9, 10, 11, 12, and 13, j = 0 014

013

012

114

113

112


Applying the two boundary conditions:

( )1

1=

=

=⎟⎟⎠

⎞⎜⎜⎝

⎛∂

∂zf

z

f mz

mR or ( )

00

==

=⎟⎟⎠

⎞⎜⎜⎝

⎛∂

∂if

i

f mz

mR

1

2

2 fff m

zmm

R o =∆

− for all j

12

2fff m

Rzmm

o

∆−= valid for all j

02

01

01

02

12

11

11

12

)22()2)(()22()2)(( ffffffff mmmR

zmmmmR

zm δδµδµδδµδµ +−−+∆

−+=−+++∆

−+−

0=∂

∂

zm f at layer 13 using the central difference method

02

1214 =∆

−

zmm j

fj

f or jf

jf mm 1214 =

013

012

113

112

)22()()22()( ffff mmmm δµδδµδµδδµ −−+++=+++++−

246

For simplicity, the following notations were used in MATLAB program and are summarized

below:

δµδµ

δδµ

δµ

222

22

+=+=++=

=−−=

+=

caedcba

03

02

01

13

12

11 ffffff cmdmamcmbmam ++=−+−

04

03

02

14

13

12 ffffff cmdmamcmbmam ++=−+−

………………………………………………

……………………………………………… 013

012

113

112 ffff dmembmem +=+−

Similarly, set of equations could be written for time steps 1 to 25. In this study, time step

was 0.5 minutes. A program was written in MATLAB (Mathworks Inc, Natick, Massachusetts)

to solve the finite difference equations with the given boundary and initial conditions. The

precision of ,µ ,δ and R was kept to two decimal places to be consistent with variations in

experimental data. Equation (12.20) represents the RMSE between experimental and modeled

data. The values of ,µ ,δ and R that produced the smallest error were taken as the material

parameter for a given set of operating conditions. The df is the degree of freedom. The three

variables ,µ ,δ and R are calculated so that the degree of freedom is 3. In equation (12.19), im̂

and im represent the experimentally measured and modeled mass values in the layer i.

( )( )

dfn

mmRMSEerrorsquaremeanRoot

n

iii

−

−=∑=1

2ˆ (12.20)

where, n = number of observations

247


The model parameters convective velocity ( v ) and diffusive parameter ( D ), and

resistance (R) values are given in Table 12.3. In Table 12.3 the convective and diffusive,

resistance and RMSE terms for size ratios 2.4:1.0 and 1.7:1.0 for potash at strains of 6% and

10% and strain rate of 0.5 Hz and size ratio of 2.0:1.0 for urea at strain of 6% and strain rates of

0.25 and 1.0 Hz are reported.

Table 12.3 Convective, diffusive, and time parameters for potash and urea Material (coarse size)

Size ratio

Condition Convective(mm/min)

Diffusive(mm2/min)

R (mm)

RMSE

2.4:1.0

Strain 6% and strain rate 0.5 Hz

1.98

97.24

12.00

1.43

1.7:1.0

Strain 6% strain rate 0.5 Hz

0.00

2.02

3.00

1.89

2.4:1.0


2.69

96.25

5.00

4.98

Potash (3,675 µm)

1.7:1.0


0.00

3.01

3.00

2.70

2.0:1.0


0.00

9.03

1.00

13.09

Urea (3,675 µm)

2.0:1.0


0.00

31.08

1.00

8.75

12.4.1 Convective and diffusive segregation model development The measured and modeled segregated mass versus time relationships for potash and

urea are given in Figure 12.5. Figure 12.5a shows the segregated mass vs. time relationship for

size ratio 2.4:1.0 of potash at strain of 6% and strain rate of 0.5 Hz. The cumulative segregated

mass increased with time. For size ratio 2.4:1.0, convective and diffusive segregation model

values were within the 95% confidence interval (CI) of measured values. For size ratio 1.7:1.0,

the modeled segregated mass values were always lower than the measured segregated mass

values but within the 95% CI (Figure 12.5b). Figure 12.5c shows the segregated mass vs. time

relationship for size ratio 2.4:1.0 of potash at strain of 10% and strain rate of 0.5 Hz. For size

248

ratio 2.4:1.0, convective and diffusive segregation model represents the measured values are also

within the 95% confidence interval. For size ratio 1.7:1.0, the modeled segregated mass values

were initially higher and after 25 minutes lower than the measured segregated mass values

(Figure 12.5d). The initial over prediction and later under prediction of segregated mass were

observed because at higher strain of 10%, time was not enough for fine particles to percolate

through the void spaces of coarse particles and also due to bridges formed in the binary mixtures.

At later stage (after 25 minutes), bridges might have collapsed and fine particles found the way

through void spaces of coarse particles because of less fines in binary mixtures. The initial

modeled segregated mass upto 10 minutes of PSSC-II operation was not within the 95% CI of

the measured segregated mass. For size ratio 2.4:1.0 and 1.7:1.0 of potash, convective and

diffusive segregation model segregated mass values were not within the 95% CI at strain of 2%

and strain rate of 0.5 Hz. At strain of 2% and strain rate of 0.5 Hz, the input energy was not

sufficient to create large void spaces so that fines could percolate and bridges might have formed

within the binary size mixtures of potash. Similar results were obtained at three strains of 2%,

6%, and 10% and strain rate of 0.25 Hz for size ratios 2.4:1.0 and 1.7:1.0; also for size ratios

2.0:1.0 and 1.4:1.0 when the coarse size was 3,075 µm. The modeled segregated mass was not

within the 95% CI for size ratios 1.7:1.0 and 1.4:1.0 when the coarse size was 2,580 µm.

Figures 12.5e and 12.5f show the segregated mass vs. time relationship at strain rate of

0.25 and 1.0 Hz, respectively, for size ratio 2.0:1.0 at strain of 6%. At strain rate of 0.25 Hz,

convective and diffusive segregation modeled segregated mass was not within the 95% CI,

however, model under-predicted in the initial phase upto 13 minutes and thereafter over-

predicted. At strain rate of 1.0 Hz, the modeled segregated mass values were not within the 95%

CI and under-predicted in the initial phase upto 22 minutes and thereafter over-predicted. In the

case of urea over and under prediction were observed in binary mixtures for the size ratio 2.0:1.0

at different times. The shape of urea was spherical and density was lower than that of potash.

Gravity is the dominant force for material separation in binary mixtures, the combined effect of

size, shape, and density was more in the case of potash compared with urea. The bridges might

have formed and energy supplied by the shear box and dominant gravity force was not sufficient

to break those bridges initially and also time was not sufficient for fines to percolate through

void spaces of coarse particles bed.

249

0.0

100.0

200.0

300.0

400.0

500.0

0 5 10 15 20 25 30 35

Time (minutes)

Segr

egat

ed m

ass

(g)

Modeled 2.4:1.0

Experimental 2.4:1.0

95%CI+

95%CI-

0.0

100.0

200.0

300.0

400.0

500.0

0 5 10 15 20 25 30 35

Time (minutes)

Segr

egat

ed m

ass

(g)

Modeled 1.7:1.0Experimental 1.7:1.095%CI+95%CI-

0.0

100.0

200.0

300.0

400.0

500.0

0 5 10 15 20 25 30 35Time (minutes)

Segr

egat

ed m

ass

(g)


0.0

100.0

200.0

300.0

400.0

500.0

0 5 10 15 20 25 30 35

Time (minutes)Se

greg

ated

mas

s (g

)


0.0

100.0

200.0

300.0

400.0

500.0

0 5 10 15 20 25 30 35

Time (minutes)

Segr

egat

ed m

ass

(g)


0.0

100.0

200.0

300.0

400.0

500.0

0 5 10 15 20 25 30 35

Time (minutes)

Segr

egat

ed m

ass

(g)


Figure 12.5 Modeled and experimental data of potash at strain rate of 0.5 Hz (a) size ratio

2.4:1.0 under 6%, (b) size ratio 1.7:1.0 under strain of 6%, (c) size ratio 2.4:1.0 under 10%, (d) size ratio 1.7:1.0 under strain of 10%, and urea of size ratio 2.0 under strain of 6% at strain rates of (e) 0.25 Hz, (f) 1.0 Hz, 95%CI+ and 95%CI- upper and lower limits of CI

If energy imparted by shear box was sufficient to break bridges, then fines particles

would and did percolate through coarse particles bed; with increasing time, proportion of fines

decreased that increased the rate of segregation causing model to under-predict segregated mass.

Similar results were obtained for size ratio 1.7:1.0 at strain rates of 0.25 Hz and 1.0 Hz and for

size ratios 2.0:1.0 and 1.7:1.0 at strains of 10% and 2% for strain rates of 0.25 Hz and 0.5 Hz.

The convective and diffusive model well represented the measured segregated mass values of

binary size ratios when the size ratios were higher than 1.4:1.0 and coarse size was larger than

2,580 µm. The accuracy of the model was the highest at strain of 6% because void space created

in the coarse particles bed and time available to percolate for fine particles was sufficient. The

(a) (b)

(d) (c)

(e) (f)

250

under and over predictions of modeled segregated mass might also have been observed because

of other physical properties involved such as surface texture, and surface property. These

properties can not be studied with the discussed continuum theory based model. To overcome the

limitation of continuum theory model, a hybrid model continuum and discrete element theories

model could be proposed and applied which combines the advantages of continuum and discrete

element model to explain segregation at particle-particle level.

12.4.2 Validation of convective and diffusive segregation model

The convective and diffusive model was validated for size ratios 2.0:1.0 at strains of 2%,

6%, and 10% and strain rates of 0.25 Hz and 0.5 Hz (Table 12.2). The convective and diffusive

parameters were estimated using linear interpolation from size ratios 2.4:1.0 and 1.7:1.0 for

potash and strain rates of 0.25 and 1.0 Hz for urea at strains of 2%, 6%, 10%. The goal of

interpolation was to determine convective, diffusive, and resistance parameters to predict

segregated mass for potash and urea of size ratio 2.0:1.0. Figure 12.6 shows the graphical

representation of modeled data and experimental data. With the help of interpolated convective,

diffusive, and resistance values, the segregated mass values were calculated but the modeled

segregated mass values under predicted the measured segregated mass values at strains of 2%,

6%, and 10%. For size ratio of 2.0:1.0 of potash, at the strain of 6% and strain rate of 0.5 Hz

after 30 minutes, the actual modeled segregated mass was 7.3 g, which is higher than the

experimental segregated mass; whereas, the segregated mass calculated from the model

operating parameters convective, diffusive, and resistance obtained from linear interpolation was

45.3 g higher than experimental segregated mass. The modeled segregated mass was within the

95% CI of the experimental values. The modeled convective, diffusive, and resistance

parameters were 0.28 mm/min, 74.18 mm2/min, and 17 mm, respectively; whereas these

parameters calculated from linear interpolation were 0.85 mm/min, 45.11 mm2/min, and 6.75

mm, respectively.

251

0.0

100.0

200.0

300.0

400.0

500.0

0 5 10 15 20 25 30 35

Time (minutes)

Segr

egat

ed m

ass

(g)

ModeledMeasured95%CI+95%CI-

0.0

100.0

200.0

300.0

400.0

500.0

0 5 10 15 20 25 30 35

Time (minutes)

Segr

egat

ed m

ass

(g)


0.0

100.0

200.0

300.0

400.0

500.0

0 5 10 15 20 25 30 35

Time (minutes)

Segr

egat

ed fi

nes

(g)


Figure 12.6 Validation at strain rate of 0.5 Hz for size ratio 2.0:1.0 (a) potash-6%, (b) potash-10%, and (c) urea-6%, 95%CI+ and 95%CI- upper and lower limits of CI

The convective parameter was higher in the case of linear interpolation but diffusive and

resistance parameters were higher in the modeled case. In the case of linear interpolation

convective parameter responsible for segregation was overestimated but the other two

parameters responsible for mixing (diffusive) and resistance responsible for offering resistance in

binary mixture due to bridging were underestimated. The convective parameter is dominant

because of dominant gravity driving force on larger fines size that resulted in over estimation of

the segregated mass. The interpolation of convective, diffusive, and resistance parameters is not

the best approach because the NSR is not linearly dependent on (ln(NSR) = m ln(size ratio),

where m is the exponent of size ratio and varies with size ratio and type of material.

For size ratio of 2.0:1.0 of potash, at the strain of 10% and strain rate of 0.5 Hz after 30

minutes, the modeled segregated mass was 8.4 g higher than the experimental segregated mass;

whereas, the segregated mass calculated from the model operating parameters convective,

diffusive, and resistance obtained from linear interpolation was 24.5 g higher than experimental

segregated mass (Figure 12.6b). The modeled segregated mass was not within the 95% CI of the

experimental values. The modeled convective, diffusive, and resistance parameters were 0.99

(a) (b)

(c)

252

mm/min, 98.24 mm2/min, and 13.00 mm, respectively; whereas these parameters calculated from

linear interpolation were 1.20 mm/min, 42.61 mm2/min, and 2.75 mm, respectively. However,

for size ratio 2.0:1.0 for potash at 6% and 0.5 Hz (12.6a), the modeled values of segregated fines

mass were within the 95% CI. For size ratio of 2.0:1.0 of urea, at the strain of 6% and strain rate

of 0.5 Hz after 30 minutes, the modeled segregated mass was 2.3 g higher than the experimental

segregated mass; whereas, the segregated mass calculated from the model operating parameters

convective, diffusive, and resistance obtained from linear interpolation was 15.4 g lower than

experimental segregated mass (Figure 12.6c). The modeled segregated mass was not within the

95% CI of the experimental values. The modeled convective, diffusive, and resistance

parameters were 0.00 mm/min, 21.05 mm2/min, and 1 mm, respectively; whereas these

parameters calculated from linear interpolation were 0.00 mm/min, 16.54 mm2/min, and 1 mm,

respectively. The sufficient size ratios were not available so that a definite relationship between

NSR and size ratio can be deduced. The segregation behavior of urea at strain of 6% and strain

rates of 0.25 and 1.0 Hz could not be used to explain the segregation behavior at intermediate

strain rate 0.5 Hz accurately. To explain the segregation behavior of fines in urea at intermediate

strain of 0.5 Hz and smaller size ratios of potash (<1.7:1.0), a hybrid model which combines the

principles of continuum and discrete element theories is recommended.

12.5 Conclusions

The primary segregation shear cell (PSSC-II) was used to quantify size-segregation and

to estimate material parameters (convective and diffusive) for percolation of fines through a

bed of coarse particles in the well-mixed binary mixtures. The segregated mass was

experimentally measured and modeled for two materials urea and potash. Based on the results

for binary mixtures, the following conclusions can be drawn.

1) For size ratio of 2.0:1.0 of urea, at the strain of 6% and strain rate of 0.5 Hz after 30

minutes, the modeled segregated mass was 2.3 g higher than the experimental segregated

mass; whereas, the segregated mass calculated from the model operating parameters

convective, diffusive, and resistance obtained from linear interpolation was 15.4 g lower

than experimental segregated mass. The modeled segregated mass was not within the

95% CI of the experimental values.

253

2) At the strain of 10% and strain rate of 0.5 Hz after 30 minutes, for size ratio 2.0:1.0 of

urea, the modeled convective, diffusive, and resistance parameters were 0.00 mm/min,

21.05 mm2/min, and 1.00 mm, respectively; whereas these parameters calculated from

linear interpolation were 0.00 mm/min, 16.54 mm2/min, and 1.00 mm, respectively.

3) For size ratio of 2.0:1.0 of potash, at the strain of 6% and strain rate of 0.5 Hz after 30

minutes, the modeled segregated mass was 7.3 g higher than the experimental segregated

mass; whereas, the segregated mass calculated from the model operating parameters

convective, diffusive, and resistance obtained from linear interpolation was 45.3 g higher

than experimental segregated mass. The modeled segregated mass was within the 95% CI

of the experimental values.


potash, the modeled convective, diffusive, and resistance parameters were 0.99 mm/min,

98.24 mm2/min, and 13.00 mm, respectively; whereas these parameters calculated from

linear interpolation were 1.20 mm/min, 42.61 mm2/min, and 2.75 mm, respectively.

12.6 Key Findings

A time-dependent percolation segregation model was developed for the binary mixtures

of urea and potash. The percolation segregation of fines in binary mixtures of urea and potash

can be determined at each time step based on requirement. The percolation segregation of fines

for intermediate size ratio, bed depth, mixing ratio, strain, and strain rate can be predicted by

interpolating the convective, diffusive, and resistance parameters of the model.

12.7 References Bridgwater, J., M. H. Cooke, and A. M. Scott. 1978. Inter-particle percolation: equipment

development and mean percolation velocities. Institution of Chemical Engineers 56: 157-167.

Bridgwater, J. 1994. Mixing and segregation mechanisms in particle flow. Ed.: Mehta, A. Granular Material-An Interdisciplinary Approach 161-193. Springer-Verlag New York, Inc.

Crank, J., and P. Nicolson. 1947. A practical method for numerical evaluation of solutions of partial differential equations of the heat-conduction type. Proceedings of the Cambridge Philosophical Society 43: 50-67.

de Silva, S., A. Dyroy, and G. G. Enstad. 2000. Segregation mechanisms and their quantification using segregation testers. Eds: Rosato, A. D. and D. L. Blackmore. IUTAM Symposium on Segregation in Granular Flows 11-29. Kluwer Academic Publishers.

254


Duffy, S. P. and V. M. Puri. 2003. Development and validation of a constitutive model for size-segregation during percolation. KONA (Powder and Particle) 21:151-162.

Jha, A. K., J. S. Gill, and V. M. Puri. 2007. Percolation segregation in binary size mixtures of spherical and angular-shaped particles of different densities. Particulate Science and Technology, An International Journal (In review).

Khakhar, D. V., A. V. Orpe, and J. M. Ottinumber 2001. Continuum model of mixing and size segregation in a rotating cylinder: concentration-flow coupling and streak formation. Powder Technology 116: 232-245.

Moakher, M., T. Shinbrot, and F. J. Muzzio. 2000. Experimental validated computations of flow, mixing and segregation of non-cohesive grains in 3D tumbling blenders. Powder Technology 109: 58-71.



Rosato, A. D. and D. L. Blackmore. 2000. Segregation in granular flows. Proceedings of the IUTAM Symposium held in Cape May, NJ, June 5-10, 1999. Kluwer Academic Press, Boston, MA. Pp. 342.

Salter, G. F. 1998. Investigations into the segregation of heaps of particulate materials with particular reference to the effects of particle size. Ph.D. diss., University of Greenwich.


Tang, P. and V. M. Puri. 2005. An innovative device for quantification of percolation and sieving segregation patterns – Single component and multi size fractions. Particulate Science and Technology, An International Journal 23(4): 335-350.


Vallance, J.W. and S.B. Savage. 2000. Particle segregation in granular flows down chutes. Eds: Rosato, A.D. and D.L. Blackmore. IUTAM Symposium on Segregation in Granular Flows 31-51. Kluwer academic Publishers.


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13. CHAPTER – MECHANISTIC THEORY BASED DIMENSIONAL ANALYSIS PERCOLATION SEGREGATION

MODEL DEVELOPMENT AND VALIDATION

13.1 Abstract

Segregation induced by percolation mechanism is widely observed in industries during

various unit operations such as mixing, flow, storage, handling, and conveying. To quantify size-

segregation in binary, ternary, and quaternary mixtures of potash and urea, a mechanistic theory

based dimensional analysis model was developed and validated. Percolation of fines in terms of

mass fractions were used when the PSSC-II was operated upto 30 minutes at three strain rates

0.25 Hz, 0.5 Hz, and 1.0 Hz and three strains 2%, 6%, and 10% to determine model parameters

and validate the model. Herein, for model development, binary, ternary, and quaternary size

ratios for each of the three coarse sizes 3,675 µm, 3,075 µm, and 2,580 µm of potash were used.

The dimensional analysis model included binary, ternary, quaternary mixtures of urea and potash

at strains of 2%, 6%, and 10% and strain rates of 0.25, 0.5, and 1.0 Hz. The strain rate of 1.0 Hz

was only included at strain of 6% for binary mixtures. Developed model was validated for binary

and ternary size ratios of urea and potash at strain rate of 0.5 Hz. Based on results, model

developed for binary mixtures of potash was sufficient to represent binary, ternary, and

quaternary mixtures of urea and potash with reasonable accuracy. The CoV of the modeled

values to the experimental values were 18%, 15%, and 11% for binary mixtures of urea and

potash at strains of 2%, 6%, and 10% and strain rate of 0.25 Hz. Accuracy of model could be

improved by incorporating small ternary and more quaternary size ratios.

13.2 Introduction Particulate materials are handled, stored, mixed, and processed in various industries

including agriculture, cosmetic, food, metal and metallurgy, nutraceutical, and pharmaceutical.

Segregation occurs in particulates during the mentioned unit operations and negatively impacts

the quality of products. Segregation in particulate materials occurs due to difference in the

constituents’ physical and mechanical properties (Rosato et al., 2002). Although segregation is

governed by several parameters, however simultaneously studying the effects of all parameters is

not feasible due to the lack of fundamental understanding of their interactions. To gain greater

256

and deeper insights, dominant variables should be identified and other variables incorporated

subsequently to study segregation. Bridgwater and his co-workers were the pioneers in

identifying the dominant parameters and mechanisms of segregation (Bridgwater et al., 1978 and

Bridgwater, 1994). In practice, segregation has been measured using coefficient, mechanism, and

model (Rosato and Blackmore, 2000). Of the three, to model the segregation process for a

specific mechanism is preferred so that the model could be applied to different operating

conditions. To date, thirteen segregation mechanisms have been identified based on different

operating conditions, i.e., trajectory, air current, rolling, sieving and sifting, impact, embedding,

angle of repose, push-way, displacement or floating, percolation, fluidization, agglomeration,

and, concentration driven displacement (Mosby et al., 1996; Salter, 1998; de Silva et al., 2000).

Of the thirteen, percolation segregation is widely observed when materials are handled, stored,

mixed, and conveyed in various industries. Percolation segregation in particulate materials

during various operations has been modeled when size, shape, and density of particulate were

included (see Chapter 2). Percolation segregation in particulates is also affected by the

mechanical conditions under which materials are handled (Tang and Puri, 2005 and Jha and Puri,

2007). Percolation segregation is defined as the migration of fine particles through a bed of

coarse particles during gravity, shear, and vibration motions when subjected to dynamic

conditions (Vallance and Savage, 2000). However, most of the studies were conducted for

specific operating conditions using ideal materials (glass beads) and a few real-world materials

(commonly used in industries). Tang and Puri in 2005 used point feed of fines in the coarse

particle bed using real-world materials (poultry feed), which is not the common approach to

handle particulates in industries. In this chapter, percolation segregation during shear motion was

selected for modeling due its wide application in the above mentioned unit operations in

industries. Segregation in particulates can be modeled by three approaches: continuum models,

kinetic theory models, and discrete models (Moakher et al., 2000). Tang (2004) developed a

mechanistic theory which included the advantages of all the three mentioned modeling

approaches. Mechanistic theory incorporated the continuum and discrete element theory by

including the segregation potential of fines sizes and kinetic theory by studying the falling path

of fines in larger size ratios.

Based on the literature review, a dimensional analysis model by combining, for the first

time, physical and mechanical parameters was developed and validated for well-mixed multi-size

257

real-world materials. The developed dimensional analysis model included size, shape, density,

size ratio, mixing ratio, strain rate, strain, and bed depth. The primary segregation shear cell

(PSSC-II) was used to measure the amount of percolated fines from well-mixed multi-size

mixtures. The specific objectives of this study were to develop and validate the segregation

model for parameters: 1) size ratio, 2) coarse particle size, 4) bed depth, 5) mixing ratio, 6) shape

of particle (different type of material), 7) strain in mixture bed, 8) strain rate, and 9) binary and

multi-component mixtures


The PSSC-II has five main components Tang (2004): shear box, measurement system,

sieve system, drive system, and main frame. Different size cams could be used to produce

different strains in the shear box and motor speed could be adjusted for different intensity of

movements or strain rate. A screen of opening size 2,360 µm was used throughout the

experiments after preliminary tests with multi-size ratios to ensure that coarse size particles did

not block the screen openings but allowed fines to exit freely.


For segregation study, three parameters including material bed depth, particle bed strain,

and strain rate were selected for operating PSSC-II based on published results (Tang and Puri,

2005). Bed depth of 85 mm (shear box height = 100 mm) was used to represent percolation of

fines within bagged fertilizers in normal orientation, i.e., depth direction along gravity, during

conveying, handling, and transportation. The selected strains of 2%, 6%, and 10% and strain

rates of 0.25, 0.5, and 1.0 Hz represent the unfilled bag volume (≤ 15%) and intensity of motion,

respectively, experienced by the fertilizer mixture in the bag during processing operations (<10

Hz) (Vursavus and Ozguven, 2004). The tests at strain rate of 1.0 Hz were conducted only at

strain of 6% for binary mixtures of urea and potash.

The three coarse sizes were for urea and potash and three and two fines sizes were

selected for potash and urea, respectively. The binary, ternary, and quaternary mixtures under

different operating conditions were studied for percolation of fines using the PSSC-II. Different

mixing ratios (MR) were used for different size ratios based on weight proportion of different

258

size distributions found in low analysis blends such as 10-10-10 fertilizer samples collected from

blend plants.


Coarse size particles were mixed with fine size particles in a 225-W six-speed bench-top



binary, ternary, and quaternary size samples within the 95% confidence interval (CI). Mixed

samples were placed in shear box of the PSSC-II very gently with a scoop to avoid segregation.

From statistical analysis of data, a separate experimental design was considered for binary,

ternary and quaternary mixtures including dissimilar amount of fines (Tables 13.1 and 13.2).

Based on published results (Duffy and Puri, 2002, and Tang and Puri, 2005), and preliminary

testing with fertilizer blends, six replications were done for each set of experiments for testing

percolation segregation using PSSC-II. A complete block design was selected for data analysis.

A set of coarse particles was considered as a block of experiment. Within each block, all

treatments (replicate = 1 × 6 = 6) were randomly assigned. Developed dimensional analysis

model was validated for binary size mixtures of urea and potash (Table 13.3). Ternary and

quaternary size ratios were not available in the sufficient quantity; therefore, these were not

included in validation. All tests were conducted in an environment-controlled laboratory with

average temperature of 22°C ± 3°C and relative humidity less than 40%.

259

Table 13.1 Experimental design for binary size mixtures for potash and urea* Material Strain rate Coarse size Fines size Size ratio Mixing ratio Number

1,550 2.4:1.0 50:50 1,850 2.0:1.0 37:63

Potash 0.25 1.00**

3,675

2,180 1.7:1.0 37:63

6

1,550 2.0:1.0 63:37 1,850 1.7:1.0 50:50

Potash 0.25 1.00**

3,075

2,180 1.4:1.0 50:50

6

1,550 1.7:1.0 1,850 1.4:1.0 60:40

Potash

0.25 1.00**

2,580

2,180 1.2:1.0 60:40

6

1,850 2.0:1.0 37:63 Urea 0.25 1.00**

3,675 2,180 1.7:1.0 37:63

4

1,850 1.7:1.0 37:63 Urea 0.25 1.00**

3,075 2,180 1.4:1.0 37:63

4

1,850 1.4:1.0 37:63 Urea 0.25 1.00**

2,580 2,180 1.2:1.0

4

Total (6 replications) 30×3×6 = 540 *Strains of 2%, 6%, and 10%

**Strain rate only at strain of 6%

Table 13.2 Experimental design for multi-size size mixtures for potash and urea* Material Strain rate Coarse size Fines size Size ratio Mixing ratio Number

1,550 2.4:2.0:1.0 28:44:28 1,850 2.0:1.7:1.0 22:39:39

Potash 0.25 0.50

3,675+3,075

2,180 1.7:1.4:1.0 22:39-39

6

1,550 2.0:1.7:1.0 33:46:21 Potash 0.25 0.50

3,075+2,580 1,850 1.4:1.4:1.0 29:42:29

4

1,550 2.4:2.0:1.7:1.0 17:28:38:17 Potash 0.25 0.50

3,675+3,075+ 2,580 1,850 2.0:1.7:1.4:1.0 13:25:37:25

4

1,850 2.4:2.0:1.0 22:39:39 Urea 0.25 0.50

3,675+3,075 2,180 2.0:1.7:1.0 22:39:39

4

Urea 0.25 3,075+2,580 1,850 2.0:1.7:1.0 29:42:29 2 Urea 0.25 3,675+3,075+ 1,850 2.0:1.7:1.4:1.0 13:25:37:25 2 Total (six replications) 22×6×3 = 396

*Strains of 2%, 6%, and 10%

260

Table 13.3 Validation design for binary size mixtures for potash and urea* Material Strain Rate

(Hz) Coarse size

(µm) Fines Size


1,550 2.4:1.0 50:50 1,850 2.0:1.0 37:63

Potash 0.5 3,675

2,180 1.7:1.0 37:63

3

1,550 2.0:1.0 63:37 1,850 1.7:1.0 50:50

Potash 0.5 3,075

2,180 1.4:1.0 50:50

3

1,550 1.7:1.0 67:33 1,850 1.4:1.0 60:40

Potash

0.5 2,580

2,180 1.2:1.0 60:40

3

1,850 2.0:1.0 37:63 Urea 0.5 3,675 2,180 1.7:1.0 37:63

2

1,850 1.7:1.0 37:63 Urea 0.5 3,075 2,180 1.4:1.0 37:63

2

1,850 1.4:1.0 60:40 Urea 0.5 2,580 2,180 1.2:1.0 60:40

2

Total (six replications) 15*6 = 90

*Strain of 6%

13.3.3 Dimensional analysis model development

Dimensional analysis applies Fourier’s principle of dimensional homogeneity (Streeter et

al., 1996). Dimensional homogeneity expresses a relationship between representative physical

quantities to a problem which are dimensionally homogeneous on both sides. The dimensional

relationship based on dimensional analysis may or may not produce analytical solutions to a

physical problem but provides very good sense of physical problem. In order to implement this

principle, the physical status of a problem must be understood and the parameters affecting that

process must be included, i.e., the user must be knowledgeable (Murdock, 1993). Care should be

taken during model development, particularly, if any significant variable is omitted, then the

relationship obtained from dimensional analysis may not accurately apply to the physical

problem. On the other hand, dimensional analysis model will lose its advantage if all the

parameters affecting a problem are included.

Based on the physics of the problem, percolation segregation in bagged fertilizer is

affected by size, shape, density, and mixing ratio, relative movement (strain), intensity of

movement (strain rate), and fill height of bagged blended fertilizers. As mechanistic theory states

261

that a mathematical relationship exists between percolation segregation in particulate materials

(e.g., fertilizer) and physical and mechanical properties of the particulates. In the case of

fertilizer, physical property includes size (SGN), size ratio (UI), shape, density, and mixing ratio

and mechanical property includes strain (displacement), strain rate (intensity of to-and-fro

motion), and bed depth. However, there are other physical parameters that indirectly affect

segregation such as surface texture, surface composition, and electrostatics; their effect being

secondary compared with the gravitational force, were not included. The physical and

mechanical parameters used in this model are defined below for the better understanding.

Coarse mean size: The (2)1/4 series of US standard sieve was used to sieve the continuous size

mixtures collected from the six blend plants. The size range is defined as the material that passed

through a sieve and retained on sieve just below it. For example, material that passed through

sieve number 6 (opening size = 3,350 µm) and retained on sieve number 7 (opening size = 2.80

µm) has size range of 2,800-3,350 µm. The average of these two limits ((2,800+3,350)/2) was

considered as the coarse mean size, i.e., 3,075 µm.

Size ratio: Size ratio for the binary mixtures is defined as the ratio of coarse mean size to fines

mean size, whereas, the ternary size ratio was defined as the ratio of each coarse mean sizes with

respect to fines mean size, for example, two coarse mean sizes 3,675 µm and 3,075 µm and one

fines mean size 1,550 µm is represented as 3,675 µm: 3,075 µm: 1,550 µm and it is rounded off

to the first decimal, i.e., 2.4:2.0:1.0. Similarly, quaternary size ratio was defined as ratio of each

of the three coarse mean sizes with respect to fines mean size.

Bed depth: Bed depth accounts for the amount of material (binary, ternary, quaternary, and

continuous mixtures) in the shear box. A constant depth of 85 mm was maintained throughout

the tests by varying the amount of materials tested, i.e., 960 g and 700 g for potash and urea,

respectively. Recall that the particle density of potash (2.26 g/cc) is larger than urea (1.45 g/cc).

Strain rate: It is defined as the number of cycles completed in one second. The speed of motor

could be increased or decreased based on specific requirements using the motor switch. The

three strain rates of 0.25 Hz, 0.5 Hz, and 1.0 Hz were used for conducting experiments.

Strain: It is defined as the ratio of relative movement of two side walls to the length of side wall.

Three strains of 2%, 6%, and 10% were used for conducting the experiments.

Mixing ratio: It is defined as the ratio of coarse particles to the fines particles.

262

It was intended to use Buckingham Pi theorem to develop dimensional analysis model

but the number of variables were not sufficient to make proper dimensionless grouping. Based

on blend plant visits, experimental data, and previous experiences of Tang and Puri (2007), the

physical and mechanical parameters that significantly affect percolation segregation are included

in the mechanistic theory and grouped in such a fashion that each term is dimensionless, a

dimensional analysis model was proposed and is given below in equation (13.1).

( ) ( )ponm

l RatioSizeStrainRatioMixingDepthBed

sizeCoarseShpcRateStrain

NSR )()(⎟⎟⎠

⎞⎜⎜⎝

⎛= (13.1)

where,

NSR = Total fines segregated/Total fines in the mixture/Total time of PSSC-II operation, kg/kg-s

Strain Rate = intensity of movement of bagged fertilizer, Hz

Shp = shape and density of fertilizer, dimensionless

Coarse Size = size guide number (SGN) or size of particle, mm*100

Bed Depth = depth of fertilizer in the bag, mm

Mixing Ratio = ratio of mass of coarse to mass of fines*100, dimensionless

Displacement = relative displacement two side walls (length wise) of bagged fertilizer, %

Size Ratio = ratio of size of coarse particles to fine particles, dimensionless

l = power, indicates the contribution of shape and density to NSR/Strain rate

m = power, indicates the contribution of coarse size to NSR/Strain rate

n = power, indicates the contribution of mixing ratio to NSR/Strain rate

o = power, indicates the contribution of strain to NSR/Strain rate

p = power, indicates the contribution of size ratio to NSR/Strain rate

The constant c and exponents’ l, m, n, o, and p were calculated using regression analysis.

The physical meaning is needed to understand the dimensional analysis model well. Segregation

under shear motion is contributed by the difference in physical and mechanical properties of

particulates. On the left side, the model has two parameters, normalized segregation rate (NSR)

and strain rate. The segregation measuring parameter NSR was developed to make segregation

rate independent of amount of initial fines in the material mixtures. The NSR contained two

fundamental dimensions, mass (M) and time (T). The second parameter strain rate is the

operating parameter of the PSSC-II and it has the unit of time (T). These two parameters made

the left side of the above equation dimensionless. Thus, the ratio of NSR to strain rate

263

⎟⎟⎠

⎞⎜⎜⎝

⎛RateStrain

NSR is a dimensionless constant, which, physically, is an index to determine the

segregation potential of the test material.

On the right side of the equation, the dominant physical and mechanical parameters of

materials are included. The dominant parameters for the PSSC-II under shear motion

contributing to segregation included coarse size, shape, mixing ratio, strain, size ratio, and bed

depth. As used, the use of porosity may not be nearly as accurate as using individual particle

shape using dimensions (length, width) or index compared with spherical-shaped particle

(Gotoh, 1997). How these parameters affect the segregation of fines in the test materials must be

understood before creating sets for making dimensionally homogenous equation. The

segregation potential of binary, ternary, and quaternary size mixtures are proportional to the

coarse size, size ratio, strain, mixing ratio, and shape and inversely proportional to bed depth.

The physical and mechanical parameters were grouped in such a way that the right side of the

equation must be dimensionless to make the dimensionally homogeneous equation. Both bed

depth and coarse size have the same dimension, length (L). The shape, mixing ratio, strain, and

size ratio are dimensionless.

The exponents’ l, m, n, o, and p can be estimated using different approaches. Here linear

regression method was used to determine these parameters. The above dimensionally

homogeneous equation was converted into linear form by taking the natural logarithm on both

sides of the above equation. The size of coarse particle and size ratio were among the main

contributors to the magnitude of NSR. Furthermore, in the binary mixtures below size ratio 2.5,

NSR exponentially increased with the size ratio. The NSR also increased with the increase in

coarse size in binary mixtures (Jha et al., 2007). Therefore, a dimensionless equation after taking

natural logarithm on both sides based on Buckingham Pi theorem is given below in equation

(13.2):

( )

)ln(

)ln()ln(lnlnln

RatioSizep

StrainoRatioMixingnDepthBed

sizeCoarsemShapelRateStrain

NSR

+

++⎟⎟⎠

⎞⎜⎜⎝

⎛+=⎥

⎦

⎤⎢⎣

⎡

………………………………………………………………………………………………..(13.2)

Now, the exponents l, m, n, o, and p can easily be determined using linear regression analysis.

The physical and mechanical parameters were obtained from the experimental data and NSR was

264

also calculated individually for these parameters. The size ratio rounded off to the first decimal

place was used for data collection. The root-mean square error (RMSE) and the coefficient of

variation (CoV) were calculated to evaluate the accuracy of the model through equations (13.3)

and (13.4).

( )

N

RPRMSE

N

iii∑

=

−= 1

2

(13.3)

RMSE = root-mean square error

iP = ith fitted value corresponding to the ith observation

iR = ith observation

N = number of observation

%100×=meanalExperiment

RMSECoV (13.4)

13.4 Results and Discussion The exponents’ l, m, n, o, and p were determined using linear regression. Equation (13.2)

was linearly regressed using data for binary mixtures of urea and potash and binary mixtures

when urea and potash were taken together. Equation (13.2) was also regressed using data of

ternary mixtures of urea and potash. Quaternary mixtures were not used individually for linear

regression because only limited (three) number of quaternary mixtures were available. Finally

equation (13.2) was linearly regressed when binary, ternary, and quaternary mixtures of urea and

potash were taken together. For multi-size mixtures, the equation was regressed in two different

ways. In the first case, the average shape or porosity (53%) was considered when the porosity of

urea and potash mixtures was 51% and 55%, respectively so that porosity could be treated as

constant to eliminate a term from the final equation. In the second approach, the actual porosity

of urea and potash was used for determining the coefficient l, m, n, o, and p.

265

13.4.1 Determination of exponents’ l, m, n, o, and p for multi-size mixtures

The regression variance of analysis for binary mixtures of potash showed that all five

terms, Constant, ln(Size Ratio), ln(Coarse Size/Bed Depth), ln(Mixing Ratio), and ln(Strain) had

significant effect on NSR/Strain Rate (p<0.05). The values of these five exponents l, m, n, o, and

p (14.6, 7.17, -8.02, -1.28, and 1.63, respectively) were obtained through regression analysis and

given in Table 13.4 with R2 = 0.90, and equation is summarized below.

( ) ( )

( )Strain

RatioMixingdepthBed

sizeCoarseRatioSizeRateStrain

NSR

ln63.1

ln28.1ln02.8ln17.76.14ln

+

−⎟⎟⎠

⎞⎜⎜⎝

⎛−+=⎟⎟

⎠

⎞⎜⎜⎝

⎛

………………………………………………………………………………………………..(13.5) Table 13.4 Results of linear regression analysis of variance for binary mixtures of potash*

Predictor Coefficient symbol Exponents value P Value Constant l 14.6 0.003 ln(Size ratio) p 7.17 0.000 ln(Coarse Size/Bed Depth) m -8.02 0.000 ln(Mixing Ratio) n -1.28 0.017 ln(Strain) o 1.63 0.000 *R-square = 0.90

The porosity of binary mixture of potash was constant (55%) and was incorporated into

constant “c” in the linear regression analysis. The contributions of Size Ratio and Strain were

proportional to NSR/Strain Rate, whereas contributions of Coarse Size/Bed Depth and Mixing

Ratio were inversely proportional. Positive constant l and exponents p and o represent that the

effect of porosity, Size Ratio, and Strain are proportional to NSR/Strain Rate, i.e., increase in

porosity, Size Ratio, and Strain will increase the NSR/Strain Rate. The negative exponents m and

n represent Coarse Size/Bed Depth and Mixing Ratio showed inverse relation with NSR/Strain

Rate, i.e., increase in Coarse Size/Bed Depth and Mixing Ratio will decrease NSR/Strain Rate.

The regression variance of analysis for ternary potash mixtures showed that all five

terms, Constant, ln(Size Ratio), ln(Coarse Size/Bed Depth), ln(Mixing Ratio), and ln(Strain) had

significant effect on NSR/Strain Rate (p<0.05). Values of these five parameters l, m, m, o, and p

(22.6, 8.64, -9.12, -2.47, and 1.88, respectively) were obtained through regression analysis and

are given in Table 13.5 with R2 = 0.943. The R-square value for ternary size mixtures (0.943)

was higher than the binary size mixture (0.90) because coarse size 2,580 µm was included only

twice compared with 5 times in the binary mixtures.

266

( ) ( )

( )Strain

RatioMixingDepthBed

SizeCoarseRatioSizeRateStrain

NSR

ln88.1

ln47.2ln12.9ln64.86.22ln

+

−⎥⎦

⎤⎢⎣

⎡−+=⎟⎟

⎠

⎞⎜⎜⎝

⎛…

………………………………………………………………………………………………..(13.6) Table 13.5 Results of linear regression analysis of variance for ternary mixtures of potash* Predictor Coefficient symbol Exponents value P Value Constant l 22.6 0.002 ln(Size Ratio) p 8.64 0.000 ln(Coarse Size/Bed Depth) m -9.12 0.003 ln(Mixing Ratio) n -2.47 0.002 ln(Strain) o 1.88 0.000 *R-square = 0.943

The porosity of ternary mixture of potash was constant (55%) and incorporated into

constant “c” in the linear regression analysis. The contribution of Constant, Size Ratio, Coarse

Size/Bed Depth, Mixing Ratio, and Strain was larger for ternary mixtures vs. binary mixtures

when the regression equation was developed. Experimental design for binary and ternary

mixtures showed that ternary mixtures had used coarse size 2,580 µm used twice vs. three times

with binary mixtures (Tables 13.1 and 13.2). Exponents of Size Ratio and Coarse Size/Bed

Depth were higher compared with Mixing Ratio and Strain (Tables 13.4 and 13.5). It means Size

Ratio and Coarse Size/Bed Depth contributed more to NSR/Strain Rate compared with Mixing

Ratio and Strain. Also, the effect of Coarse Size/Bed Depth was the highest among five variables

followed by Size Ratio. Results showed that size was the most dominant variable contributing

towards segregation of fines from well mixed systems.

The regression variance of analysis for binary mixtures of urea showed that only ln(Size

Ratio) and ln(Strain) had significant effect on NSR/Strain Rate (p<0.05), whereas ln(Coarse

Size/Bed Depth), Constant, and ln(Strain) were not significant (p>0.05). In the case of binary

mixtures of urea, the effect of small coarse size 2,580 µm was very dominant on the NSR

because the largest size ratio 2.4:1.0 was absent. The values of these five parameters l, m, n, o,

and p (-1.10, 5.85, -0.91, -0.57, and 0.86, respectively) were obtained through regression analysis

and are given in Table 13.6, with R2 = 0.835.

( ) ( )

( )Strain

RatioMixingDepthBed


NSR

ln86.0

ln57.0ln91.0ln85.510.1ln

+

−⎥⎦

⎤⎢⎣

⎡−+−=⎟⎟

⎠

⎞⎜⎜⎝

⎛

………………………………………………………………………………………………..(13.7)

267

Table 13.6 Results of linear regression analysis of variance for binary mixtures of urea* Predictor Coefficient symbol Exponents value P Value Constant l -1.10 0.942 ln(Size Ratio) p 5.85 0.000 ln(Coarse Size/Bed Depth) m -0.91 0.853 ln(Mixing Ratio) n 0.57 0.754 ln(Strain) o 0.86 0.000 *R-square = 0.835

The porosity of binary mixture of urea was constant (51%) and was incorporated into

Constant “c” in the linear regression analysis. The contributions of Size Ratio, Mixing Ratio and

Strain were proportional to NSR/Strain Rate, whereas contributions of Coarse Size/Bed Depth

were inversely proportional. The effect of Constant, Coarse Size/Bed Depth, and Mixing Ratio

on the NSR/Strain Rate was not significant (p>0.05) compared with binary and ternary mixtures

of potash where these variables had significant effect (p<0.05). The effect of Size Ratio on

NSR/Strain Rate was higher for potash compared with urea because shape of urea is spherical

compared with angular shape of potash and higher particle density of potash vs. urea, i.e.,

Cumulative effect of size, shape, and density of potash contributed more to NSR/Strain Rate

compared with only size of urea. Mixing ratio exponent was negative and smaller compared with

potash binary mixtures because of the absence of small fines size (1,550 µm).

The regression variance of analysis for binary, ternary, and quaternary mixtures of urea

and potash when porosity was kept constant (53%) showed that Constant, ln(Size Ratio),

ln(Coarse Size/Bed Depth), and ln(Strain) had significant effect (p<0.05). Exponents l, m, m, o,

and p (10.4, 6.86, -5.95, 0.77, and 1.30, respectively) were obtained through regression analysis

and are given in Table 13.7 with R2 = 0.827. Experimental results showed that the mixing ratio

had significant effect (p<0.05) on NSR (Jha and Puri, 2007). Regression analysis results showed

that mixing ratio effect is not as significant because of presence of large coarse size 2,580 µm

and small fines size 2,180 µm and absence of fines size 1,550 µm of urea.

( ) ( )

( )Strain

RatioMixingDepthBed


NSR

ln30.1

ln77.0ln95.5ln86.64.10ln

+

−⎥⎦

⎤⎢⎣

⎡−+=⎟⎟

⎠

⎞⎜⎜⎝

⎛

………………………………………………………………………………………………..(13.8)

268

Table 13.7 Results of linear regression analysis of variance for binary mixtures of potash and urea when porosity was kept constant*

Predictor Coefficient symbol Exponents value P Value Constant l 10.4 0.028 Ln(Size Ratio) p 6.86 0.000 Ln(Coarse Size/Bed Depth) m -5.95 0.005 Ln(Mixing Ratio) n -0.77 0.139 Ln(Strain) o 1.30 0.000 *R-square = 0.827

The porosity of binary mixtures of urea and potash was taken to be the average 53%, i.e.,

((51+55)/2 = 53) and was incorporated into constant “c” in the linear regression analysis. The

contributions of constant, Size Ratio, and Strain were proportional to NSR/Strain Rate, whereas

contributions of Coarse Size/Bed Depth and Mixing Ratio were inversely proportional. Effect of

Mixing Ratio on the NSR/Strain Rate was not significant (p>0.05) compared with binary and

ternary mixtures of potash where mixing ratio had significant effect. Total nine binary size and

six binary size mixtures of potash and urea, respectively, were used for dimensional analysis

model development. Also the constant, exponents of Size Ratio, Coarse Size/Bed Depth, and

Strain were smaller compared with binary mixtures of potash. The lower values of the constant

and coefficients were contributed by binary mixtures of urea.

The regression variance analysis for binary, ternary, and quaternary mixtures of urea and

potash when porosity of 51% and 55% was used for urea and potash, respectively showed that

ln(Shape), ln(Size Ratio), and ln(Strain) had significant effect on NSR/Strain Rate (p<0.05),

whereas other three Constant, ln(Coarse Size/Bed Depth), and Mixing Ratio were not significant

(p>0.05). The linear regression equation with different shapes of potash and urea was not the

best representative based on experimental observation whereas urea and potash NSR were

significantly different at higher strains of 6% and 10%. The linear regression equation with

constant porosity also did not include the Mixing Ratio when it had significant effect. For linear

regression analysis, the values of five exponents l, m, m, o, and p (10.4, 6.86, -5.95, 0.77, and

1.30) were obtained through regression analysis and are given in Table 13.8 with R2 = 0.827 and

given in the following equation:

( ) ( )

( ) ( )StrainRatioMixingDepthBed

SizeCoarseRatioSizeShapeRateStrain

NSR

ln40.1ln12.0

ln05.0ln15.4ln65.66.26ln

++

⎥⎦

⎤⎢⎣

⎡−++−=⎟⎟

⎠

⎞⎜⎜⎝

⎛

………………………………………………………………………………………………..(13.9)

269

Table 13.8 Results of linear regression analysis of variance for binary mixtures of potash and urea when porosity was included*

Predictor Coefficient symbol Exponents value P Value Constant C -26.6 0.047 Shape L 6.65 0.000 Ln(Size Ratio) P 4.15 0.051 Ln(Coarse Size/Bed Depth) M -0.05 0.192 Ln(Mixing Ratio) N 0.12 0.164 Ln(Strain) O 1.40 0.000 *R-square = 0.827

The porosity of binary mixtures of urea and potash was considered as separate entity

from constant “c” in the linear regression analysis. The contributions of Constant, Size Ratio,

Coarse Size/Bed Depth, and Mixing Ratio on NSR/Strain Rate were not significantly different

(p>0.05). Experimental results showed that the variables Size Ratio, Coarse Size/Bed Depth, and

Mixing Ratio had significant effect on NSR/Strain Rate. Based on experimental results, inclusion

of urea and potash as separate entity in the linear regression model was not verified and is not

considered further for discussion. The linear regression analysis of quaternary mixtures was not

performed separately because only a few mixtures were available. The linear regression

equations for binary and ternary mixtures of potash were used for further study because other

models do not represent the physical process well.

When careful investigations of all regression equation for the above discussed cases were

performed, it was found that regression equation (13.5) developed using binary mixtures of

potash was the best to represent physical segregation process with R2 = 0.90, and is given below:

( ) ( ) ( ) 63.128.102.8

17.76.14 StrainRatioMixingdepthBed

sizeCoarseRatioSizeRateStrain

NSR⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛ (13.5)

13.5 Validation of the dimensional analysis segregation model The accuracy of the model developed using binary mixtures of potash was determined

through the comparison of experimental values to modeled values for binary mixtures of potash

and urea (Tables 13.9 through 13.11). When equation (13.5) was used for validation purposes,

the CoV, RMSE, and overall mean of the modeled values when compared with the experimental

values were 18%, 0.63, and 2.85, respectively, for binary mixtures of urea and potash at strain of

2% and strain rate of 0.25 Hz. The CoV, RMSE, and overall mean of the modeled values when

270

compared with the experimental values were 15%, 0.82, and 4.64, respectively, for binary

mixtures of urea and potash at strain of 6% and strain rate of 0.25 Hz; whereas, at strain of 10%

and strain rate of 0.25 Hz, the CoV, RMSE, and overall mean of modeled values when compared

with experimental values were 11%, 0.58, and 5.47, respectively. However, the overall mean of

the NSR for binary mixtures increased with the increase in strain from 2% to 10% although CoV

for binary mixtures of urea and potash decreased with the increase in strain from 2% to 10% for

the same size ratios.

Table 13.9 Comparison of the experimental and modeled values for binary mixtures of

potash and urea at strain of 2% and strain rate of 0.25 Hz Material Coarse

size (µm) Size ratio Experimental SD Modeled RMSE CoV

(%) 3,675 2.4:1.0 4.97 0.23 4.37 0.59 12 3,675 2.0:1.0 4.37 0.22 3.83 0.54 12 3,675 1.7:1.0 2.74 0.12 2.59 0.16 6 3,075 2.0:1.0 4.59 0.13 3.90 0.70 15 3,075 1.7:1.0 4.18 0.13 3.33 0.86 21 3,075 1.4:1.0 2.50 0.15 1.94 0.61 24 2,580 1.7:1.0 4.06 0.07 3.73 0.33 8 2,580 1.4:1.0 3.47 0.09 2.82 0.65 19

Potash

2,580 1.2:1.0 2.41 0.41 1.72 0.68 28 3,675 2.0:1.0 4.73 0.23 3.06 1.68 36 3,675 1.7:1.0 3.44 0.24 2.67 0.79 23 3,075 1.7:1.0 4.31 0.14 2.73 0.34 8 3,075 1.4:1.0 3.05 0.15 1.94 0.39 13 2,580 1.4:1.0 3.66 0.15 2.33 0.46 13

Urea

2,580 1.2:1.0 2.81 0.00 1.72 0.68 24

271

Table 13.10 Comparison of the experimental and modeled values for binary mixtures of potash and urea at strain of 6% and strain rate of 0.25 Hz

Material Coarse size (µm)

Size ratio Experimental SD Modeled RMSE CoV (%)

3,675 2.4:1.0 6.98 0.15 6.16 0.82 12 3,675 2.0:1.0 6.56 0.16 5.62 0.93 14 3,675 1.7:1.0 4.79 0.17 4.38 0.43 9 3,075 2.0:1.0 6.72 0.18 5.69 1.01 15 3,075 1.7:1.0 6.30 0.12 5.12 1.18 19 3,075 1.4:1.0 4.91 0.13 3.73 1.18 24 2,580 1.7:1.0 6.16 0.14 5.52 0.61 10 2,580 1.4:1.0 5.44 0.19 4.61 0.82 15

Potash

2,580 1.2:1.0 4.30 0.20 3.51 0.79 18 3,675 2.0:1.0 5.99 0.09 4.85 1.14 19 3,675 1.7:1.0 5.05 0.08 4.46 0.60 12 3,075 1.7:1.0 5.16 0.22 4.52 0.25 5 3,075 1.4:1.0 4.93 0.23 3.73 1.43 29 2,580 1.4:1.0 4.34 0.11 4.12 0.25 6

Urea

2,580 1.2:1.0 4.25 0.00 3.51 0.79 19


potash and urea at strain of 10% and strain rate 0.25 Hz Material Coarse


(%) 3,675 2.4:1.0 7.43 0.33 6.99 0.45 6 3,675 2.0:1.0 6.99 0.22 6.46 0.54 8 3,675 1.7:1.0 5.11 0.12 5.21 0.10 2 3,075 2.0:1.0 7.04 0.13 6.52 0.53 8 3,075 1.7:1.0 6.85 0.17 5.95 0.90 13 3,075 1.4:1.0 5.38 0.15 4.56 0.82 15 2,580 1.7:1.0 6.13 0.14 6.35 0.26 4 2,580 1.4:1.0 5.83 0.16 5.45 0.38 7

Potash

2,580 1.2:1.0 4.57 0.00 4.34 0.24 5 3,675 2.0:1.0 6.30 0.22 5.69 0.60 10 3,675 1.7:1.0 4.76 0.21 5.29 0.54 11 3,075 1.7:1.0 5.64 0.26 5.35 0.78 14 3,075 1.4:1.0 4.77 0.23 4.56 1.08 23 2,580 1.4:1.0 4.62 0.24 4.96 1.26 27

Urea

2,580 1.2:1.0 3.69 0.00 4.34 0.24 7

272

The accuracy of developed model using binary mixtures of potash was determined

through the comparison of experimental values to modeled values for ternary mixtures of potash

and urea (Tables 13.12 and 13.13). When equation (13.5) was used for validation purposes, the

CoV, RMSE, and overall mean of the modeled values when compared with the experimental

values were 19%, 0.64, and 2.23, respectively for ternary mixtures of urea and potash at strain of

2% and strain rate of 0.25 Hz; whereas, at the strain of 10% and strain rate of 0.25 Hz, the CoV,

RMSE, and overall mean of modeled values when compared with experimental values were

15%, 0.90, and 4.85, respectively. However, the overall mean of the NSR for ternary mixtures

increased with the increase in strain from 2% to 10% although CoV for ternary mixtures of urea

and potash decreased with the increase in strain from 2% to 10% for the same size ratios. The

effects of size ratio and coarse size are very dominant so the binary mixtures might not represent

accurately segregation process in ternary mixtures.

Table 13.12 Comparison of the experimental and modeled values for ternary mixtures of



(%) 3,308 2.4:2.0:1.0 4.59 0.23 3.15 1.44 31 3,291 2.0:1.7:1.0 4.31 0.27 2.52 1.17 27 3,291 1.7:1.4:1.0 2.74 0.11 1.34 0.40 15 2,787 2.0:1.7:1.0 2.94 0.13 2.81 0.25 9

Potash

2,782 1.7:1.4:1.0 2.41 0.15 2.08 0.69 29 3,291 2.0:1.7:1.0 4.88 0.24 2.52 0.21 4 3,291 1.7:1.4:1.0 2.05 0.21 1.34 0.25 12

Urea

2,782 1.7:1.4:1.0 2.94 0.24 2.08 0.69 23

Table 13.13 Comparison of the experimental and modeled values for ternary mixtures of



(%) 3,308 2.4:2.0:1.0 7.21 0.28 5.78 1.435 20 3,291 2.0:1.7:1.0 6.99 0.24 5.14 1.850 26 3,291 1.7:1.4:1.0 5.57 0.23 3.96 1.604 29 2,787 2.0:1.7:1.0 6.60 0.17 5.43 0.58 9

Potash

2,782 1.7:1.4:1.0 6.05 0.15 4.70 0.36 6 3,291 2.0:1.7:1.0 6.00 0.13 5.14 0.10 2 3,291 1.7:1.4:1.0 5.05 0.14 3.96 0.90 18

Urea

2,782 1.7:1.4:1.0 4.87 0.12 4.70 0.36 7

273

To validate the model, comparison between the modeled data and experimental values

was performed for the size ratios for which model was developed but at intermediate strain rate

(Table 13.14). When equation (13.5) was used for validation purposes, the CoV, RMSE, and

overall mean of the modeled values to the experimental values were 9.1%, 0.47, and 4.48,

respectively (Figures 13.1 and 13.2). To validate the model, comparison between the modeled

data and experimental values was performed for size ratios for which model was developed but

at intermediate strain rate of 0.5 Hz (Table 13.15). When equation (13.6) was used for validation

purposes, the CoV, RMSE, and overall mean of the modeled values to the experimental values

were 38%, 1.78, and 6.75, respectively (Figures 13.3 and 13.4).


potash and urea Material Coarse


(%) 3,675 2.4:1.0 6.75 0.31 5.89 0.59 9 3,675 2.0:1.0 6.22 0.12 5.41 0.59 10 3,675 1.7:1.0 4.27 0.13 4.21 0.20 5 3,075 2.0:1.0 6.48 0.14 5.47 0.79 12 3,075 1.7:1.0 6.16 0.10 4.95 1.05 17 3,075 1.4:1.0 4.51 0.11 3.62 0.79 18 2,580 1.7:1.0 5.37 0.14 5.35 0.19 4 2,580 1.4:1.0 4.84 0.21 4.51 0.23 5

Potash

2,580 1.2:1.0 3.60 0.00 3.45 0.09 3 3,675 2.0:1.0 5.84 0.22 4.64 0.99 17 3,675 1.7:1.0 4.22 0.11 4.29 0.25 6 3,075 1.7:1.0 4.87 0.12 4.36 0.36 7 3,075 1.4:1.0 4.14 0.13 3.62 0.46 11 2,580 1.4:1.0 3.89 0.10 4.02 0.25 6

Urea

2,580 1.2:1.0 3.32 0.00 3.45 0.19 6

The accuracy of the model developed using ternary size potash mixtures was determined

through the comparison of experimental values to modeled values (Table 13.15). When equation

(13.6) was used for validation purposes, the CoV, RMSE, and overall mean of the modeled

values to the experimental values were 37.9%, 1.78, and 6.75, respectively (Figures 13.3 and

13.4). The higher CoV values (>25%) was observed for 12 cases out of 15 cases of binary

mixtures. The lower strain 2% and lower coarse size have contributed substantially in

274

determining the NSR/Strain rate of binary mixtures of potash. If the effect of strain 2% is

eliminated then ternary mixtures can be represented by binary mixtures.

Table 13.15 Comparison of the experimental and modeled values for ternary mixtures of potash and urea

Material Coarse size (µm)

Size ratio Experimental SD Modeled RMSE CoV (%)

3,675 2.4:1.0 6.75 0.13 8.81 2.05 30 3,675 2.0:1.0 6.22 0.12 8.71 2.49 40 3,675 1.7:1.0 4.27 0.12 7.15 2.90 68 3,075 2.0:1.0 6.48 0.31 7.70 1.23 18 3,075 1.7:1.0 6.16 0.17 7.45 1.29 21 3,075 1.4:1.0 4.51 0.15 5.77 1.26 28 2,580 1.7:1.0 5.37 0.14 7.10 1.75 33 2,580 1.4:1.0 4.84 0.33 6.37 1.53 32

Potash

2,580 1.2:1.0 3.60 0.00 5.04 1.45 40 3,675 2.0:1.0 5.84 0.12 7.23 1.38 24 3,675 1.7:1.0 4.22 0.22 7.31 3.09 73 3,075 1.7:1.0 4.87 0.23 6.30 1.40 29 3,075 1.4:1.0 4.14 0.24 5.77 1.69 41 2,580 1.4:1.0 3.89 0.13 5.43 1.49 39

Urea

2,580 1.2:1.0 3.32 0.00 5.04 1.72 52

275

0.0

2.0

4.0

6.0

8.0

10.0

P3675

-2.4:1

.0

P3675

-2.0:1

.0

P3675

-1.7:1

.0

P3075

-2.0:1

.0

P3075

-1.7:1

.0

P3075

-1.4:1

.0

P2580

-1.7:1

.0

P2580

-1.4:1

.0

P2580

-1.2:1

.0

Binary-Potash

NS

R/S

train

rate

ExperimentalModeled

Figure 13.1 Validation of dimensional analysis model by comparison of modeled values to

experimental values for potash at strain rate of 0.5 Hz, with ±SD as error bars

0.0

2.0

4.0

6.0

8.0

10.0

U3675

-2.0:1

.0

U3675

-1.7:1

.0

U3075

-2.0:1

.0

U3075

-1.7:1

.0

U2580

-2.0:1

.0

U2580

-1.7:1

.0

Binary-Urea

NSR

/Stra

in ra

te ExperimentalModeled


experimental values for urea at strain rate of 0.5 Hz, with ±SD as error bars

276

0.0

2.0

4.0

6.0

8.0

10.0

P3675

-2.4:1

.0

P3675

-2.0:1

.0

P3675

-1.7:1

.0

P3075

-2.0:1

.0

P3075

-1.7:1

.0

P3075

-1.4:1

.0

P2580

-1.7:1

.0

P2580

-1.4:1

.0

P2580

-1.2:1

.0

Binary-Potash

NS

R/S

train

rate

ExperimentalModeled


experimental values for potash at strain rate of 0.5 Hz, with ±SD as error bars

0.0

2.0

4.0

6.0

8.0

10.0

U3675

-2.0:1

.0

U3675

-1.7:1

.0

U3075

-2.0:1

.0

U3075

-1.7:1

.0

U2580

-2.0:1

.0

U2580

-1.7:1

.0

Binary-Urea

NSR

/Stra

in ra

te ExperimentalModeled


experimental values for urea at strain rate of 0.5 Hz, with ±SD as error bars

277

13.6 Conclusions

Percolation segregation in binary, ternary, and quaternary mixtures of urea and potash

was quantified using primary segregation shear cell (PSSC-II). For model development, binary

size mixtures of potash was found to be the best representative of experimental data at three

strains of 2%, 6%, and 10% and three strain rates 0.25, 0.5, and 1.0 Hz. Dimensional analysis

model included the range of variables, i.e., size ratio, shape, density, strain rate, and strain to

predict NSR. Developed dimensional analysis model was validated for binary mixtures of urea

and potash. Furthermore, all the binary, ternary, and quaternary mixtures were combined with

and without keeping porosity constant but found not be the representative of experimental data.

Based on results, the following conclusion can be drawn:

1. When equation (13.5) was used for validation purposes, the CoV of the modeled values

to the experimental values were 18%, 15%, and 11% for binary mixtures of urea and

potash at strains of 2%, 6%, and 10% and strain rate of 0.25 Hz.

2. The dimensional analysis model developed by the binary mixtures of potash was

sufficient to represent the binary, ternary, and quaternary mixtures of urea and potash.

13.6 Key Findings

A time-independent percolation segregation model was developed and validated in

addition to time-dependent model for urea and potash. All the physical and operating parameters

were grouped into dimensionless terms but that comes with a price by removing time variable

from the equation. This time-independent percolation segregation model could be generalized for

scale-up process from lab scale to pilot scale leading to production scale.

13.7 References Bridgwater, J., M. H. Cooke, and A. M. Scott. 1978. Inter-particle percolation: equipment

development and mean percolation velocities. Institution of Chemical Engineers 56: 157-167.

Bridgwater, J. 1994. Mixing and segregation mechanisms in particle flow. Ed.: Mehta, A. Granular material-an interdisciplinary approach 161-193. Springer-Verlag New York, Inc.

de Silva, S., A. Dyroy, and G. G. Enstad. 2000. Segregation mechanisms and their quantification using segregation testers. Eds: Rosato, A. D. and D. L. Blackmore. IUTAM Symposium on Segregation in Granular Flows 11-29. Kluwer Academic Publishers.

278

Gotoh, K. 1997. Particle shape characterization. Ed: Gotoh, K., H. Masuda, and K. Higashitani. Powder Technology Handbook (2nd Ed.). Marcel Dekker Inc.

Jha, A. K. and V. M. Puri. 2007. Percolation segregation of binary mixtures under periodic movement. Powder Technology (In review).

Moakher, M., T. Shinbrot, and F.J. Muzzio. 2000. Experimental validated computations of flow, mixing and segregation of non-cohesive grains in 3D tumbling blenders. Powder Technology 109:58-71.


Murdock, J. W., 1993. Fundamental fluid mechanics for the practicing engineer. Marcel Dekker, Inc. New York, NY.


Rosato, A. D. and D. L. Blackmore. 2000. Segregation in granular flows. Proceedings of the IUTAM Symposium held in Cape May, NJ, June 5-10, 1999. Kluwer Academic Press, Boston, MA. pp. 342.

Salter, G. F. 1998. Investigations into the segregation of heaps of particulate materials with particular reference to the effects of particle size. Ph.D. diss., University of Greenwich.

Shinohara, K. and B. Golman. 2002. Particle segregation of binary mixture in a moving bed by penetration model. Chemical Engineering Science 57:277-285.

Streeter, R. L., G. Z. Watters, and J. K. Vennard. 1996. Elementary fluid mechanics. John Wiley & Sons, Inc.

Tang, P. 2004. Percolation and sieving segregation patterns-Quantification, mechanistic theory, model development and validation, and application. Ph.D. diss. The Pennsylvania State University, University Park, PA.

Tang, P. and V. M. Puri. 2005. An innovative device for quantification of percolation and sieving segregation patterns – Single component and multiple size fractions. Particulate Science and Technology, An International Journal 23 (4): 335-350.

Vallance, J. W. and S. B. Savage. 2000. Particle segregation in granular flows down chutes. Eds: Rosato, A D. and D. L. Blackmore. IUTAM Symposium on Segregation in Granular Flows 31-51. Kluwer academic Publishers.


279

14. CHAPTER - CONCLUSIONS AND RECOMMENDATIONS FOR FUTURE WORK

The PSSC-II was capable of quantifying segregation in binary, ternary, and quaternary

size mixtures of urea and potash as well continuous mixtures of 10-10-10 blend. Materials

chosen were major raw ingredients of blended fertilizer that represent two extremes based on

shape and density. In this study, the coarse and fine particles were classified using particle size

larger and smaller than 2,360 µm, respectively. The operating parameters for PSSC-II used were:

strain, strain rate, and bed depth. Strains of 2%, 6%, and 10% and strain rates of 0.25, 0.5, and

1.0 Hz were used, while bed depth was kept constant at 85 mm. The magnitude of strain rate of

1.0 Hz, being too high for fertilizer mixtures using PSSC-II, was included in tests at strain of 6%

only. Binary, ternary, and quaternary size mixtures were prepared from three coarse mean sizes

3,675 µm, 3,075 µm, and 2,580 µm for potash and urea and three fines mean sizes 2,180 µm,

1,850 µm, and 1,550 µm and two fines mean sizes 2,180 µm and 1,850 µm for potash and urea,

respectively. Test samples were prepared using a bench-top mixer.

The percolation segregation and flowability of urea, the most hygroscopic and expensive

among the three major raw ingredients: urea, phosphate, and potash, was quantified for binary

mixtures at three equilibrium relative humidities of 40%, 50%, and 60%. The PSSC-II and CTT

were used for quantifying segregation and flowability, respectively, for binary mixtures of urea.

Strain of 6% and strain rate of 0.5 Hz were used for determining percolation segregation of fines

and confining pressures of 3.5 kPa and 7.0 kPa were used for determining flowibitlity

parameters: angle of internal friction and cohesion using Mohr-Coulomb model. Percolation

segregation of fines in fertilizer bags was also quantified under vibration conditions using

industrial vibrator at vibration frequencies of 5 and 7 Hz. For vibration tests, amplitude and

frequency of industrial vibrators were inter-dependent. According to the PSSC-II test results, a

convective and diffusive model and a mechanistic theory based dimensional analysis model were

developed to predict the segregation behavior of fines from coarse and fines mixtures.

The following key conclusions were drawn based on percolation segregation, sampling,

flowability, and modeling studies:

280

14.1 Quantification of Percolation Segregation in Binary Mixtures

1) Both NSR and SR depend on mixing ratio in binary mixtures, NSR decreased with

increasing amount of fines 67:33>50:50>33:67, however, SR increased with

increasing amount of fines 67:33>50:50>33:67 for the same size ratio.

2) The NSR decreased almost 96% from 1.54 kg/kg-h for size ratio 2.4:1.0 to 0.13

kg/kg-h for size ratio 1.7:1.0.

3) The NSR was dependent on size of coarse and fine particles, NSR decreased from

0.39 kg/kg-h to 0.13 kg/kg-h with increasing size of fines 1,550 µm for the size ratio

2.4:1.0 vs. 2,180 µm for the size ratio 1.7:1.0.

4) The NSR was dependent on type of material selected, the NSR of spherical-shaped

urea (0.62 kg/kg-h) was lower than the NSR of angular-shaped potash (0.90 kg/kg-h)

at the end of 30 minutes of PSSC-II operation.

5) For both materials, the NSR of binary mixtures depended on strain rate when

subjected to shear motion. Furthermore, the NSR increased when the strain rate

increased from 0.25 Hz to 1.0 Hz; for instance, the NSR increased from 0.95 to 1.70

kg/kg-h, almost 79% for the size ratio 2.4:1.0 of potash when the strain rate increased

by four-fold.

6) For size ratio 2.4:1.0 at strain rate of 0.25 Hz , when the strain was increased by three

times from 2% to 6% the NSR increased by 7.31 times. When the strain increased

five times from 2% to 10%, the NSR increased by 11.86; times, whereas, the NSR

increased only by 1.61 times for the increase in strain from 6% to 10%.

14.2 Quantification of Percolation Segregation in Ternary and Quaternary Mixtures

1) At strain of 2%, the segregation of fines was governed by the diffusive mechanism vs.

higher strains 6% and 10% where the convective mechanism was dominant.

2) At strain rate of 0.5 Hz and strain of 2%, the percent segregated fines decreased by

19.9%, 47.1%, 57.7% for binary vs. ternary, ternary vs. quaternary, and binary vs.

quaternary mixtures of potash.

3) At strain rate of 0.5 Hz and strain of 6%, for potash, at the end of end 30 minutes, the

NSR decreased by 29.2%, 58.8%, 70.8% when binary vs. ternary, ternary vs.

quaternary, and binary vs. quaternary mixtures were compared, respectively.

281

14.3 Quantification of Segregation and Flowability in Binary Mixtures

Percolation segregation of binary size mixtures of urea by blending fines (1,700-2,000

µm) with coarse (3,350-4,000 µm and 2,800-3,350 µm) equilibrated at three relative humidity

(ERHs) (40%, 50%, and 60%) was measured using PSSC-II. All tests were conducted at bed

depth of 85 mm, strain of 6%, and strain rate of 0.5 Hz. Results showed that the PSSC-II is

capable of quantifying segregation of binary size mixtures. For quantification of segregation,

four metrics; 1) segregated fines mass, 2) segregation rate, 3) normalized segregation rate, and 4)

distribution segregation rate of fines were used. The following conclusions were drawn from this

study.

14.3.1 Size ratios 2.0:1.0 and 1.7:1.0

1) NSR decreased from 0.33 kg/kg-h to 0.32 kg/kg-h to 0.22 kg/kg-h when ERH

increased from 40% to 50% to 60%, respectively. Only 2.8% of decrease in NSR was

recorded for increase in ERH by 10 points (from 40% to 50%), whereas 36.0%


2) NSR decreased from 0.17 kg/kg-h to 0.16 kg/kg-h to 0.10 kg/kg-h when ERH

increased from 40% to 50% to 60%, respectively. Only 7.0% decrease in NSR was

recorded for increase in ERH by 10 points (from 40% to 50%), whereas 45%


14.3.2 Flowability of binary mixtures With the two different mixture of fines (1700-2000 µm) and coarse (3350-4000 µm and

2800-3350 µm) at three different ERHs (40%, 50% and 60%), conventional triaxial compression

tests were performed to evaluate flowability using the CTT. From those results, the following

conclusions were drawn:

1) For size ratios 2.0:1.0 and 1.7:1.0, angle of internal friction increased from 31.3° to

35.9° to 39.0° and 27.4° to 32.0° to 36.0°, respectively, when ERH increased from

40% to 50% to 60%, respectively.

2) The measured negligible cohesion values were not significantly different (p>0.05) for

both size ratios 2.0:1.0 and 1.7:1.0 at all three ERHs.

282

14.4 Sampling of Solid Fertilizers and Comparison of Samples from Two Triers of Opening Widths 12.7 and 19.1 mm

The following concluding observation can be made based on size analyses of samples

obtained from the three blend plants.

14.4.1 Raw ingredient samples

1) Size analysis of ingredients from the three blend plants showed that there was a large

spread in SGNs and UIs, with appreciable variability from plant-to-plant.

2) One out of five ingredients in BP1, two out of six ingredients in BP2, and five out of

six ingredients in BP3 were not size-matched.

14.4.2 10-10-10 blend samples using 12.7 and 19.1 mms triers:

1) From all three blend plants and for all 10-10-10 bagged fertilizers sampled, the

average SGN of samples was 257 when using 19.1 mm width trier compared with

254 (-1.2% compared with SGN=257) when using 12.7 mm width trier; the

corresponding UIs were 45 and 44 (-2.2%), respectively.

2) While the SGN of 19.1 mm width trier was larger than the 12.7 mm width trier, there

were no substantial differences between the SGNs and UIs of the two different width

triers, i.e., except for 10-10-10(2) from BP1, all SGNs and UIs were within 7 and 2,

respectively.

3) Eleven out of the twelve samples from bagged fertilizers using 12.7 mm vs. 19.1 mm

had the same outcomes, i.e., only one sample from BP3 10-10-10(3) using 12.7 mm

vs. 19.1 mm had a conflicting outcome – the sample obtained using 19.1 mm width

trier (SGN=259, UI=47) passed, whereas, the sample with 12.7 mm trier (SGN=256,

UI=47) failed the AOAC chemical analysis test.

4) The mass collected by 12.7 mm trier was higher than the mass collected by 19.1 mm

trier.

5) The percent mass collected by 19.1 mm and 12.7 mm triers was the highest for sieve

number 8.

6) Caine and Hancock reported the largest SGN difference of 12 for five different blends

when using 12.7 mm vs. 19.1 mm trier for sampling. Therefore, the differences in the

283

SGN values measured in this study are similar to those reported by Caine and

Hancock.

7) From the analyses of 10-10-10 samples in each of the four quarters, segregation

during discharge of the blend from the storage bin was observed.

8) Overall, only minor differences were observed between the chemical and size

analyses of samples from bagged fertilizers obtained using the 19.1 mm vs. 12.7 mm

width triers.

14.5 Quantification of Percolation Segregation of Fines from Fertilizer Bags during Vibration

The following key findings were drawn based on size analyses of samples obtained from

bagged 10-10-10 fertilizers.

1) At higher frequency 7 Hz, triers of opening widths 12.7 mm and 19.1 mm received

larger and smaller size particles compared with frequency 5 Hz.

2) The particle size distributions changed at a location with respect to time when

subjected to vibration frequencies of 5 and 7 Hz.

3) The SGN and UI of samples collected by 12.7 mm and 19.1 mm did not have definite

trend at frequency of 5 Hz.

4) The SGN and UI of samples collected by 12.7 mm and 19.1 mm increased with time

at frequency of 7 Hz.

14.6 Convective and Diffusive Percolation Segregation Model

The segregated mass was calculated under different variables such as size ratio, shape,

density, strain rate, and strain. Based on the results for binary mixtures, the following

conclusions can be drawn.

1) For size ratio of 2.0:1.0 of urea, at the strain of 6% and strain rate of 0.5 Hz after 30

minutes, the modeled segregated mass was 2.3 g higher than the experimental

segregated mass; whereas, the segregated mass calculated from the model operating

parameters convective, diffusive, and resistance obtained from linear interpolation

was 15.4 g lower than experimental segregated mass.

284


urea, the modeled convective, diffusive, and resistance parameters were 0.00

mm/min, 21.05 mm2/min, and 1 mm, respectively; whereas these parameters

calculated from linear interpolation were 0.00 mm/min, 16.54 mm2/min, and 1 mm,

respectively.

3) For size ratio of 2.0:1.0 of potash, at the strain of 6% and strain rate of 0.5 Hz after 30

minutes, the modeled segregated mass was 7.3 g higher than the experimental

segregated mass; whereas, the segregated mass calculated from the model operating

parameters convective, diffusive, and resistance obtained from linear interpolation

was 45.3 g higher than experimental segregated mass.


potash, the modeled convective, diffusive, and resistance parameters were 0.99

mm/min, 98.24 mm2/min, and 13.00, respectively; whereas these parameters

calculated from linear interpolation were 1.20 mm/min, 42.61 mm2/min, and 2.75

mm, respectively.

14.7 Mechanistic Theory Based Dimensional Analysis Percolation Segregation The primary segregation shear cell (PSSC-II) was used to develop dimensional analysis

model for percolation of fines through a bed of coarse particles in the well-mixed binary, ternary,

and quaternary mixtures. The percent segregated mass was calculated under the different

variables such size ratio, shape, density, strain rate, and strain. Based on results, the following

conclusion can be drawn.

1) The dimensional analysis model developed by the binary mixtures of potash was

sufficient to represent the binary, ternary, and quaternary mixtures of urea and

potash.

2) Validation results show that, the CoV of the modeled values to the experimental

values were 17.5%, 15.1%, and 10.7% for binary mixtures of urea and potash at

strains of 2%, 6%, and 10% and strain rate of 0.25 Hz.

285

14.7 Recommendations for Future Work 1) Percolation segregation under shear motion in binary, ternary, and quaternary

mixtures and segregation in fertilizer bags during vibration were studied. An

experimental set-up could be designed to study the percolation segregation under

shear and vibration conditions so that percolation segregation can be better

understood in multi-component and continuous mixtures.

2) Only two materials urea and potash were studied, additional materials should be

studied based on their extreme physical properties, such as size, shape, density,

surface texture, and electrostatic charge.

3) The maximum size ratio for binary mixture was 2.4:1.0; larger size distributions

of material could be studied so that larger number of ternary and quaternary

mixtures could be studied to better understand the segregation in continuous

mixture.

4) Three strain rates of 0.25, 0.5, and 1.0 Hz and three strains of 2%, 6%, and 10%

were considered for studying binary, ternary, and quaternary. More number of

strain and strain rate could be considered for development of a robust model.

5) Measurement system should be re-designed so that particles of different sizes

could be tested for distribution of segregation rate. More number of load-cell

could be installed to have complete picture of materials distribution. Current

measurement was not sufficient to measure larger particle size (>1, 000 µm)

beyond 3 g.

6) Different materials should be tested for different mixing ratios and bed depths to

optimize the process condition in industry.

7) Convective and diffusive model should be developed for higher order mixtures to

make this model more robust and meaningful to industrial process conditions.

8) Time-independent dimensional model should be correlated to time-dependent

convective and diffusive model to overcome the shortcomings of time-

independent study.

9) Continuous feeding of well-mixed mixtures to the shear box should be designed

to reduce or eliminate the limitations of batch-feed.

286

10) Materials of different physical property could be tested at the same time to have

understanding of materials behavior in multi-component, poly-disperse mixtures.

11) Develop a relationship between multi-component mixtures and continuous

mixtures under different motion conditions and bed depth and validate with data

during conveying of bagged fertilizers within a plant.

VITA

Anjani K. Jha

The Pennsylvania State University, University Park, PA, USA Ph.D. Agricultural and Biological Engineering May 2008 Dissertation title: Percolation Segregation in Multi-Size and Multi-Component Particulate Mixtures: Measurement, Sampling, and Modeling

Indian Institute of Technology, Kharagpur, WB, India M. Tech. Post Harvest Engineering, January 2003 Thesis title: Design and Development of Evaporative Cooling System for Bulk Preservation of Fruits and Vegetables

Rajendra Agricultural University, Pusa, Bihar, India B. Tech. Agricultural Engineering, 2001 Thesis title: Testing of Seat Performance of Power Tiller

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