The effect of mechanical vibration on gas fluidization of a fine aeratable powder

c h e m i c a l e n g i n e e r i n g r e s e a r c h a n d d e s i g n 8 6 ( 2 0 0 8 ) 3 5 9 – 3 6 9

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The effect of mechanical vibration on gas fluidization ofa fine aeratable powder

Diego Barletta, Giorgio Donsı, Giovanna Ferrari, Massimo Poletto *, Paola Russo

Dipartimento di Ingegneria Chimica e Alimentare, Universita degli Studi di Salerno, Via Ponte Don Melillo, I-84084 Fisciano (SA), Italy

a r t i c l e i n f o

Article history:

Received 16 April 2007

Accepted 18 September 2007

Keywords:

Vibrated fluidization

Aeratable powders

Minimum fluidization velocity

Interparticle forces

Homogeneous fluidization

a b s t r a c t

Fluidization behaviour of a fine aeratable FCC powder assisted by mechanical vibration was

studied in a 85 mm i.d. transparent column. The investigated parameters of vibration were

the peak acceleration value (a/g = 0.5, 1 and 2) and the frequency (between 7 and 200 Hz). The

most significant variations obtained by changing these parameters regard the voidage of the

fixed bed, the effects of aeration on bed expansion and fluidization, the maximum bed

expansion and the onset of bubbling conditions. The typical fluidization curve in presence of

mechanical vibration is characterized with the introduction of key fluidization velocities: a

minimum bed expansion velocity, a minimum velocity for fluid dynamic suspension, the

minimum bubbling velocity and a minimum velocity for stable bubbling. The possibility to

apply the Ergun equation under gas fluidization assisted by vibration was also verified.

Differential pressure drops at different heights inside the bed were used to investigate on

the effects of vibrations on the gas fluidized bed. Changes of differential pressure drop along

ted in the light of some internal bed structure.

of Chemical Engineers. Published by Elsevier B.V. All rights reserved.
# 2007 The Institution
the bed were interpre

1. Introduction

In industrial applications of powder technology vibrations have

been used together with gas fluidization in order to overcome

cohesion problems arising in the treatment of sticky particles,

as for example in the case of powder drying operations.

Vibrations, in fact, are able to interact directly with structures of

the dispersed phase determined by cohesive forces such as

aggregates and channels. This property has suggested their use

to induce the proper gas fluidization of very fine particles

belonging to the Group C of the Geldart (1973) classification. For

these powders, beds have been often vibrated by means of the

application of sound waves. Vibration without aeration was

also studied on coarser powders because it can determine the

bed expansion. It can, therefore, be used to uncouple the bed

expansion from the gas velocity and provide more flexibility in

the design of process units using fluidized beds.

Fluidization is not the only phenomenon which can be

observed by application of vibrations on a powder bed. An

indication of the complexity of this operation is the number of

phenomena, which were observed in these systems, such as

* Corresponding author. Tel.: +39 089 964 132; fax: +39 089 964 132.E-mail address: [email protected] (M. Poletto).

0263-8762/$ – see front matter # 2007 The Institution of Chemical Endoi:10.1016/j.cherd.2007.10.002

heaping (Hsiau and Pan, 1998), compaction (Thomas et al.,

2000; Kudrolli, 2004), size segregation (Williams, 1976; Kudrolli,

2004), arching (Hsiau et al., 1998), convection (Hsiau and Chen,

2000; Tai and Hsiau, 2004) and, finally, fluidization (Luding

et al., 1994). A consistent part of these studies concerned the

application of vibration to beds of very coarse particles (Group

D of the Geldart classification), for which cohesive and fluid

dynamic effects are negligible, and were performed using beds

of very low depth (a few layers of solids grains). Thomas et al.

(2000) reported the different phenomena observed when

vibrating, at a fixed frequency of 25 Hz, shallow beds of

powders belonging to different groups of the Geldart classi-

fication, including an aeratable Group A and a cohesive Group

C powder. They hypothesized a modified classification of

powders applicable to vibrated fluidization. They also sug-

gested the necessity to investigate the significance of the bed

height in powder vibration.

Pioneering works in the field of application of vibrations to

gas fluidized bed were carried out by Gupta and Mujumdar

(1980) with the use of mechanical vibrations and by Morse

(1955) with the use of sound waves. The different effects of

gineers. Published by Elsevier B.V. All rights reserved.

mailto:[email protected]

http://dx.doi.org/10.1016/j.cherd.2007.10.002

Nomenclature

a acceleration due to vibration (m s�2)

A vibration amplitude (m)

dp particle diameter (m)

f frequency (s�1)

g acceleration due to gravity (m s�2)

H bed height (m)

Hmb bed height at the minimum for bubbling (m)

Hmf bed height at the minimum for fluidization (m)

DH distance between taps (m)

M bed mass (kg)

P pressure (Pa)

DP gas pressure drop through the bed (Pa)

DPCal gas pressure drop between taps calculated with

Eq. (6) (Pa)

DPErg gas pressure drop through the bed calculated

with Eq. (3) (Pa)

DPErgDH gas pressure drop between taps calculated with

Eq. (4) (Pa)

DPFlDH gas pressure drop between taps calculated with

Eq. (5) (Pa)

u fluid superficial velocity (m s�1)

umb minimum fluid superficial velocity for bubbling

(m s�1)

ume minimum fluid superficial velocity for bed

expansion (m s�1)

umf minimum fluid superficial velocity for fluidiza-

tion (m s�1)

umsb minimum fluid superficial velocity for stable

bubbling (m s�1)

umsf minimum fluid superficial velocity for fluid

dynamic suspension (m s�1)

Greek letters

e bed voidage

mf fluid viscosity (Pa s)

rf fluid density (kg m�3)

rp particle density (kg m�3)

S bed cross section (m2)

v pulsation (s�1)


vibrations on Group D powders reported by these authors

suggest different mechanisms of action of these two techni-

ques. In particular, application of sound has been proved to be

very effective for the fluidization of fine powders (Chirone et al.,

1993; Russo et al., 1995; Nowak et al., 1993; Levy et al., 1997).

Russo et al. (1995) demonstrated that this kind of vibration

technique was able to break particle aggregates when acting at

the resonance frequencies of the aggregate structure (>100 Hz).

Also mechanical vibration was demonstrated to be effective on

Group C powders (Marring et al., 1994; Janssen et al., 1998;

Mawatari et al., 2002b, 2003; Valverde et al., 2001; Valverde and

Castellanos, 2006) by breaking the aggregates into smaller

pieces which become primary fluidizable particles. These

smaller aggregates may be homogeneously fluidized in gas

streams as typical for Group A powders. The effectiveness of

mechanical vibration has also been proved, even at frequencies

lower than those in the range in which acoustic vibration is

effective. This supports the idea of different mechanisms of

action of these two vibration techniques.

Considering the previous observations on homogenous

expansion in the vibrated gas fluidization of Group C powders

we believe that the full understanding of this kind of

fluidization can only come from a complete understanding

of the effect of vibration on Group A powders. This effect was

the object of several studies (Jaraiz et al., 1992; Wang et al.,

2000, 2002; Mawatari et al., 2002a,b), however, the experiments

reported in the literature on vibrated gas fluidization did not

cover low frequency ranges. Furthermore, often the effects of

frequency were not studied independently of the imparted

vibrational acceleration.

The purpose of this paper is a better understanding of the

separated effects of vibration frequency and acceleration on

the gas fluidization of aeratable powders. To this end an

extensive study on the vibrated gas fluidization of a Group A

powder was carried out. The frequency was changed in a range

between 7 and 100 Hz and the vibrational acceleration was

applied at levels close to the gravity acceleration (a/g = 0.5, 1.0

and 2.0). In addition to conventional fluidization analysis in

which bed expansion and pressure drops were measured at

different gas superficial velocities, also differential gas

pressure measurements at different heights within the bed

were carried out to observe possible internal non-uniformity

of the particulate phase generated by the vibration imparted

by the bed distributor.

2. Methods and materials

2.1. Apparatus

The core of the apparatus is a fluidization perspex column

85 mm i.d. and about 400 mm high. At the bottom the air is

distributed by a 10 mm thick porous plate of sintered brass

particles of about 10 mm diameter. The porous plate is

clamped by the flange connecting the air wind box and the

fluidization column. In the column flange a pressure port is

connected to a u-tube manometer filled with water. For local

gas pressure drop evaluations we used a second column

provided with pressure taps aligned on two arrays of equally

spaced taps each located on two opposite sides of the column

and numbered as indicated in Fig. 1. Couples of these taps

were connected to the ends of the u-tube manometer to

measure differential pressure drops. Desiccated air from the

laboratory line is fed to the wind box by a thermal mass flow

controller (Fe-771000 Aera, F) with a maximum flow rate of

0.17 � 10�3 std m3 s�1 (0 8C and atmospheric pressure). The

column is fixed to the vibrating plane of the actuator by means

of a rigid steel and aluminium structure. The actuator is an

electric inductance vibrator (V100 Gearing and Watson, USA)

which is able to produce a sinusoidal vertical movement in

the range 2–6500 Hz with displacement amplitudes up to

12.7 mm, exerting a maximum force of 26.7 kN. The vibrator

amplifier is connected to a vibration controller Sc-121 (Lab-

works Inc., USA) which is able to work with frequencies

between 2 and 6500 Hz. The controller measures the effective

vibrations by means of a piezoelectric accelerometer

(8636B60M05 Kistler, USA) fixed on the metal structure

supporting the fluidization column.

2.2. Materials

The powder used in the experiments is a sieved fluid cracking

catalyst (FCC) powder with a mean Sauter diameter of 77 mm

Fig. 1 – (a) Experimental apparatus: 1, fluidization column;

2, electro-dynamic vibrator; 3, metallic frame; 4, mass flow

controller; 5, accelerometer; 6, water manometer; 7,

vibration control block. (b) Longitudinal section of the

multi-tap column for differential pressure measurements.

Fig. 2 – Fluidization curve (a) and bed expansion curve (b)

for a 0.8 kg bed of FCC powder: (~) increasing gas velocity,

(5) decreasing gas velocity.

c h e m i c a l e n g i n e e r i n g r e s e a r c h a n d d e s i g n 8 6 ( 2 0 0 8 ) 3 5 9 – 3 6 9 361

with the 80% of the distribution between 58 and 109 mm. The

effective particle density is 1520 kg m�3 evaluated from the

mass of a fixed bed in which the effective fluid dynamic

porosity has been estimated from the gas pressure drops by

the application of the Ergun equation. The sphericity in this

equation was put equal to 1 due to the round shape of FCC

particles verified with electron microphotography. Before

being used in the experiments and after long inactivity

intervals between the experiments, the powder was always

conditioned with some hours of fluidization with desiccated

air. The fluidization and expansion curves obtained with

0.800 kg of powder are reported in Fig. 2. The curve is

significantly different at increasing and decreasing gas

velocities, due to the different packing conditions attained

in the two experiments. The powder shows a wide uniform

expansion range between the minimum velocity for fluidiza-

tion, at about 4.0 mm s�1, and the minimum bubbling velocity,

at about 12.5 mm s�1.

2.3. Procedures

As it was shown in the powder fluidization curve (Fig. 2), the

initial packing state of the bed depends on the most recent

history of the bed. Therefore, a conventional initialization

procedure was adopted for each fluidization experiment. The

bed was fully fluidized for a few minutes; vibration was

started in this conditions at the desired frequency and

acceleration level; then the bed was gradually defluidized

and finally the aeration stopped. Without stopping or

modifying the vibration condition, the fluidization curves

were taken at increasing and, then, decreasing fluidization

gas rates. At each fluidization condition, the system is left

unchanged for few minutes. This time was necessary to let

the system attaining stationary conditions and to read and

take note of the gas pressure drops, total or local, and of the

bed height. For a new vibration condition the whole

procedure was repeated.

3. Experimental results and discussion

3.1. Fluidization experiment

Applying vibrations, the maximum acceleration, a, is related

to the vibrating sinusoidal movement, and namely to the

oscillation amplitude, A, i.e. half of the maximum vibration

Table 1 – Maximum vibration displacement evaluated with Eq. (1) for the couples of frequency and acceleration levelvalues used in the experiments

f (Hz)

7 9 12 15 17 20 22 25 30 40 50 65 100

a/g 2A (mm)

0.5 5.07 3.07 1.73 1.10 0.86 0.62 0.51 0.40 0.28 0.16 0.10 0.06 0.02

1.0 10.14 6.14 3.45 2.21 1.72 1.24 1.03 0.80 0.55 0.31 0.20 0.12 0.05

2.0 6.90 4.42 3.44 2.48 2.05 1.59 1.10 0.62 0.40


for a 0.8 kg FCC bed at acceleration level a/g = 1.0 and

different vibration frequencies: (T) 7 Hz; (*) 12 Hz; (~)

15 Hz; (^) 20 Hz; (&) 25 Hz; (!) 65 Hz; (*) 100 Hz. Symbols

on top and bottom frequency axes connected by dashed

lines provide observed umb values.


displacement, and to the oscillation frequency, f, or its

proportional pulsation value, v. Namely, it is

a ¼ Av2 ¼ Að2p fÞ2 (1)

In vibrated fluidization the vertical acceleration due to

vibrations directly competes with the vertical acceleration due

to gravity which keeps the bed fixed at low aeration velocities.

For the vibrated suspension of coarse particles the maximum

acceleration is assumed as a key parameter to determine the

fluidization state (Gupta and Mujumdar, 1980). For the fine

powder used in this experiment the acceleration imparted to

the fluidizing column is not necessarily transmitted to the

powder bed since vibration attenuation may occur. For

simplicity, however, acceleration and oscillation frequency

were assumed as characterizing parameters of vibration.

Fixed the frequency and the maximum acceleration, the

amplitude of the corresponding vibration is given by Eq. (1).

Three different acceleration levels have been chosen for the

experiments. These were conventionally referred to the

acceleration due to gravity, g, and correspond to values of a/

g of 0.5, 1.0 and 2.0. At each of these acceleration levels,

fluidization curves were measured at several frequencies in

the range between 7 and 100 Hz. The lower frequency limit

depends on the maximum displacement limit of the experi-

mental apparatus. At a fixed acceleration, in fact, by means of

the Eq. (1), the vibrating device limit on the maximum

displacement results in a limitation for the minimum

applicable frequency. Table 1 summarizes the vibration


for a 0.8 kg FCC bed at acceleration level a/g = 0.5 and

different vibration frequencies: (T) 7 Hz; (*) 12 Hz; (~)

15 Hz; (^) 20 Hz; (&) 25 Hz; (!) 65 Hz; (*) 100 Hz. Symbols

on top and bottom frequency axes connected by dashed

lines provide observed umb values.

conditions used in the experiments and reports for each

couple of frequency and acceleration level values the

corresponding maximum vibration displacement 2A.

Figs. 3–5 show the bed expansion and fluidization curves

obtained with the 0.8 kg FCC bed at the three acceleration

levels tested. The expansion curve is given in terms of bed

height, H that is the directly measured variable. Average

values of the bed voidage, e, can be obtained from the bed

height, H

e ¼ 1� MrpSH

(2)

where M is the bed mass, rp the particle density and S the bed

cross section. In the tests used to draw Figs. 3–5 M, rp and S do

not change and therefore it is possible to univocally relate bed

height with the bed voidage. This result allowed to draw a

secondary axis on the bed expansion panel (b) with a scale for

e. All the fluidization experiments were carried out with

increasing and decreasing steps of the fluidization velocities

obtaining two branches of the fluidization and bed expansion

curves, one relative to the increasing fluidization velocity and

the other relative to the decreasing fluidization velocity. In all

the cases the two branches of the fluidization curve were very

close and the differences were contained in the worst cases

within 5%. For this reason and for simpler interpretation of the

results in Figs. 3–5 only data relative to the decreasing velocity

Fig. 5 – Bed expansion and fluidization curves with 0.8 kg

FCC bed at acceleration level a/g = 2.0 for different

vibration frequencies: (*) 12 Hz; (~) 15 Hz; (^) 20 Hz; (&)

25 Hz; (!) 65 Hz. Symbols on top and bottom frequency

axes connected by dashed lines provide observed umb

values.

Fig. 6 – Graphical evaluation procedure for ume, umsf and

umsb from the fluidization (a) and bed expansion (b) curves.


branches of these curves are reported. In addition to the

mentioned absence of hysteresis, other common features of

the vibrated gas fluidization appear clearly from the inspec-

tion of these figures:

(1) T
he bed packing degree reached by the vibrated bed
without gas flow is always higher than that reached

without vibration.

(2) T
he pressure drop in the fully fluidized bed may be equal or
smaller, sometimes significantly, than those obtained

without vibration. The latter always correspond to the

bed weight per unit cross sectional area.

(3) T
he bed starts expanding when the gas pressure drop is
consistently smaller than the necessary for fluidization or,

in any case, of the maximum pressure drop obtained at

high gas velocities.

(4) T
he largest bed expansion of the vibrated bed is always
smaller than that attained without vibration.

(5) If
the discrepancies between vibrated and not vibrated
fluidization are assumed as a measure of the significance

of the effect of vibration, these are generally larger at low

frequencies and tend to become less important at high

frequencies. In particular, this happens under thorough

fluidization conditions.

There are other observations, closely related to point (3)

above, which can be made starting from a closer view of the

fluidization/expansion curves, as it is shown in Fig. 6. The

onset of bed expansion, in fact, corresponds to a reduction in

the slope of the rising branch of the fluidization curve. This

can be expected from the fact that, in the constant bed height

region, the increase of the gas pressure drop is exclusively

dependent on the increase of the gas velocity. When the bed

height increases, instead, the pressure drop rise, due to

increasing gas velocity, is partially compensated by an

increase of the bed permeability due to its expansion. The

onset of bed expansion, therefore, determines a double slope

of the fluidization curve that has also been observed in the

past by Gupta and Mujumdar (1980) and by Mawatari et al.

(2002b). These authors, however, did not have the possibility to

correlate this slope variation with the onset of bed expansion

and did not explicitly relate it to the bed expansion at gas

velocities lower than the minimum for fluidization. As shown

schematically in Fig. 6, we defined the minimum velocity for

bed expansion, ume, which can be clearly evaluated from the

bed expansion curve as the transition value from the constant

bed height region to the increasing bed height region. As

mentioned above, this velocity always corresponds to a slope

change in the bed gas pressure drop curve.

The minimum velocity for bed expansion, ume, is com-

pletely different in the meaning and in the determination

procedure from the minimum fluidization velocity. The latter,

in the case of vibrated fluidization, is more similar to the

minimum velocity for fluid dynamic suspension, umfs, which

has been defined as the intersection between two lines in the

fluidization diagram: (1) the first line is the one that can be

evaluated from the linear regression on the points on the

second rising branch of the fluidization curve, corresponding

to bed expansion; (2) the other line is the horizontal

corresponding to the plateau value of pressure drops. For

conventional fluidization this velocity corresponds to the

attainment of pressure drop values equal to the bed weight per

unit cross sectional area. For vibrated fluidization, instead, the

maximum pressure drop values at high gas velocities might be

smaller than the bed weight per unit cross sectional area.

Therefore, the similitude between the conventional minimum

fluidization velocity and the minimum velocity for fluid

dynamic suspension as defined above is limited to the

procedure to obtain them rather than to the exact physical

meaning.

A further difference with conventional fluidization of

Group A powders has been observed from the direct observa-

tion of vibrated fluidization. In the former case, in fact, the

onset of bubbling corresponds to a visible reduction in the

slope of the bed expansion curve. With vibrated fluidization,

instead, the first bubble appears at velocities not much larger

than umfs and may not correspond to such change of the bed

expansion slope. The value of this velocity, called umb, was

Fig. 7 – ume (a), corresponding bed height (b) and

corresponding pressure drop (c). a/g values for

experimental results: (*) 0.5; (&) 1.0; (^) 2.0. Values for

pressure drop evaluated by application of Ergun equation

for a/g: (*) 0.5; (&) 1.0; (^) 2.0.

Fig. 8 – umsf (a) corresponding bed height (b) and




for a/g: (*) 0.5; (&) 1.0; (^) 2.0.


registered during fluidization experiment at the appearance of

the first bubble. The end of the bed expansion, instead, was

associated with intense bubbling and, therefore, it was used to

define a fourth characteristic velocity that is the minimum

velocity for stable bubbling, umsb. This latter was intended as

the end of the bed expansion velocity range. In particular, it is

significant for the observation reported in point (4) on the

reduced bed expansion with vibration. This observation seems

to be in contrast with the findings of Mawatari et al. (2002a)

regarding the reported increase in the umb/umf andHmb/Hmf for

Group A powder for the acceleration range used in this work. It

ought to be noted, however, that Mawatari et al. (2002a)

worked at frequencies between 30 and 54 Hz at which,

according to our observations, the effect of vibrations on

the maximum bed expansion is limited but it is significant in

increasing the initial fixed bed compaction. Mawatari et al.

(2002a) do not report the absolute values of bed height and,

therefore, the reported results might be attributed to a

reduction of Hmf rather than to an increase of Hmb produced

by vibrations. A similar phenomenological picture of the effect

of vibration on the onset of bubbling is given by Valverde et al.

(2001). These authors show that vibration can promote the

onset of bubbling in homogenous gas fluidized beds. However,

the experimental procedure followed by them, application of

vibration on gas fluidized bed at a certain gas velocity, is

somewhat different from the one followed in this work and

does not allow a definite comparison of results.

Intensity of vibration has an important effect on the onset

of bubbling. Fig. 5 relative to a/g = 2.0 in particular shows

minimum bubbling velocities which are close and sometimes

lower than the minimum fluidization velocities. Especially in

these cases the eruption of bubbles may be associated to bed

channelling phenomena. Unfortunately it was not possible to

neatly differentiate between the onset of bubbling and

channelling due to very similar surface phenomena. As a

first approximation, however, we can say that bubbling

applies when umb > umsf and channelling applies when

umb < umsf.

The values of ume, umsf, umb and umsb with the correspond-

ing bed heights and pressure drops are plotted as a function of

the vibration frequency for the different acceleration levels in

Figs. 7–10, respectively. In general all plots show the largest

variations at low vibration frequencies, where larger values of

ume and smaller values of umb and umsb are found. At

frequencies larger than 30–40 Hz, instead, very limited

variations with frequency are observed. In the low frequency

range 0–30 Hz the most significant variations occur for umb and

umsb. For these two velocities trends are so similar to clearly

indicate the direct connection between the two values. This

might be expected from the fact that both these values are

connected to bubbling, even if these two are associated to

different fluidization condition and may differ significantly in

value.

In general, it is possible to say that for Group A powders

vibration has a negative effect on homogeneous fluidization.

This can be explained with the disrupting action of vibration

on the structures generated by interparticle forces. In case of

Group A powders labile structures due to interparticle forces

are responsible of stabilizing homogenous fluidization (Donsı

and Massimilla, 1973) and these might not resist the action of

vibration that, therefore, can determine bubbling at gas

velocities lower than in non-vibrated gas fluidized beds. The

role of frequency on the vibration effectiveness is evident from

Figs. 9 and 10. Lower frequency vibrations produce large and

Fig. 9 – umb (a) corresponding bed height (b) and




for a/g: (*) 0.5; (&) 1.0; (^) 2.0.

Fig. 10 – umsb (a) corresponding bed height (b) and


experimental results: (*) 0.5; (&) 1.0; (^) 2.0.


visible fluctuations on the bed height and are closer to the

natural frequencies of the fluidized bed dynamics dependent

on bubbling. This might possibly explain the larger effective-

ness of low frequency vibration in promoting fluidized bed

bubbling.

It is well known that the interpretation of bed stability

supported by interparticle forces is still not generally accepted

and that also fluid dynamic stabilization is hypothesized in

linear stability analyses (Foscolo and Gibilaro, 1984; Batchelor,

1988) and claimed to explain some experimental observations

(Valverde et al., 2001, 2003). Non-linearity of disturbance

growth might also justify the onset of bubbling in presence of

finite and continuous voidage variations, such as those

induced by vibrations, at operating conditions in which

homogenous fluidization could be stabilized by fluid dynamics

without vibration. Fluid dynamic stabilization, however,

cannot explain other observations such as the formation of

channels in apparently stable beds.

Mawatari et al. (2003) showed that the minimum

fluidization condition can be obtained from the Ergun

equation even for fluidization in presence of vibrations.

The application of the Ergun equation, or rather the Carman–

Kozeny simplified form for viscous regimes, is also often

assumed valid in sound vibration (i.e. Russo et al., 1995) in

which the fluidization pressure drops are generally equal to

the bed weight. It is also given for granted by Erdesz and

Mujumdar (1986) who used this equation to correlate the

minimum fluidization velocity under vibration with the gas

pressure drop without knowledge of the exact bed height. In

order to verify if the presence of vibration significantly

altered the bed fluid dynamics, we checked if the Ergun

equation could be applied to the vibrated bed. The Ergun

equation to predict the bed pressure drops, DPErg, is

DPErg ¼ H 150ð1� eÞ2

e3

mfud2

p

þ 1:751� ee3

rfu2

dp

" #(3)

where rf and mf are the fluid density and viscosity, u is the fluid

superficial velocity, dp is the particle diameter. It has to be

recalled here that the Ergun equation is adequate to describe

the pressure drop in a fixed bed, but, generally, it might not be

suited for fluidized beds especially at larger bed expansion

degrees (see for example Gibilaro et al., 1985). In any case, the

hypothesis of homogeneous gas flow distribution, on which

the Ergun equation is derived, is inadequate for a bubbling gas

fluidized bed in which strong gas bypass flow of the particulate

phase occurs. For this reason the comparison between the

pressure drop evaluated with Eqs. (2) and (3) is limited to ume,

umsf and umb, and reported in Figs. 7c, 8c and 9c respectively.

Inspection of these figures indicates that the Ergun equation

correlates well the experimental results at ume for all frequen-

cies and acceleration levels tested. Data are satisfactorily

correlated for umsf and even for umb in spite of what above

said regarding fluidization.

In general, but not with umb, the pressure drop evaluated

with Eq. (3) is smaller than the experimental value. The most

likely reason for this may be a plug like oscillation of the bed,

with some space gap at the bottom such as that described by

Janssen et al. (1998). The gap is not visible in our experiments

for the presence of the connection flange between the wall of

the fluidization column and the distributor. The presence of

this gap brings to an overestimation of the bed height and,


therefore, of the bed voidage, which justifies the observed

deviation between the Ergun estimate and the pressure drop

measurements. For umb the pressure drop evaluated with

Eq. (3) is generally larger than the experimental value. This is

expected in this case because of the gas bypass of the bed

determined by bubbles which brings to an overestimation of

both the gas velocity and the gas pressure drops in the

particulate phase. From these results we might conclude that

the vibration applied through the fluidization column does not

affect directly the gas–solid interactions inside an aerated bed,

even in condition in which the overall pressure drops through

the bed are consistently different from the bed weight.

Vibrations, instead, are able to change the packing degree of

the bed, determining pressure drops in a vibrated bed different

from those in a non-vibrated bed at the same gas velocity.

3.2. Differential pressure drops

Fig. 11 shows differential pressure measurements carried out

with vibration acceleration a/g = 2 at different vibration

frequencies as a function of the aeration velocity. In particular

three differential pressures were considered. Defining DPij the

differential pressure measured between taps i and j according

to taps numbering in Fig. 1, values of DP13, DP24 and DP35 were

collected and compared. These three couples correspond to

pressure drops in the bed at a distance of 48 mm measured at

increasing height inside the bed. Experiments show in general

limited differences between these three pressure drops

Fig. 11 – Differential pressure drop evaluated at an acceleration l

DP35; (– – –) calculated with Eq. (4). Characteristic velocities: (*)

values. It has to be recalled that the differential manometer

was connected to a single couple of pressure taps at a time and

each of these curves, therefore, derives from a different

experiment. Superposition of curves in Fig. 11 at 12 Hz,

therefore, is not fortuitous and gives an idea of the measure-

ment repeatability. Values of ume, umsf and umb were evaluated

according to the procedure reported in the previous section

and are reported on the same diagrams. The precision in the

determination of ume and umsf is therefore dependent on the

interpretation of the different linear sections of the fluidiza-

tion and expansion curves as defined in Fig. 6. It can also be

recalled that the bubble onset is dependent on the direct

observation of the appearance of bubbles on the bed surface

and that it was not possible to neatly differentiate between

channelling and bubbling. According to what was defined in

the previous section, we can say that bubbling applies when

umb > umsf ( f > 25 Hz) and channelling applies when

umb < umsf ( f � 25 Hz).

The most striking effect of the vibration frequency is on the

shape of the curves. At low frequencies (12–20 Hz) we have a

monotonic increase of the pressure drops with gas velocity,

while at higher frequencies pressure drops show a maximum,

generally, close to the minimum for fluidization. This latter

circumstance is expected when, at fluidization velocity larger

then the minimum, the bed expands and this determines a

reduction of the bed mass confined in the fixed space

contained between the two horizontal sections corresponding

to the pressure taps used to measure the differential pressure

evel a/g = 2 and different frequencies: (^) DP13; (!) DP24; (&)

ume; (5) umfs; (^) umb.

Fig. 12 – Differential pressure drop evaluated at a vibration

frequency of 30 Hz and different acceleration levels: (^)

DP13; (!) DP24; (&) DP35; (– – –) calculated with Eq. (4).

Characteristic velocities: (*) ume; (5) umfs; (^) umb.


drop. The absence of a maximum in the differential pressure

measurement at fixed heights is therefore the consequence of

a limited or absent bed expansion at gas velocities higher than

the minimum for fluidization. The frequencies at which this

happens are those characterized by bubbling or channelling

onset at fluidization velocities close to or even lower than the

minimum for fluidization. The set up of a gas bypass flow of

the particulate phase determined either by bubbling or

channelling may be the reason for the absence of bed

expansion.

The frequencies which determine some differences

between the differential pressure measurements at different

height depends on the fluidization state of the aerated bed.

The largest differences below and around fluidization were

found at relatively high frequencies and in particular while

vibrating the bed at 30 and 50 Hz. The lowest frequencies

between 10 and 20 Hz produce larger differences on the fully

fluidized beds. These differences in the effect of vibration can

be explained with the changes induced by the bed expansion

on the overall bed mechanical properties. In our opinion the

most significant property is the bed stiffness. This is larger for

fixed beds than for fluidized beds and therefore corresponds to

larger natural oscillation frequencies of the whole bed.

According to us, this phenomenological picture is an indirect

proof of the fact that, in the vibration range observed and for

the considered particle size, the effect of vibrations on the

aerated bed depends not only the inference between vibra-

tions and particle to particle interactions, but also on the

vibration response of the whole bed to vibrations.

Some further observations also support this view. In

particular it can be noticed that, when some difference in

the pressure drops occur, the larger pressure drops are always

found at the bed bottom as if the state of compaction in the

lower layers can be affected by the dynamics of the layers

above. Since the variation of the gas properties with bed height

cannot explain this finding because there is no reason why

these properties should be affected by vibration, a possible

explanation is that the long-range interactions between upper

and lower layers are transmitted within the solid phase. This

is not surprising for the case in which pressure drop

differences are observed at gas velocities below the minimum

for fluidization, in which the bed is already expanding but it is

still supported by particle–particle interactions as it is

indicated by overall bed pressure drops lower than the bed

weight per unit cross sectional area. Decreasing differential

pressure drops with the height were also observed in fully

fluidized condition at low frequencies. In these cases the

vertical variations of the differential pressure drops shown for

the fixed bed tend to be maintained also above the minimum

for fluidization. This finding further supports the idea that

long range effects of particle–particle interaction play a role

also in the fluidized state. In other words, also these

observations suggest the existence of some internal structure

to the bed of the sort observed by Donsı and Massimilla (1973),

hypothesized by Rietema and Piepers (1990) and described by

Valverde et al. (2001, 2003) as a solid-like behaviour of fluidized

beds.

In Fig. 11 experimental pressure drops are compared with

the values of pressure drops evaluated according to the

hypothesis of ideal fluidization. Namely the average bed

voidage, e, is evaluated from the bed height, H according to

Eq. (2). Pressure drops for the distance between taps, DH, are

evaluated according both to the Ergun equation (4) DPErgDH, and

to the theoretical value (5) for suspended solids, DPFlDH

DPErgDH ¼ DH 150ð1� eÞ2

e3

mfud2

p

þ 1:751� ee3

rfu2

dp

" #(4)

DPFlDH ¼ DHgð1� eÞðrp � rfÞ (5)

The calculated value, DPCal is assumed as the minimum

between the two

DPCal ¼minðDPErgDH;DPFlDHÞ (6)

Values of DPCal are reported in Fig. 11 as dashed lines.

Significant differences between measured and calculated

values of pressure drop are mostly found under fully aerated

conditions. The frequencies atwhich this wasobserved were 12,

50 and 65 Hz, at which the experimental pressure drops

appeared to be smaller than the calculated values. Such finding

is consistent with the presence of some support to the bed

weight internal to the particulate phase and, therefore, with the

existence of some internal structure in it. Theoretical differ-

ential pressure drops smaller than all measured values, as

observed at 20 Hz, can be explained, instead, with plug like

oscillations of the bed, with some space gap at the bottom, as

those describedinthe previoussection. This space gap ishidden

by the lower flange of the fluidization column and brings to an

apparent overall bed height larger than real and, therefore, to an

overestimation of the bed voidage calculated with Eq. (2).

The fluidization behaviour at 30 and 50 Hz at which the

largest differences between differential pressure drops at

Fig. 13 – Differential pressure drop evaluated at a vibration

frequency of 50 Hz and different acceleration levels: (^)

DP13; (!) DP24; (&) DP35; (– – –) calculated with Eq. (4).

Characteristic velocities: (*) ume; (5) umfs; (^) umb.


different heights within the bed were observed was further

examined by repeating the experiments and changing the

acceleration levels (a/g = 0.5, 1.0 and 2.0). Results are shown in

Figs. 12 and 13. Inspection of these figures shows that at low

acceleration levels differences between differential pressure

drops at different heights appear larger at the highest gas

velocities, while at high acceleration levels larger differences

appear at gas velocities around the minimum for fluidization.

These findings might be considered as a further proof of the

existence of some internal structure in the expanded bed. This

structure is labile but, at low acceleration levels (a/g = 0.5) can

withstand the effects of vibrations and produce a distribution

of the differential pressure drop in the fluidized state similar to

what is observed below fluidization. At high acceleration

levels (a/g = 2.0), instead, vibration is sufficiently high to

change the internal structure in the fluidized bed and produce

in the fluidized state response to the vibration different from

what observed in the same bed below fluidization. At

intermediate acceleration levels (a/g = 1.0) the onset of

bubbling helps the disruption of the expanded structure and

produces results similar to those obtained at lower velocities

at high acceleration levels (a/g = 2.0).

4. Conclusions

The experimental results shown indicate the key role of

vibration frequency that is even more significant than the

vibration acceleration level. In particular, the largest effects in

bed expansion and differential pressure drops are found at low

frequencies close to the natural bubbling frequencies of the

fluidized bed. Vibrations, however, do not affect directly the

gas–solid fluid dynamic interactions which are still correctly

described by the Ergun equation. On the other hand, vibrations

have significant effects on the powder compaction and on the

maximum bed expansion. These effects produce changes of

the shape of the fluidization curve. In particular the bed

compaction due to vibrations needs a better understanding if

an appropriate prediction of the gas velocity necessary for bed

suspension is sought. Another phenomenon which has been

observed, and deserves further efforts for a better under-

standing to be correctly predicted, is the onset of bed

expansion that, differently from conventional fluidization,

does not coincide with bed fluidization but determines a range

of gas velocities in which bed mobility occurs below fluidiza-

tion.

In general the effect of vibration seems to change according

the expansion degree of the aerated bed suggesting an

important role of the overall mechanical properties of the

bed. Also the measurements of differential pressure drops at

different height within the bed support this view. Experi-

mental results of this work suggest the existence of an internal

structure of the bed created by interparticle forces, such those

observed by Donsı and Massimilla (1973), hypothesized by

Rietema and Piepers (1990) and described by Valverde et al.

(2001, 2003). Support to this view is found in the overall

pressure drop through the bed, which is lower than the bed

weight per unit cross sectional area, and in the differential

pressure drop values which show an increase with the depth

from the bed surface. At certain frequencies for sufficiently

high acceleration levels, vibration seems to be able to break

such structures and promote fluidized bed bubbling.

Acknowledgements

This project was partially financed by the Italian Ministry of

University and Research in the framework of PRIN funding,

year 2005. The authors are grateful to Mr. Carlo Scuoppo and

Ms. Maria Alba Fusco for their help with the experiments.

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The effect of mechanical vibration on gas fluidization of a fine aeratable powder

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