Rheological evaluation of non-Newtonian Mexican nixtamalised maize and dry processed masa flours

Journal of Food Engineering 60 (2003) 55–66

www.elsevier.com/locate/jfoodeng

Rheological evaluation of non-Newtonian Mexican nixtamalisedmaize and dry processed masa flours

M.C. N�uu~nnez-Santiago a, E. Santoyo b,*, L.A. Bello-P�eerez a, S. Santoyo-Guti�eerrez c

a Centro de Desarrollo de Productos Bi�ooticos (IPN) Km. 8.5 Carr. Yautepec-Jojutla. Col. San Isidro Yautepec, Mor. 62731, Mexicob Centro de Investigaci�oon de Energ�ııa (UNAM), Apartado Postal 34 Priv. Xochicalco s/n, Centro. Temixco, Mor. 62580, Mexico

c Instituto de Investigaciones El�eectricas, Unidad Geotermia, Av. Reforma 113, Col. Palmira, Temixco, Mor. 62490, Mexico

Received 1 August 2002; accepted 5 January 2003

Abstract

An experimental programme for evaluating the rheological properties of thirteen maize flour samples collected from several

Mexican commercial producers was conducted. Measurements of shear stress and shear rate were performed under calibrated

conditions using a rotational Haake viscometer. A comprehensive analysis of the rheometric data obtained during the experimental

runs was carried out for studying the actual non-Newtonian behaviour of the maize flour pastes. Non-Newtonian rheological

models based on the classical Power Law, the Robertson–Stiff and the Rational Polynomial were used for fitting the rheometric data

over a wide range of shear rates (24–3200 s�1). The best description of the non-Newtonian behaviour in most of the maize flour

pastes was obtained using the Rational Polynomial Model. Details of the experimental methodology and the results obtained in the

rheological evaluation are outlined.

� 2003 Elsevier Science Ltd. All rights reserved.

Keywords: Non-Newtonian fluids; Masa; Nixtamalisation; Effective viscosity; RVA measurement

1. Introduction

The nixtamalisation of maize is an ancient process

developed by the Aztecs which is still used in the pro-

duction of high quality ‘‘tortillas’’ and other maize

related food products (such as ‘‘pozole’’). The maize

grains are ground after alkali and heating treatments in

a process known as nixtamalisation (Mensah-Agyapong

& Horner, 1992; Ar�aambula, Barr�oon, Gonz�aalez, Moreno,& Luna, 2001). After grinding and washing the ‘‘nixta-

mal’’ with water, a soft paste known as ‘‘masa’’ is ob-

tained. This product is widely used in Mexico for the

production of tortillas (Campus-Baypoli, Rosas-Burgos,

Torres-Ch�aavez, Ramirez-Wong, & Serna-Sald�ııvar,1999). In spite of the production of masa is carried out

at industrial and commercial scale, there is no an ap-

propriated quality control of the nixtamalisation pro-cess. Such a problem sometimes causes a low quality

production of tortillas due to a poor texture and physi-

cal stability. The masa obtained from the nixtamalisa-

*Corresponding author. Tel.: +52-55-56229774; fax: +52-55-

56229791.

E-mail address: [email protected] (E. Santoyo).

0260-8774/03/$ - see front matter � 2003 Elsevier Science Ltd. All rights res

doi:10.1016/S0260-8774(03)00018-9

tion is a m�eelange characterised by a mixture of starchpolymers containing starch gelatinised granules, intact

starch granules, pieces of endosperm, and some lipids

(G�oomez, Rooney, Waniska, & Pflugfelder, 1987).

The alkali-thermal treatment used in the nixtamali-

sation, acts on the components of cell walls for con-

verting the hemicellulose into soluble gums (Ar�aambula,Mauricio, Figueroa, Gonz�aalez-Hern�aandez, & Ordorica,

1999). This treatment has several functions, such as, togelatinise the starch, to saponify part of the lipids, and

also to solubilise some proteins surrounding the starch

granules (Rooney & Suhendro, 1999). Cooking and

grinding treatments must be also carried out at optimum

levels for producing a masa with a high quality. Since

nixtamalisation typically provides the rheological and

texture properties of the masa products, gelatinisation

must be carefully controlled because large amounts ofgelatinised starch can produce stickiness, which could

affect the handling of the masa (Rooney & Suhendro,

1999).

In spite of the traditional nixtamalisation is widely

used in Mexico for producing fresh commercial masas,

there are other industrial processes where the main

target is to produce nixtamalised maize flours (NMF).

erved.

mail to: [email protected]

56 M.C. N�uu~nnez-Santiago et al. / Journal of Food Engineering 60 (2003) 55–66

These flours must be re-hydrated to produce masaproducts, such as tortillas (Flores-Far�ııas et al., 2000).For studying the quality of commercial masas and

NMF, and considering the physical differences that ac-

tually exist between them, a dehydration process must

be applied to the commercial masas to obtain a homo-

geneous pulverised material (here defined as dry pro-

cessed masa flours, DPMF).

For evaluating and to compare the quality features ofthese DPMF samples, a comprehensive experimental

programme needs to be carried out for determining their

chemical composition and also, the measure of their

physicochemical properties. Generally, the determina-

tion of the chemical composition in either masa or flour

samples includes analyses of ash, fat, protein, and

moisture content (e.g. Mart�ıınez-Bustos, Garc�ııa, Chang,S�aanchez-Sinencio, & Figueroa, 2000). The particle sizedistribution (PSD), pH, the water retention capacity

(WRC), and the rheological properties are the major

physicochemical analyses to be determined (e.g Flores-

Far�ııas et al., 2000; Ar�aambula et al., 2001). PSD, pH and

WRC are readily carried out by standardised methods

commonly found in the literature (Flores-Far�ııas et al.,2000; Mart�ıınez-Bustos et al., 2000).The determination of the rheological properties

(shear rate, shear stress, and effective viscosity) is a more

complex experimental task due to the non-Newtonian

nature that the maize flour pastes typically exhibit.

Comprehensive studies of the rheological behaviour of

pastes prepared with DPMF or NMF samples have

been seldom reported in the literature. The rheological

measurements of flour pastes are frequently performed

by use of simple rapid viscosity analysers (RVA), whichmay have some disadvantages to predict absolute values

of viscosity (e.g. Tecante & Doublier, 1999). Some ex-

perimental rheological works using RVA have been

performed by Almeida-Dom�ıınguez, Cepeda, and Roo-ney (1996), Campus-Baypoli et al. (1999), Flores-Far�ııaset al. (2000), Mart�ıınez-Bustos et al. (2000), and Ar�aam-bula et al. (2001). These viscometers measure the torque

produced during the cooking of the starches, which islater used for calculating the viscosity in thoroughly

arbitrary units, known as Brabender units (BU). Such

units do not provide an actual quantitative measure-

ment of the viscosity (Thomas & Atwell, 1999). How-

ever, RVA measurements are qualitatively used to

obtain reproducible gelatinisation and pasting profiles

by a careful control programme of the mixing, heating

and cooling processes. Since this kind of measurementdoes not provide data related to flow curves, nor

quantitative data of the effective viscosity, they actually

present a clear disadvantage for studying the non-

Newtonian behaviour exhibited by the paste samples.

In this context, rotational measurements of shear

stress and shear rate are preferred for defining more

accurately the actual non-Newtonian behaviour of the

pastes, as well as for a better estimation of the effectiveviscosity. In the present work, we have carried out an

experimental rheological programme using a rotational

Haake viscometer to measure rheometric properties of

some Mexican maize flour pastes. The goal of this work

is to present the rheometric results obtained in this ex-

perimental programme for evaluating the non-Newto-

nian rheological behaviour of twenty-six Mexican maize

flour pastes. The classical Power Law, as well as theother two available non-Newtonian rheological models

such as Robertson–Stiff and the Rational Polynomial

have been successfully employed, for the first time in the

food industry, to analyse and to fit the rheometric data

obtained.

1.1. Non-Newtonian rheological models

The choice of appropriate rheological models, to-

gether with the fitting procedures, can sometimes result

in poor fits of the rheometric data. Hence, the experi-

mental data analysis using non-Newtonian rheologicalmodels has been recognised as a difficult task for the

accurate and reliable prediction of the viscosity in flour

pastes (e.g. Rao & Tattiyakul, 1999). It has been gene-

rally accepted that the Ostwald-de Waele or better

known as the Power Law model (PLM) typifies the

rheological behaviour of rheometric data for a wide

variety of non-Newtonian fluids, including starch-

in-water pastes (e.g. Holland, 1964; Lauzon & Reid,1979; Doublier, 1987; Holland & Bragg, 1995; Santoyo,

1997; Rao & Tattiyakul, 1999; Santoyo, Santoyo-

Guti�eerrez, Garc�ııa, Espinosa, & Moya, 2001; Sopade &

Kiaka, 2001). However, it has also been observed, at

higher shear rate and shear stress values, that PLM does

not always describes the non-Newtonian pattern of the

rheometric data measured at the laboratory. Such a

problem enables other complex non-Newtonian modelsto be employed for improving the fit goodness of these

rheometric data.

Starch-in-water flour pastes are widely recognised as

complex substances both rheologically and chemically.

Such features enable the pastes to be generalised as non-

Newtonian fluids because there is no single constitutive

equation to describe exactly their relationship between

the shear stress (srz) and the shear rate (c ¼ dvz=dr) overa wide range of shear rates (e.g. Holdsworth, 1993;

Thebaudin, Lefebre, & Doublier, 1998; Tecante &

Doublier, 1999). Three major categories of non-New-

tonian fluids are basically recognised, namely, time in-

dependent, time dependent and viscoelastic (Holland,

1964; Holland & Bragg, 1995; Santoyo et al., 2001). The

time independent category has received a substantial

degree of attention in comparison with the other twocategories. The large majority of starch-in-water pastes

falls into this category (e.g. Thebaudin et al., 1998;

Tecante & Doublier, 1999; Sopade & Kiaka, 2001). As

M.C. N�uu~nnez-Santiago et al. / Journal of Food Engineering 60 (2003) 55–66 57

was earlier mentioned, it has been generally acceptedthat starch-in-water pastes can be moderately typified by

the Ostwald-de Waele or PLM, which is described by the

following equation:

srz ¼ k � cn ð1Þ

where k and n are defined as the consistency index andthe dimensionless flow behaviour index, respectively.

The development and the validation of this equation are

fully reported by Lauzon and Reid (1979), and Muller

(1973). There are other available non-Newtonian mo-

dels, such as Herschel-Bulkley, Casson, Mizrahi-Berk,Heinz-Casson, Vocadlo, and the generalised Herschel-

Bulkley (see Sopade & Kiaka, 2001), which have been

sometimes used for describing the rheological behaviour

of these pastes. Most of these non-Newtonian models

(including the PLM) have shown an appropriate fit of

raw rheological data collected from the analysis of

starch-in-water pastes, at low shear rates (e.g. Thebau-

din et al., 1998; Chamberlain & Rao, 1999; Tecante &Doublier, 1999). However, at higher shear rates (ranging

from 600 to 3200 s�1), it has been generally observed

that some of these rheological models do not describe

accurately the non-Newtonian behaviour.

Such a limitation motivated in this work to evaluate

alternative non-Newtonian models (Robertson–Stiff:

RSM, and the Rational Polynomial: RPM) in order to

obtain a better fit of the rheometric data in a wide rangeof shear rates (24–3200 s�1). It is very important to point

out that these models have not been used before in the

rheological studies of food products. In fact, these

models have been successfully employed in the oil and

geothermal industries for describing reliably the non-

Newtonian behaviour of drilling fluids during the con-

struction of deep producer wells (e.g. Robertson & Stiff,

1976; Santoyo, 1997; Kumar, Saboo, Sheth, Pilehvari, &Serth, 2000; Santoyo et al., 2001).

Robertson and Stiff (1976) proposed an improved

mathematical equation to describe a yield stress in a

pseudoplastic non-Newtonian fluid. In this model, they

combined both the classical Bingham plastic and the

traditional PLM patterns by use of the following equa-

tion:

srz ¼ Aðc þ CÞB ð2Þ

where A, B and C coefficients are parameters that de-

pend on the shear rate. When B ¼ 1 and C ¼ 0, the

equation describes the form of a Newtonian fluid; if

B ¼ 1 and C 6¼ 0, the fluid behaviour is represented as a

Bingham plastic. Finally, if B 6¼ 1 and C ¼ 0 are pre-

sented as a Power Law fluid. The parameters A and Bcan be considered similarly to the parameters of the

PLM. However, the parameter C, has a somewhat dif-ferent implication than the yield stress of the Bingham

model. In this model, C appears as a correction to the

shear rate rather than the shear stress, and the term

(c þ C) can be considered as the effective shear rate orthe shear rate that would be required for a Power Law

fluid to produce the same shear stress.

The last non-Newtonian model used was the Rational

Polynomial Model (RPM), which was originally pro-

posed by Kumar et al. (2000). These authors suggested

using a ratio of two polynomial functions as a general

correlating equation to obtain a better fitting of experi-

mental rheometric data. The RPM is apparently suitableto accurately describe the rheogram of virtually any time

independent non-Newtonian fluid. In fact, high accu-

racy should be achieved with a reduced number of ad-

justable parameters, as is usually required by the limited

number of rheometric data to be obtained with most of

commercial rheometers. The equation of the RPM is

represented by the following equation:

srz ¼P1c þ P2c2 þ P3c3

1þ Q1c þ Q2c2 þ Q3c3ð3Þ

where P1, P2, P3, Q1, Q2 and Q3 are parameters that

strongly depend on the shear rate according to the

rheological theory proposed by Kumar et al. (2000).

1.2. Effective viscosity of starch-in-water pastes

The effective viscosity of starch-in-water pastes is

estimated by an application of any of the above des-

cribed rheological models (PLM, RSM or RPM) to the

shear stress and the shear rate data collected from sim-

ple rotational coaxial viscometers (e.g. Haake RV20).

However, dynamic and direct measurements of the fluidviscosity can be reliably determined by use of sophisti-

cated viscometers, such as Haake CV20 (Tecante &

Doublier, 2002). For the purposes of our experimental

work, the shear stress data were measured using a

Haake RV20 viscometer at shear rates that normally

ranged from 0.1 s�1 to 3200 s�1 under isothermal con-

ditions.

2. Experimental procedure

2.1. Sample preparation

Ten crude masa samples (M-1 to M-10) were directlyobtained from several commercial tortilla producers of

the South of Mexico (Acapulco, Gro.). These masa

samples were carefully dried in a convective oven at 45

�C, grounded with a mortar, sieved through a 100 USsieve, and stored at room temperature in glass sealed

containers, to obtain the DPMF samples to be evaluated

(M-1 to M-10). On the other hand, the NMF samples

were obtained from the two largest flour producercompanies of M�eexico (MASECA, Le�oon, Gto.; andMINSA, Tlanepantla, Edo. de M�eexico), here identifiedas M-11 and M-12 samples, respectively. A control masa

%M

oist

ure

5

10

15

%Pr

otei

n

6

8

10

%Fa

t

5

10

15

Crude maize flour samples

M-1 M-2 M-3 M-4 M-5 M-6 M-7 CMS M-8 M-9 M-10 M-11 M-12

%A

sh

1

2

3

(a)

(b)

(c)

(d)

Fig. 1. Results of the chemical composition of the commercial crude

maize flours. The error bars were not plotted for samples which pre-

sented small experimental errors.


sample (CMS) was additionally prepared at laboratoryconditions using a strict control of the nixtamalisation

process. CMS was elaborated from commercial maize

treated with lime (with a concentration of 1% w/w) and

cooked for one hour at 92 �C. The nixtamal so producedwas then ground in a commercial windmill. This masa

was finally dried at the same conditions than those used

with DPMF and NMF samples. CMS sample was used

in the present experimental work, for having a referencesample under controlled conditions of nixtamalisation,

since DPMF and NMF samples were collected under

unknown nixtamalisation conditions.

2.2. Pasting procedure

Two set of samples with concentrations of 5% and

15% (w/v) were separately prepared using crude DPMF,

NFM and CMS. A total number of twenty-six pastesamples was so elaborated for carrying out the experi-

mental work (twenty pastes were prepared using DPMF,

four from NMF and two samples were set up by use of

the CMS). All the samples were homogeneously mixed

with deionised water at room temperature using a con-

tinuous magnetic stirring to avoid settling. All the

-in-water samples were then heated up to 80 �C (at a heat-ing rate of 1.5 �C/min), and keep them under isothermalconditions for 10 min. The paste samples were finally

cooled down to 60 �C (at a cooling rate of 1.5 �C/min).

2.3. Determination of the chemical composition

The determination of the chemical composition in the

crude masa samples (M-1 to M-10) involved a typical

bromatologic analysis of ash, fat, protein and moisture

content. Moisture content was determined by gravime-

try after heating (130� 2 �C for 2 h) using 3 g of sample.Ash, protein, and fat tests were analysed according to

standardised American Association of Cereal Chemists

methods sections: 08-01, 46-13, and 30-25, respectively

(Grami, 2000).

2.4. Measurement of rheological properties

The raw rheological data (srz and c) were measured ina rotational viscometer (Haake RV20) using a cone/platesystem (2 cm diameter with an angle of 1�). The instru-ment was previously calibrated using a standard solution

of known viscosity (12 Pa � s at 25 �C). Two consecutiveup–down shear rate scans from 0 to 3200 s�1, followed by

a descent scan from 3200 to 0.1 s�1, in a total time of 12

min were used for logging the rheometric data of each

sample. Such an experimental task was employed ac-

cording to the methodology reported by Tecante andDoublier (1999). The experimental errors obtained for

the rotational speed and the torque measurements were

smaller than 3% and 5%, respectively.

3. Results and discussion

3.1. Chemical composition

Results of the chemical composition of the dried

crude masa samples (M-1 to M-12 and CMS) are shown

in Fig. 1. As can be seen, the moisture content (in per-

cent) for all the masa samples was completely different

(Fig. 1a). Moisture content ranged from 4.2% to 12.1%.Most of the crude DPMF samples (M-1 to M-10) were

characterised by lower values of moisture content (4.2%

to 10.4%), while crude NMF samples (M-11 and M-12)

exhibited higher values. The CMS showed an inter-

mediate moisture content of 7:3%� 0:1%. The vari-

ability and heterogeneity observed in most of the sample

moisture values are probably due to the different nix-

tamalisation processes, which were used for preparingeach sample.

The analysis of fat content obtained in the samples

also showed very different values as was expected (Fig.

1b). Such a variability was confirmed by applying sig-

nificance statistical tests of ANOVA (one-way with a

significance level a ¼ 0:05% or 95% confidence level),

which enable to define that these samples actually come


from different sample populations. The highest values offat content were obtained for CMS and some crude

DPMF samples (M-4, M-5, M-8 and M-9), while NMF

samples showed lower values, which were similar to

those obtained for the remaining DPMF (M-1–M-3,

M-6, M-7, and M-10).

The protein content of the samples showed an aver-

age value of 8:2%� 0:5%, which could be considered

constant for all the samples (Fig. 1c). Such an averagevalue was slightly higher than some values reported for

maize flours (e.g., Mart�ıınez-Bustos et al., 2000). TheCMS samples showed a protein content of 7:6%� 0:3%.The ash content of the samples indicated an average

value of 1:2%� 0:3%, which could be considered con-stant for all the samples (Fig. 1d). Such an average value

was slightly higher than some values reported for maize

flours (Flores-Far�ııas et al., 2000). The CMS sampleshowed an ash content value of 1:4%� 0:1%.

Table 1

Measurements of shear stress and shear rate obtained in the rheological eva

c(s�1)

s (Pa)

DPMF-

1

DPMF-

2

DPMF-

3

DPMF-

4

DPMF-

5

DPMF-

6

D

7

24 5.0 2.1 3.4 2.2 0.4 1.4 1

32 6.2 4.3 4.1 2.7 1.1 2.2 3

40 7.9 5.3 4.8 3.9 1.8 3.4 3

51 7.9 9.7 5.0 8.6 2.5 4.5 4

68 11.4 10.4 8.8 10.8 4.0 7.1 7

89 13.6 14.0 9.1 13.7 4.4 7.2 7

114 19.7 15.3 12.9 17.5 6.2 10.6 10

149 22.1 17.7 14.4 19.8 6.5 11.6 11

191 27.9 22.6 18.6 25.3 9.0 15.6 15

245 30.3 24.6 19.8 27.2 9.2 16.0 16

318 37.2 29.6 23.2 33.9 12.4 19.9 19

403 40.9 32.5 26.2 36.4 13.0 21.9 21

683 54.9 42.7 34.3 48.8 18.0 29.6 29

1141 72.2 56.7 45.3 65.5 25.0 39.2 39

1906 95.9 74.7 60.2 87.3 34.5 52.5 52

3177 124.0 98.8 79.9 116.9 48.1 69.8 69

DPMF-

14

DPMF-

15

DPMF-

16

DPMF-

17

DPMF-

18

DPMF-

19

D

20

24 2.2 3.2 4.8 3.9 2.7 2.5

32 3.2 5.4 6.2 5.4 3.1 4.7

40 5.9 8.7 7.9 6.9 5.4 11.3

51 7.6 10.4 8.5 7.6 4.3 12.8

68 9.6 12.1 11.5 11.0 8.1 15.5

89 11.9 13.2 14.8 11.1 7.3 12.4 1

114 15.7 18.2 20.6 16.4 13.2 20.9 1

149 19.0 20.2 15.7 18.7 13.7 18.2 1

191 25.3 26.3 29.9 24.1 23.8 29.3 2

245 28.8 29.8 28.7 27.9 25.3 27.7 2

318 35.7 36.7 44.0 37.4 34.3 40.3 3

403 41.5 42.0 48.0 38.5 40.0 42.3 3

683 59.0 61.3 70.5 56.0 57.5 60.8 5

1141 84.0 84.9 96.8 83.0 85.3 87.0 7

1906 104.8 113.1 123.8 109.5 114.0 115.5 10

3177 131.5 145.7 146.3 137.0 142.0 144.8 13

3.2. Measurement of rheological properties

Twenty-six maize paste samples were rheologically

analysed. A total number of 416 measurements of shear

stress (s in Pa) and shear rate (c in s�1) data were logged.Table 1 summarises all the rheometric data measured for

the paste samples considered in the present experimental

work. Such data set comprises sixteen viscometer dial

readings of shear rate ranging from 24 to 3177 s�1 foreach sample analysed. These data profiles were sepa-

rately plotted, in order to determine their particular

behaviour of each paste sample in a classical plot of

shear stress versus shear rate (commonly known as

rheogram or flow curve). For discussion purposes and

also, in order to limit the size of the paper, only four

plots of the total number of experimental runs have been

selected (Fig. 2a–d). Such data correspond to the rheo-logical evaluation of the DPMF-4, CMS-2, NCF-3 and

luation of DPMF and NMF samples

PMF- DPMF-

8

DPMF-

9

DPMF-

10

DPMF-

11

DPMF-

12

DPMF-

13

.4 3.2 1.4 2.5 6.0 3.3 4.2

.2 3.6 2.6 3.6 6.8 4.6 5.0

.4 6.2 3.4 5.0 8.0 11.1 7.2

.5 7.7 4.1 8.2 7.9 13.9 9.0

.1 10.5 5.9 10.1 11.7 15.2 13.4

.2 11.8 9.5 12.2 11.6 18.8 16.0

.6 15.5 12.2 15.4 18.1 21.8 20.6

.6 17.9 14.4 17.0 17.3 14.9 22.9

.6 22.4 18.5 21.3 29.3 29.9 31.4

.0 27.2 20.3 23.4 24.7 24.5 32.2

.9 32.9 24.2 28.2 34.1 38.6 42.2

.9 36.6 27.4 30.7 38.5 37.2 45.2

.6 49.9 37.5 41.3 58.0 58.5 67.5

.2 66.8 48.8 54.6 78.5 83.3 92.5

.5 90.5 65.3 72.8 105.0 112.1 127.8

.8 121.7 83.3 96.0 133.0 143.6 142.8

PMF- CMS-

1

CMS-

2

NMF-

1

NMF-

2

NMF-

3

NMF-

4

4.1 1.8 4.7 2.6 0.5 3.2 6.6

5.9 2.4 7.8 3.6 0.9 6.0 9.6

6.8 3.4 8.5 5.5 1.4 6.1 10.9

8.5 4.5 11.3 8.1 1.8 8.9 12.4

8.6 5.3 12.4 9.4 3.1 10.0 15.7

1.8 5.5 15.5 12.6 5.6 11.9 17.2

7.3 7.8 18.2 17.1 8.6 16.7 22.9

3.1 8.1 20.9 19.6 10.7 17.4 23.2

5.2 11.3 27.7 25.5 14.9 25.1 32.1

1.9 11.6 29.3 27.7 16.2 27.8 33.2

3.7 14.4 40.3 33.8 20.7 36.5 45.4

2.8 16.0 42.3 38.0 23.4 39.6 45.6

0.3 22.0 60.8 51.8 32.3 60.4 67.9

6.5 30.4 87.0 84.6 39.6 87.0 92.6

8.8 41.2 115.5 93.0 61.5 114.8 120.4

5.0 56.0 144.8 123.5 82.9 142.1 147.4

-1

0 1000 2000 3000-1

0 1000 2000 3000

(Pa)

0

50

100

150

200

(Pa)

0

50

100

150

200

(c) (d)

(a) (b)

PLMRSMRPM

Exp. data CMS 2PLMRSMRPM

Exp. data DPMF-4

PLMRSMRPM

Exp. data NMF 3

PLMRSMRPM

Exp. data DPMF 13

ττ

Fig. 2. Rheological behaviour typified by PLM, RSM, and RPM

rheological models using the experimental rheometric data of some

maize dried flour pastes: (a) DPMF-4, (b) CMS-2, (c) NMF-3, and

(d) DPMF-13.


DPMF-13 paste samples, respectively. They were con-

sidered quite representative for describing the rheologi-cal behaviour exhibited by most of the samples

analysed. In some figures, the raw rheometric data to-

gether with their experimental errors were represented as

error bars. However, these error bars were not plotted

for samples that presented small experimental errors. As

can be observed, most of the samples exhibited a rheo-

logical behaviour typified by a non-linear increase of

shear stress as the shear rate was increased. Such a be-haviour clearly does not obey a Newtonian pattern (i.e.,

a linear relationship at shear rates greater than 250 s�1),

but also it is more properly defined by a non-Newtonian

behaviour, as was initially expected. In fact, this kind of

patterns have been previously associated as a pseudo-

plastic fluid behaviour (e.g., Makosco, 1994).

3.3. Analysis of rheometric data using non-Newtonian

models

All the flow curves obtained during the experimental

runs were used both for classifying and for selecting the

most suitable rheological model to accommodate the

wide variety of rheometric profiles logged. With these

purposes, three different rheological models (PLM,

RSM, and RPM) for the non-Newtonian analysis have

been employed. The results obtained in this analysis aredescribed as follows.

Power Law Model (PLM). As was previously cited,

this model has been traditionally used as a standard

analysis tool for evaluating the rheological behaviourof a wide variety of paste products in the food indus-

try. The application of this model required that the

shear stress and shear rate data, for each sample, were

plotted for analysing their particular flow curve. A

subsequent conversion of the original PLM equation

into its logarithmic form (log s ¼ logK þ n log c) wasalso needed to fit the experimental data as a straight

line. This fit procedure enabled to calculate all themodel parameters with the slope (n) and the intercept(K) values, which were inferred by using a weighted

linear regression algorithm (WLRA) for transporting

the experimental errors (Bevington, 1969). The para-

meters of the PLM and the squared correlation factors

(R2) obtained in the regression processes are presentedin Table 2.

After analysing this information, it can be observedthat PLM provides a satisfactory fit of most of the

rheometric data logged at lower shear rates (<1000 s�1),

except for the sample DPMF-4, in which the PLM

covers the non-linear relationship up to 2000 s�1.

However, at higher shear rates (>1000 s�1, except the

sample DPMF-13), the fit goodness provided by PLM is

not totally adequate, as can be clearly seen in most of

the plots presented (Fig. 2a–d: dashed line curves).Robertson–Stiff Model (RSM). As a result of the

poor fitting of the raw rheometric data afforded by the

PLM, the alternative rheological model proposed by

Robertson and Stiff (1976) was also evaluated. As was

previously mentioned, this model was successfully used

for evaluating non-Newtonian behaviour of drilling

fluids in both oil and geothermal industries. To the best

of our knowledge, there is no any evidence in the foodindustry literature related to the use of the RSM to

evaluate non-Newtonian fluids. In consequence, this is

the first time that the RSM is used and examined for

analysing rheometric data derived from food samples.

The application of RSM required that the s versus cplot was transformed in its logarithmic form, i.e.,

log s ¼ logAþ B logðc þ CÞ. Thus, a plot of s versus

c þ C provided a straight line on log-log coordinates,where the parameters A and B represented the interceptand the slope of the straight line, respectively. All the

RSM parameters were similarly obtained by use of a

WLRA. The results derived from this numerical analysis

were summarised in Table 2.

After fitting all the rheometric data set, it was clearly

observed that RSM provides a much better description

of the non-Newtonian behaviour in most of the pastesamples, at shear rates ranging from 0 to 2000 s�1 (Fig.

2a–d: dotted line curves), except for the sample CMS-2,

where the fitting was lost at a shear rate value of 500 s�1

(Fig. 2b). Even though, the fit goodness of the RSM was

generally good at shear rates <2000 s�1, some problems

were found at shear rates higher than 2000 s�1 (e.g., Fig.

2b–d).

Table 2

Regression coefficients computed for the non-Newtonian rheological models (PLM, RSM, and RPM)

Sample PLM RSM RPM

5% CONC. n k R2 A B C R2 P1 P2 Q1 Q2 R2

DPMF-1 0.668 0.6886 0.983 1.340 0.567 )16.7 0.991 0.216 1.61e)04 4.12e)03 4.52e)07 0.994

DPMF-2 0.652 0.6137 0.970 1.158 0.557 )16.6 0.987 0.199 1.63e)04 5.40e)03 4.91e)07 0.998

DPMF-3 0.696 0.3698 0.948 1.028 0.543 )22.6 0.989 0.145 8.35e)05 4.19e)03 1.96e)07 0.992

DPMF-4 0.777 0.3133 0.978 1.361 0.554 )21.9 0.998 0.186 9.31e)05 3.46e)05 1.06e)07 0.999

DPMF-5 0.756 0.1324 0.969 0.268 0.651 )16.0 0.982 0.063 4.34e)05 3.54e)03 1.04e)07 0.987

DPMF-6 0.746 0.2285 0.948 0.701 0.576 )21.7 0.992 0.112 6.39e)05 3.61e)03 1.84e)07 0.992

DPMF-7 0.725 0.2618 0.953 0.783 0.559 )21.7 0.994 0.114 7.16e)05 3.84e)03 2.31e)07 0.999

DPMF-8 0.732 0.4139 0.976 0.937 0.609 )18.2 0.994 0.168 9.21e)05 3.02e)03 1.39e)07 0.989

DPMF-9 0.773 0.2328 0.959 0.668 0.617 )23.9 0.988 0.122 5.49e)05 7.99e)03 1.95e)07 0.998

DPMF-10 0.675 0.5081 0.967 1.017 0.572 )17.3 0.988 0.182 1.52e)04 5.09e)03 4.83e)07 0.989

CMS-1 0.683 0.2582 0.985 0.635 0.546 )19.8 0.988 0.092 1.20e)04 5.93e)03 7.01e)07 0.999

NMF-1a 0.768 0.3499 0.964 1.008 0.611 )20.5 0.992 )0.213 1.43e)02 2.71e)02 1.39e)03 0.962

NMF-2 1.007 0.0432 0.909 0.226 0.754 )22.4 0.952 0.085 2.50e)05 1.80e)03 )4.16e)08 0.994

15% CONC n k R2 A B C R2 P1 P2 Q1 Q2 R2

DPMF-11 0.672 0.6653 0.988 1.465 0.551 )18.0 0.969 0.127 )3.48e)04 )2.08e)03 )1.81e)06 0.989

DPMF-12 0.681 0.6486 0.924 0.758 0.658 )4.4 0.925 0.368 3.27e)03 1.27e)05 1.27e)05 0.940

DPMF-13 0.669 0.8018 0.927 1.156 0.615 )10.1 0.967 0.658 1.41e)02 1.02e)01 6.60e)05 0.970

DPMF-14b 0.777 0.3443 0.970 1.462 0.567 )44.5 0.996 0.151 3.01e)04 3.31e)03 1.79e)06 0.990

DPMF-15 0.681 0.6792 0.986 0.724 0.671 )2.6 0.986 0.255 1.18e)03 1.29e)02 4.54e)06 0.982

DMPF-16 0.683 0.7204 0.988 1.770 0.555 )21.8 0.955 0.006 1.16e)01 7.84e)01 5.43e)02 0.989

DPMF-17 0.732 0.4613 0.980 0.703 0.669 )10.6 0.981 0.191 9.06e)04 9.70e)03 3.87e)06 0.989

DPMF-18 0.838 0.2213 0.976 0.508 0.714 )16.1 0.969 0.117 4.06e)04 3.92e)03 1.79e)06 0.999

DPMF-19c 0.758 0.6660 0.956 1.000 0.624 8.0 0.954 136.650 8.00e)00 45.9e)01 1.88e)02 0.998

DPMF-20 0.704 0.5046 0.954 0.546 0.692 )2.2 0.953 0.767 1.53e)02 1.67e)01 6.14e)05 0.944

CMS-2d 0.666 0.7585 0.956 1.069 0.635 )6.0 0.925 0.939 4.28e)02 2.28e)01 1.88e)02 0.999

NMF-3 0.745 0.4335 0.958 0.591 0.699 )7.9 0.958 0.131 )3.59e)04 )2.16e)03 1.66e)06 1.000

NMF-4 0.624 1.0914 0.976 1.416 0.585 )7.9 0.975 0.460 3.45e)03 2.97e)02 1.49e)05 0.940

P3 and Q3 ¼ 0 for the rest of the experimental cases.a P3 ¼ 1:36e)4, Q3 ¼ 7:12e)7.b P3 ¼ 1:15e)8.c P3 ¼ 0:13.d P3 ¼ 1:37e)4, Q3 ¼ 6:762e)7.


Rotational Polynomial Model (RPM). In order to

evaluate another rheological model to the raw rheo-

metric data set, a general correlating equation based on

the RPM was applied in this work. This model was re-

cently suggested by Kumar et al. (2000) as an improved

analysis tool for fitting rheometric data of a wide variety

of non-Newtonian fluids. For the application of this new

model, a non-linear regression method based on a ratioof polynomial functions was applied to the rheometric

data set for obtaining the coefficients of the two poly-

nomial functions correlated in Ec. 3 (P1, P2, P3, Q1, Q2,

and Q3). A computer programme that uses the Mar-

quardt–Levenbergnumerical algorithmwas implemented

for performing the non-linear regression analyses and

the mathematical treatment of the ratio of polynomial

functions. The theoretical details of the overall numeri-cal method are reported by Hanna and Sandall (1995).

The results obtained during the non-linear regression

treatment of all the twenty-six flour paste samples, in-

cluding the coefficient values of the two polynomial

functions are presented in Table 2. As can be observed

in Fig. 2a–d, the RPM provides an excellent fit of the

rheometric data in most of the paste samples evaluated

at a wide shear rate range (24–3200 s�1). RPM affords

the best fit procedure for all the experimental data log-

ged. It is important to note that even the RPM usually

requires more parameters than other standard rheologi-

cal models to accurately describe the raw rheological

data, the number of parameters involved in this modelcan be considered small to be compatible with the size of

most rheological data sets (Kumar et al., 2000).

After this analysis, it can be pointed out that the

RPM is quite capable of accurately describing the flow

curve of any non-Newtonian paste sample evaluated.

This fact was also verified by an estimation of the errors

derived from the prediction of the shear stress data using

each one of the rheological model (Tables 3 and 4). Inthese tables, it was included only the rheometric data at

shear rates greater than 600 s�1, since at these shear rates

the PLM and RSM did not provide an appropriate fit.

Highest error percents (in absolute values) were due to

the PLM (up to 75.3%) compared than the RSM (up to

Table 3

Relative error difference (RED) of shear stress data (DPMF and NMF: 5% w/w) estimated between the measured and predicted values by the

rheological models (PLM, RSM, and RPM)

Sample 5%

(w/w)

Shear rate

(s�1)

Shear stress (Pa) Error

Measured Predicted RED (%)

PLM RSM RPM PLM RSM RPM

DPMF-1 1141 72.2 75.9 71.9 72.7 5.12 0.42 0.69

1906 95.9 106.9 96.5 95.1 11.47 0.63 0.83

3177 124.0 150.4 129.2 124.2 21.29 4.19 0.16

DPMF-2 1141 56.7 60.4 57.9 56.5 6.53 2.12 0.35

1906 74.7 84.4 77.4 74.5 12.99 3.61 0.27

3177 98.8 117.8 103.0 98.8 19.23 4.25 0.00

DPMF-3 1141 45.3 49.6 46.5 45.4 9.49 2.65 0.22

1906 60.2 7.9 61.7 59.8 86.88 2.49 0.66

3177 79.9 101.2 81.6 80.0 26.66 2.13 0.13

DPMF-4 1141 65.4 74.4 66.5 65.5 13.76 1.68 0.15

1906 87.3 110.8 88.8 86.7 26.92 1.72 0.69

3177 116.8 164.8 118.1 117.0 41.10 1.11 0.17

DPMF-5 1141 25.0 27.1 25.9 24.9 8.40 3.60 0.40

1906 34.5 39.9 36.4 34.3 15.65 5.51 0.58

3177 48.1 58.8 50.8 48.1 22.25 5.61 0.00

DPMF-6 1141 39.2 43.6 40.0 39.4 11.22 2.04 0.51

1906 52.5 63.9 54.0 52.1 21.71 2.86 0.76

3177 69.8 93.6 72.7 69.8 34.10 4.15 0.00

DPMF-7 1141 39.2 43.1 39.6 39.3 9.95 1.02 0.26

1906 52.5 62.5 53.0 52.2 19.05 0.95 0.57

3177 69.8 90.5 70.8 69.8 29.66 1.43 0.00

DPMF-8 1141 66.8 71.5 67.5 67.3 7.04 1.05 0.75

1906 90.5 104.2 92.7 90.0 15.14 2.43 0.55

3177 121.7 151.4 126.8 121.8 24.40 4.19 0.08

DPMF-9 1141 31.0 33.7 31.0 30.9 8.71 0.00 0.32

1906 41.6 51.3 43.2 41.6 23.32 3.85 0.00

3177 54.9 77.8 59.9 54.9 41.71 9.11 0.00

DPMF-10 1141 54.6 58.8 56.5 54.7 7.69 3.48 0.18

1906 72.8 83.1 76.0 72.4 14.15 4.40 0.55

3177 96.0 117.4 102.1 96.0 22.29 6.35 0.00

CMS-1 1141 30.4 31.6 29.4 30.2 3.95 3.29 0.66

1906 41.2 44.9 39.0 41.3 8.98 5.34 0.24

3177 56.0 63.6 51.7 55.9 13.57 7.68 0.18

NMF-1 1141 84.6 77.9 73.6 76.1 7.92 13.00 10.05

1906 93.0 115.6 101.1 99.0 24.30 8.71 6.45

3177 123.5 171.2 138.5 121.8 38.62 12.15 1.38

NMF-2 1141 39.6 51.8 45.0 43.4 30.81 13.64 9.60

1906 61.5 86.8 66.7 59.3 41.14 8.46 3.58

3177 82.9 145.2 98.4 83.2 75.15 18.70 0.36

RED ¼ ½ðMeasured� PredictedÞ=Measured � 100.


23.5%), and the RPM (up to 10.1%). Average errors (in

absolute values) of 13.2%, 5.9%, and 0.9% were also

calculated for the PLM, RSM, and RPM, respectively.

From this analysis, it is also evident that the RPM

provides the best fit of rheometric data.

The high apparent values of R2 (Table 2), as a mea-sure of the fit goodness of the models, do not always

provide an appropriate criterion to choice the most

suitable model for describing the non-Newtonian be-

haviour of fluids. This parameter is not totally true for

non-linear models as was suggested by Weir and Bailey

(1996). Since the models considered here are non-linear,

the use of the R2 is not totally relevant for evaluating thefit quality on the experimental rheometric data. In fact,

there are some works reported in the literature which

object to the calculation and the use of R2 as a funda-

Table 4

Relative error difference (RED) of shear stress data (DPMF and NMF: 15% w/w) estimated between the measured and the predicted values from the

rheological models (PLM, RSM, and RPM)

Sample

15% (w/w)

Shear rate

(s�1)

Shear stress (Pa) Error

Measured Predicted RED (%)

PLM RSM RPM PLM RSM RPM

DPMF-11 1141 78.5 79.7 70.2 82.3 1.52 10.57 4.84

1906 105.0 116.2 93.5 106.9 10.66 10.95 1.81

3177 133.0 168.8 124.2 130.0 26.91 6.61 2.26

DPMF-12 1141 83.3 78.3 77.7 82.8 6.00 6.72 0.60

1906 112.1 111.1 109.0 112.1 0.89 2.76 0.00

3177 143.6 157.3 152.7 143.7 9.54 6.33 0.07

DPMF-13 1141 92.5 79.8 87.3 94.2 13.72 5.62 1.84

1906 127.7 116.1 119.9 120.9 9.08 6.10 5.32

3177 142.7 168.8 164.4 146.1 18.29 15.20 2.38

DPMF-14 1141 84.0 81.9 75.7 81.9 2.49 9.88 2.50

1906 104.7 121.8 103.0 105.8 16.33 1.62 1.05

3177 131.5 181.1 139.2 131.5 37.71 5.85 0.00

DPMF-15 1141 84.9 82.0 81.4 84.7 3.41 4.12 0.24

1906 113.1 116.3 114.9 113.8 2.82 1.59 0.62

3177 145.6 164.7 162.0 145.4 13.11 11.26 0.14

DPMF-16 1141 96.7 88.6 87.4 95.7 8.37 9.61 1.03

1906 123.7 125.9 116.7 122.5 1.77 5.65 0.97

3177 146.3 178.4 155.4 147.5 21.94 6.22 0.82

DPMF-17 1141 83.0 79.8 77.5 81.6 3.85 6.62 1.69

1906 109.5 116.1 109.6 108.9 6.02 0.09 0.55

3177 137.0 168.8 154.4 137.4 23.21 12.70 0.29

DPMF-18 1141 85.2 80.7 76.3 84.9 5.28 10.44 0.35

1906 114.0 124.1 110.5 113.6 8.85 3.07 0.35

3177 142.0 190.4 159.5 142.1 34.08 12.32 0.07

DPMF-19 1141 87.0 82.4 81.2 86.1 5.28 6.66 1.03

1906 115.5 116.0 112.1 115.8 0.43 2.94 0.26

3177 144.8 163.0 154.3 144.7 12.56 6.56 0.07

DPMF-20 1141 76.5 78.3 71.1 76.6 2.35 7.05 0.13

1906 108.7 111.1 101.5 105.3 2.20 6.62 3.13

3177 135.0 157.3 144.6 136.5 16.51 7.11 1.11

CMS-2 1141 87.0 82.4 93.1 86.4 5.28 7.01 0.69

1906 115.5 116.0 129.1 114.9 0.43 11.77 0.52

3177 144.7 163.0 178.7 145.1 12.64 23.49 0.28

NMF-3 1141 87.0 82.1 80.7 87.5 5.63 7.24 0.57

1906 114.7 120.4 115.7 115.0 4.96 0.87 0.26

3177 142.1 176.2 165.6 141.4 23.99 16.53 0.49

NMF-4 1141 92.6 88.3 86.6 92.4 4.64 6.47 0.22

1906 120.4 121.6 117.2 119.9 0.99 2.65 0.42

3177 147.4 167.2 158.1 147.6 13.43 7.25 0.14

RED ¼ ½ðMeasured� PredictedÞ=Measured � 100.


mental criterion of fit (Draper, 1984; Healy, 1984; Hel-

land, 1987; Weir & Bailey, 1996). In this respect, a sta-

tistical analysis of residuals is more suitable for detecting

inadequacies of a rheological model. For supporting and

complementing this evidence, a comprehensive statisti-

cal analysis of the residual sum of squares (RSS) and the

residual mean square (RMS) was carried out. This study

also enabled to compare the fit goodness among the

three rheological models (PLM, RSM, and RPM). RSS

was calculated by means of the following equation:

RSS ¼Xn

i¼1ðsi � spÞ2 ð4Þ

where si and sp are the observed and predicted shear

stress data, respectively. On the other hand, RSM was

computed by using the following equation:

Non-Newtonian rheological models

PLM RSM RPM

Res

idua

lmea

nsq

uare

(RM

S)

0

50

100

150

200

250

Confidence level (95 %)

outliers

Fig. 3. RMS boxplots of fitting models for a 95% of confidence level.


RMS ¼ RSS

ðn� pÞ ð5Þ

where n is the total number of data points and p thenumber of parameters in the rheological model (Weir &

Bailey, 1996).

All the rheological models (PLM, RSM, and

RPM) and their goodness of fit were assessed by

examining their RMS performance over the 416 rheo-

metric measurements. The statistical results of theRMS analysis per sample are summarised in Table 5.

The whole RMS analysis, in terms of the statistical

distribution (extreme, quartile, and median values) ob-

served with the fitted results is presented numerically

in Table 6, and graphically by use of boxplots in Fig. 3.

The size of the box and the bars are directly pro-

portional to the errors associated with the rheometric

data prediction computed by use of the rheologicalmodels.

With the aim of this information, it can be totally

confirmed that the use of the RPM provides a better

description than PLM and RSM for all the rheometric

data sets. Such a capability demonstrates that the

RPM is quite flexible for accommodating the wide

variety of non-Newtonian profiles exhibited by most of

the paste samples analysed. The attributes provided byRPM clearly enable a well-suited analysis tool for fit-

ting the rheological data in a wide variety of non-

Newtonian fluids, as was earlier suggested by Kumar

et al. (2000).

Table 5

Resulting RMS values from the least squares parameter estimates for the va

Rheo-

logical

model

DPMF-

1

DPMF-

2

DPMF-

3

DPMF-

4

DPMF-

5

DPMF-

6

D

7

PLM 65.9 37.7 46.2 223 11.6 55.1 4

RSM 4.9 3.3 1.2 2.2 1.3 1.6 0

RPM 1.0 0.9 0.9 2.5 0.3 0.7 0

DPMF-

14

DPMF-

15

DPMF-

16

DPMF-

17

DPMF-

18

DPMF-

19

D

2

PLM 221 29.9 110 80.7 187 33.1 4

RSM 22.4 24.6 30.8 28.8 34.8 18.7 2

RPM 1.4 1.3 10.6 2.9 3.2 8.2 1

Bold number represented the outliers detected in the statistical distribution

Table 6

RMS summary statistics for the models (at 95% confidence level)

Rheological model Lower extreme Lower quartile Media

PLM 6.00 33.87 48.00

RSM 0.66 3.40 19.27

RPM 0.30 0.88 2.08

4. Conclusions

An experimental programme for evaluating the rheo-

logical properties and the non-Newtonian behaviour of

twenty-six maize flour pastes prepared from 13 Mexican

commercial producers was carried out. A total number

of 416 measurements of shear stress and shear rates were

rious models using the twenty-six ma�ııze paste samples

PMF- DPMF-

8

DPMF-

9

DPMF-

10

DPMF-

11

DPMF-

12

DPMF-

13

2.2 83.8 113 46.1 107 31.2 43.8

.6 3.6 16.9 5.0 29.6 26.3 47.9

.6 0.5 1.1 0.6 12.6 17.5 9.7

PMF-

0

CMS-

1

CMS-

2

NMF-

1

NMF-

2

NMF-

3

NMF-

4

9.7 6.0 33.1 210 246 93.5 36.1

1.7 2.2 123 33 28.5 51.5 19.8

1.2 0.3 8.2 11.4 4.3 5.1 6.6

test.

n Upper quartile Upper extreme Maximum RMS

103.63 218.62 223.00

28.73 50.62 123.60

7.80 12.37 17.50


used for evaluating the non-Newtonian behaviour ofthese samples.

The classical Power law (PLM), the Robertson–Stiff

(RSM) and the rational polynomial (RPM) models have

been used for fitting the rheometric data over a wide

range of shear rates. From the experimental data and a

comprehensive statistical methodology, it has been

clearly demonstrated that there are far more appropriate

rheological models (RSM and RPM) to be consideredthan the classical PLM. RSM provided a more satis-

factory fit of the rheometric data at shear rates ranging

from 0 to 2000 s�1. However, RPM was consistently

more capable of providing excellent fluid characterisa-

tion over a wide range of shear rates examined in this

experimental work (24–3200 s�1). Considering all these

results, it can be concluded that the RPM can be con-

sidered as a reliable analysis tool for studying thenon-Newtonian behaviour of fluids, also in the food

industry.

Research is underway for extending the present sta-

tistical methodology to the evaluation of a wide number

of the rheological models available in the literature.

Acknowledgements

Financial support from the Instituto Polit�eecnicoNacional, M�eexico (Project CGPI-200098) are gratefullyacknowledged. The second author expresses additional

thanks to the Master�s of Engineering programme atUAEM-Mor due to the opportunity to teach an applied

statistics course, which motivated to write this paper

together with the M.Sc student (first author) and the

other authors.

References

Almeida-Dom�ıınguez, H. D., Cepeda, M., & Rooney, L. (1996).

Properties of commercial nixtamalized corn flour. Cereal Foods

World, 41, 624–630.

Ar�aambula, V. G., Barr�oon, A. L., Gonz�aalez, H. J., Moreno, M. E., &

Luna, B. G. (2001). Efecto del tiempo de cocimiento y reposo del

grano de ma�ıız (Zea mayz L.) nixtamalizado, sobre las car�aacter�ıısti-cas fisicoqu�ıımicas, reol�oogicas, estructurales y texturales del grano,

masa y tortillas de ma�ıız. Archivos Latinoamericanos de Nutrici�oon,

51, 187–194.

Ar�aambula, V. G., Mauricio, S. R. A., Figueroa, C. J. D., Gonz�aalez-Hern�aandez, J., & Ordorica, F. C. A. (1999). Corn masa and

tortillas from extruded instant corn flour containing hydrocolloids

and lime. Engineering Processing, 64, 120–124.

Bevington, P. R. (1969). Data reduction and error analysis for physical

sciences. New York, USA: McGraw-Hill.

Campus-Baypoli, O. N., Rosas-Burgos, E. C., Torres-Ch�aavez, P. I.,

Ramirez-Wong, B., & Serna-Sald�ııvar, S. O. (1999). Physicoche-mical changes of starch during maize tortilla production. Starch/

Starke, 51, 173–177.

Chamberlain, E. K., & Rao, M. A. (1999). Rheological properties of

acid converted waxy maize starches in water and 90% DMSO/10%

water. Carbohydrated Polymers, 40, 251–260.

Doublier, J. L. (1987). A rheological comparison of wheat, maize, faba

bean and smooth pea starches. Journal of Cereal Science, 5, 247–

262.

Draper, N. R. (1984). The Box–Wetz criterion versus R2. Journal of

Royal Statistical Society of America, 147(4), 100–103.

Flores-Far�ııas, R., Mart�ıınez-Bustos, F., Salinas-Moreno, Y., Chang,

Y. K., Gonz�aalez-Hern�aandez, J., & R�ııos, E. (2000). Physicochemical

and rheological characteristics of commercial nixtamalised Mexi-

can maize flours for tortillas. Journal of the Science of Food and

Agriculture, 80, 657–664.

G�oomez, M. H., Rooney, L. W., Waniska, R. D., & Pflugfelder, R. L.

(1987). Dry corn masa flours for tortilla and snack food produc-

tion. Cereal Foods World, 32, 372–377.

Grami, B. (2000). Approved methods of the American Association of

Cereal Chemists. Sections: : 08-01, 46-13, and 30-25, 10th edition.

American Association of Cereal Chemists, Minneapolis, USA.

Hanna, O., & Sandall, O. (1995). Computational Methods in Chemical

Engineering. Upper Saddle River, NJ, pp. 185–196.

Healy, M. J. R. (1984). The use of R2 as a measure of goodness of fit.Journal of Royal Statistical Society of America, 147(4), 608–

609.

Helland, I. S. (1987). On the interpretation and use of R2 in regressionanalysis. Biometrics, 43(1), 61–69.

Holland, F. A. (1964). Another look at non-Newtonian flow. Chemical

Engineering, August, 17, 4.

Holland, F. A., & Bragg, R. (1995). Fluid flow for chemical engineers.

London, UK, p. 358.

Holdsworth, S. D. (1993). Rheological models used for the prediction

of the flow properties of food products. Transaction of the

Institution of Chemical Engineering, 71, 139–179.

Kumar, A., Saboo, S., Sheth, S., Pilehvari, A., & Serth, R. (2000).

Correlation of rheometric data and hydraulic calculations using

rational polynomials. Chemical Engineering Communication, 183,

99–117.

Lauzon, R. V., & Reid, K. I. G. (1979). New rheological model offers

field alternative. The Oil and Gas Journal, 5, 51–57.

Makosco, Ch. W. (1994). Rheology: principles, measurements, and

applications. USA: Wiley-VCH, pp. 83–92.

Mart�ıınez-Bustos, F., Garc�ııa, M. N., Chang, Y. K., S�aanchez-Sinencio,

F., & Figueroa, C. J. C. (2000). Characteristics of nixtamalised

maize flours produced with the use of microwave heating produced

with the use of microwave heating during alkaline cooking. Journal

of Science Food Agricultural, 80, 651–656.

Mensah-Agyapong, J., & Horner, W. F. (1992). Nixtamalisation of

Maize (Zea mays. L) using a single screw cook-extrusion process on

lime-treated grits. Journal of Science Food Agriculture, 60, 509–514.

Muller, H. G. (1973). An introduction to food rheology. London, UK:

Heinemann, pp. 36–55.

Rao, M. A., & Tattiyakul, J. (1999). Granule size and rheological

behavior of heated tapioca starch dispersions. Carbohydrate

Polymers, 38, 123–132.

Robertson, R. E., & Stiff, H. A. (1976). An improved mathematical

model of relating shear stress to shear rate in drilling fluids and

cement slurries. Society of Petroleum Engineers Journal, 2, 31–37.

Rooney, L. W., & Suhendro, E. L. (1999). Perspectives on nixtamali-

zation (alkaline cooking) of maize for tortillas and snacks. Cereal

Foods World, 44, 466–470.

Santoyo, E. (1997). Transient numerical simulation of heat transfer

processes during drilling of geothermal well. Ph.D. Thesis.

University of Salford. UK., pp. 136–138.

Santoyo, E., Santoyo-Guti�eerrez, S., Garc�ııa, A., Espinosa, G., & Moya,

S. L. (2001). Rheological property measurement of drilling fluids

used in geothermal wells. Applied Thermal Engineering, 21, 283–

302.


Sopade, P. A., & Kiaka, K. (2001). Rheology and microstructure of

sago starch from Papua New Guinea. Journal of Food Engineering,

50, 47–57.

Tecante, A., & Doublier, J. L. (1999). Steady flow and viscoelastic

behavior of cross-linked waxy corn starch-j-carrageenan pastes

and gels. Carbohydrate Polymers, 40, 221–231.

Tecante, A., & Doublier, J. L. (2002). Rheological investigation of the

interaction between amylose and carageenan. Carbohydrate Poly-

mers, 49, 177–183.

Thebaudin, J. Y., Lefebre, A. C., & Doublier, J. L. (1998). Rheology of

starch pastes of different origins: Applications to starch-based

Sauces. Food Science and Technology––Lebensmitted-Wisserschaft

& Technologie, 31(4), 354–360.

Thomas, D. J., & Atwell, W. A. (1999). Starches, pp. 19–22. American

Association of Cereal Chemists, Minneapolis, USA.

Weir, I. S., & Bailey, W. J. (1996). A statistical study of rheological

models for drilling fluids. Society of Petroleum Engineers Journal,

12, 473–486.

Rheological evaluation of non-Newtonian Mexican nixtamalised maize and dry processed masa flours

Documents

Transcript of Rheological evaluation of non-Newtonian Mexican nixtamalised maize and dry processed masa flours