Rheology of Tapioca Starch

Rheology of tapioca starch

C.R. Chen1, H.S. Ramaswamy*

Department of Food Science, Macdonald Campus of McGill University, Ste. Anne de Bellevue, PQ, Canada H9X 3V9

Received 24 September 1998; accepted 18 May 1999

Abstract

Rheological properties of tapioca starch solutions were evaluated using a computer controlled rotational viscometer in relation tofour factors: temperature, 20±80�C; concentration, 2±6%; pH, 4±8 and cooking time, 5±35 min. All test solutions showed power-

law ¯ow behavior. A second order composite design was used to investigate the e�ects of concentration, temperature, pH value andcook time on rheological property parameters (consistency coe�cient, m, and ¯ow behavior index, n), and develop second ordermultiple response models of parameters related to concentration, temperature, pH value and cook time. # 1999 Published by

Elsevier Science Ltd. All rights reserved.

Keywords: Tapioca starch; Rheology; Concentration; Temperature; pH; Cooking

1. Introduction

Design of food processing operations (mixing, pumping,heating, cooling) requires data on rheological properties.The ¯ow characteristics of a pumpable food product aredependent on the ¯uid viscosity and density. Calculationof thermal treatment times for processing of liquid foodscontaining particulates is complex because the residencetime distribution (RTD) of particulates and carrier ¯uidare in¯uenced by concentration and the type of carrier¯uid as well as other process parameters (time, tempera-ture, pressure, and the system con®guration). Data onrheological characteristics, relative velocity between ¯uidand particles and ¯uid to particle heat transfer coe�cientsare needed for optimizing the heat exchanger and holdingtube designs in aseptic processing of liquid foods contain-ing particulates (Dail & Ste�e, 1990a,b; Ramaswamy,Abdelrahin, Simpson & Smith, 1995).Starches are commonly added to popular foods such as

soups and sauces to increase their consistency and improvemouth-feel characteristics. The thickening activity of star-ches results from the swelling of starch granules occurringat gelatinization temperatures (Self, Wilkin, Morley &Bailey, 1990). Recently, modi®ed cross-linked starches

have been used to simulate carrier ¯uids in aseptic proces-sing of liquid foods containing particulates (Abdelrahim,Ramaswamy & Van de Voort, 1995; Harrod, 1989a,b,c).Tapioca starch is widely used in delicately ¯avored pud-dings, pastry ®llings and baby food products (Whistler,Bemiller & Paschall, 1984). Of non-cereal starches, tapiocahas ranked ®rst in order of importance in North America(Kerr, 1950). There have beenmany research reports on therheological properties of starch solutions (Bhattacharya &Bhat, 1997; Bhattacharya & Bhattacharya, 1994, 1996;Biliaderis, 1991; Dail & Ste�e, 1990a,b; Harrod, 1989a,b,c;Ramaswamy, Busak, Abbatemarco & Sablani, 1995;Sandhya & Bhattacharya, 1995; Taylor, 1979), but nopublished information is available on the rheologicalmodeling of tapioca starch solutions. Further, themajorityof reported experimental data on rheological propertiesfocuses on the e�ects of temperature and concentration,and little on those of pH value and cook time.The objective of this work was, therefore, to study the

e�ect of concentration (2±6%), temperature (20±80�C), pH(4±8) and cook time (5±35 min) on the rheological proper-ties of tapioca starch solutions and develop predictingmodels for the rheological parameters.

2. Materials and methods

Tapioca starch was obtained from a local market(modi®ed waxy starch, powdered form, produced byYat Loong Company, Hong Kong, China, packed and

0963-9969/99/$20.00 # 1999 Published by Elsevier Science Ltd. All rights reserved.

PI I : S0963-9969(99 )00090-3

Food Research International 32 (1999) 319±325

www.elsevier.com/locate/foodres

* Corresponding author. Tel.: +1-514-398-7919; fax:+1-514-398-

7977.

E-mail address [email protected] (H.S. Ramas-

wamy)1 Visiting Professor, Department of food science, Zhejiand Uni-

versity, Hangzhou, People's Republic of China.

distributed in Canada). The pH value of water wasinitially adjusted by adding acid (citric) or NaOH.Appropriate amounts of starch and water were mixedthoroughly and brought to boiling in a steam-jacketedkettle. The mixture was then allowed to slowly simmerat �100�C for selected time intervals (cook time from 5to 35 min) under atmospheric conditions. The solutionwas covered during cooking to minimize loss of moist-ure during cooking. The lost moisture (about 5±10% byweight) was added back at the end to maintain theconcentration level.Rheological measurements (shear rate±shear stress data)

were made using a rotational viscometer (Haake ModelRV20; Haake Mess-Technik, Karlsrulhe, Germany),equipped with an M-05 OSC measuring head and MVI(radius of the rotor,Rb, 20.04mm; height, h, 60mm, radiusof the cylindrical cup, Rc, 21 mm) rotor assembly inter-faced to a microcomputer for control and data acquisition.The sample compartment was kept at a constant tempera-ture using a water bath/circulator (Haake,Model FK-2).For each test, the ®lled sample cup and spindle were

temperature equilibrated for about 20 min and shearedat a programmed rate linearly increasing from 0 to 200sÿ1 in 10 min. Shear stress±shear rate data were col-lected continuously at 12 s intervals throughout the test.Flow curves (rheograms) were evaluated by the instru-ment operating software (Haake RV20 version 2.3)using the following models.

1: Power law model : � � m n �1�

where � is the shear stress (Pa), is the shear rate (sÿ1),m is the consistency coe�cient (Pasn), and n is the ¯owbehavior index (dimensionless).

2: HerschelÿBulkley model : � � �0 �m n �2�

where �0 is the yield stress.

3: Casson model : �0:5 � �k0�0:5 � k1� n�0:5 �3�

where k0 and k1 are Casson yield stress and Cassonviscosity, respectively.A shear analysis test as recommended in Ste�e (1992)

was used to assess the validity of using the power-lawmodel for test data. A second order central compositedesign (Gacula & Singh, 1984; Piggott,1986) was used inorder to develop predictive models of rheological para-meters. The experimental factors and levels are shownin Table 1. The ®tted response model is:

Y � b0 ��biXi ��biiX2i ��bijXiXj

�i � 1ÿ4; j � 1ÿ4; i 6� j� �4�

The relationships between coded variables and prac-tical variables(Table 1) were as follows:

X1 � Cÿ 4; X2 � �Tÿ 50�=15; X3 � Pÿ 6;

X4 � �tÿ 20�=7:5 �5�

Fig. 1. Comparison of ¯ow curves of three starch solutions: tapioca,

maize and potato at a 4% concentration level.

Table 1

Experimental factors and levels

Factor Concentration

C (%)

temperature

T (�C)pH

value P

Cook time

t (min)

Coded

variable (Xi)

ÿ2 2 20 4 5

ÿ1 3 35 5 12.5

0 4 50 6 20

1 5 65 7 27.5

2 6 80 8 35

Fig. 2. Typical ¯ow curves of tapioca starch solutions: (1) T=10�C,C=4%, pH=7, t=20 min; (2) T=20�C, C=4%, pH=7, t=20 min;

(3) T=20�C, C=4%, pH=7, t=40 min; (4) T=20�C, C=4%,

pH=4, t=20 min.

320 C.R. Chen, H.S. Ramaswamy / Food Research International 32 (1999) 319±325

3. Results and discussion

3.1. Rheological characterization of tapioca starch

Fig. 1 shows the ¯ow curves for tapioca, sweet potatoand maize starch solutions under the same conditions.

The curves for sweet potato and tapioca were experi-mentally obtained at a 4% concentration after a 20 mincook time. The maize starch data are from Ramaswamy,Basak et al. (1995) also at a 4% starch concentrationlevel. From Fig. 1, it was found that the shear stress fortapioca starch solution was much higher than those for

Table 2

Comparison of di�erent models for the rheology of tapioca starch solutions at di�erent temperatures (T), concentrations (C), pH values and cook

times (t)a

Typical conditions Model m�k1� n �o�ko� R2

T=10�C, C=4%, pH=7, t=20 min Powder lawb 1.02 0.417 0.98

Herschel±Bulkleyc 1.08 0.413 0.95 0.95

Cassond 0.97 0.843 0.92 0.96

T=20�C, C=4%, pH=7, t=20 min Power lawb 0.87 0.691 0.99

Hersche±Bulkleyc 0.86 0.684 0.49 0.97

Cassond 0.84 1.401 0.42 0.97



Cassond 0.621 1.422 0.38 0.98



Cassond 0.159 0.1692 0.19 0.97

a The number of data points regressed is 50.b Power law model: � � m n� �.c Herschel±Bulkely model: � � �0 �m n.d Casson model; �0:5 � �k0�0:5 � k1� n�0:5.

Table 3

Second order design matrix and calculation results of rheology parameters: consistency coe�cient, m, and ¯ow behavior index, n

Order x0 x1 x2 x3 x4 x1�x2 x1�x3 x1�x4 x2�x3 x2�x4 x3�x4 x12 2x2 x32 x42 m (Pasn) n

1 1 ÿ1 ÿ1 ÿ1 ÿ1 1 1 1 1 1 1 1 1 1 1 0.423 0.5122 1 ÿ1 ÿ1 ÿ1 1 1 1 ÿ1 1 ÿ1 ÿ1 1 1 1 1 0.38 0.5223 1 ÿ1 ÿ1 1 ÿ1 1 ÿ1 1 ÿ1 1 ÿ1 1 1 1 1 0.531 0.494 1 ÿ1 ÿ1 1 1 1 ÿ1 ÿ1 ÿ1 ÿ1 1 1 1 1 1 0.470 0.4955 1 ÿ1 1 ÿ1 ÿ1 ÿ1 1 1 ÿ1 ÿ1 1 1 1 1 1 0.321 0.6136 1 ÿ1 1 ÿ1 1 ÿ1 1 ÿ1 ÿ1 1 ÿ1 1 1 1 1 0.301 0.6257 1 ÿ1 1 1 ÿ1 ÿ1 ÿ1 1 1 ÿ1 ÿ1 1 1 1 1 0.387 0.5878 1 ÿ1 1 1 1 ÿ1 ÿ1 ÿ1 1 1 1 1 1 1 1 0.360 0.6089 1 1 ÿ1 ÿ1 ÿ1 ÿ1 ÿ1 ÿ1 1 1 1 1 1 1 1 1.043 0.20110 1 1 ÿ1 ÿ1 1 ÿ1 ÿ1 1 1 ÿ1 ÿ1 1 1 1 1 0.883 0.23111 1 1 ÿ1 1 ÿ1 ÿ2 1 ÿ1 1 1 ÿ1 1 1 1 1 1.109 0.18112 1 1 ÿ1 1 1 ÿ1 1 1 ÿ1 ÿ1 1 1 1 1 1 0.950 0.19513 1 1 1 ÿ1 ÿ1 1 ÿ1 ÿ1 ÿ1 ÿ1 1 1 1 1 1 0.632 0.47114 1 1 1 ÿ1 1 1 ÿ1 1 ÿ1 1 ÿ1 1 1 1 1 0.611 0.46515 1 1 1 1 ÿ 1 1 ÿ1 1 ÿ1 ÿ1 1 1 1 1 0.721 0.38916 1 1 1 1 ÿ1 1 1 1 1 1 1 1 1 1 1 0.703 0.37217 1 ÿ2 0 0 0 0 0 0 0 0 0 4 0 0 0 0.38 0.60218 1 2 0 0 0 0 0 0 0 0 0 4 0 0 0 0.98 0.21419 1 0 ÿ2 0 0 0 0 0 0 0 0 0 4 0 0 0.88 0.28920 1 0 2 0 0 0 0 0 0 0 0 0 4 0 0 0.336 0.6221 1 0 0 ÿ2 0 0 0 0 0 0 0 0 0 4 0 0.321 0.65122 1 0 0 2 0 0 0 0 0 0 0 0 0 4 0 0.613 0.21123 1 0 0 0 ÿ2 0 0 0 0 0 0 0 0 0 4 0.35 0.61524 1 0 0 0 2 0 0 0 0 0 0 0 0 0 4 0.33 0.62625 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.558 0.47126 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.549 0.46927 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.63 0.45828 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.661 0.47129 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.583 0.42330 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.559 0.49831 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.513 0.514

C.R. Chen, H.S. Ramaswamy / Food Research International 32 (1999) 319±325 321

the other two starch solutions at the same shear rate.Tapioca starch solutions thus had much higher viscositythan the other two starch solutions which is one of thereasons for selecting tapioca sample in this study.Typical ¯ow curves for tapioca starch suspensions

under di�erent test conditions are shown in Fig. 2. Acomparison of di�erent rheological models as shown inTable 2 for describing the ¯ow behavior of starch sus-pensions under typical conditions indicated slightly bet-ter R2 of 0.97±0.99 with the power law model. Thepower law model generally gave a higher R2 and showeda better ®t for data points under most other circum-stances as well. Shear rate corrections to the experi-mental data were applied, for a range of test conditions,as outlined in Ste�e (1992) and the power law coe�-cients were recalculated. The recalculated values of mand n did not di�er much from those calculated fromthe software (most were within 2% of the software cal-culated value while in one case it was 7% higher).Hence, the software calculated values were retained andused for all subsequent analysis in this study.

3.2. Regression models of rheological parameters (m, n)

From a practical stand-point, it will be useful todescribe the e�ects of temperature, concentration, pHand cook time by one composite model. In literature,the Arrhenius model has been frequently used to model

the e�ects of temperature, while the e�ect of concentra-tion has been described by either an exponential or apower relationship (Ramaswamy & Basak, 1991).However, Abdelrahim et al. (1995) found the Arrheniusmodel to be less desirable for describing the temperaturedependence of power law parameters for starch espe-cially at the low concentration levels because the asso-ciated coe�cients of determination were generally lessthan 0.7. The alternative is a Turian approach takinginto account the e�ects of both temperature and con-centration on consistency coe�cient and ¯ow behaviorindex (Ramaswamy & Basak, 1991). However, none ofthe above studies take into account the e�ects of pHand cook time on rheological properties. In this study,m and n were related to temperature, concentration, pHand cook time by a multiple regression analysis. Thefollowing predictive equations involving temperature,concentration, pH and cook time were developed usinga second order response methodology:

m � 0:579� 0:195X1ÿ 0:118X2� 0:051X3

ÿ 0:02X4� 0:047X12 ÿ 0:027X22 ÿ 0:011X32

ÿ 0:046X42 ÿ 0:055X1�X2ÿ 0:0006X1�X3ÿ 0:0129X1�X4ÿ 0:0015X2�X3� 0:021X2�X4ÿ 0:001X3�X4

�R2 � 0:95;Sy;x � 0:0693�

�6�

Table 4

Analysis of variance for regression models

Source of variance DF m (Pasn) n

SS MS F Ratio SS MS F Ratio

Total 30 1.613 0.669

Model 14 1.530 0.1093 21.06a 0.609 0.0435 8.38a

Linear

b1 1 0.913 0.913 175.98a 0.310 0.310 59.75a

b2 1 0.336 0.336 64.76a 0.162 0.162 31.23a

b3 1 0.062 0.062 11.95a 0.060 0.060 11.56a

b4 1 0.009 0.009 1.73c 0.0 0.0 0.0

Quadratic

b11 1 0.064 0.064 12.336a 0.016 0.016 3.084c

b22 1 0.021 0.021 4.048c 0.003 0.003 0.579

b33 1 0.004 0.004 0.77 0.008 0.008 1.540c

b44 1 0.062 0.062 11.951a 0.035 0.035 6.746b

Interaction

b12 1 0.049 0.049 9.455a 0.013 0.013 2.50c

b13 1 0.0 0.0 0.0 0.001 0.001 0.193

b14 1 0.0003 0.003 0.57 0.0 0.0 0.0

b23 1 0.0 0.0 0.0 0.001 0.001 0.193

b24 1 0.007 0.007 1.349 0.0 0.0 0.0

b34 1 0.0 0.0 0.0 0.0 0.0 0.0

Error 16 0.083 0.0048 0.06 0.0038

Lake of ®t 10 0.075 0.0075 5.625 0.054 0.0054 5.40

Experimental 6 0.008 0.00013 0.006 0.001

a p40.01.b p40.005.c p40.1.


n � 0:455ÿ 0:114X1� 0:082ÿ 0:05X3� 0:02X4

ÿ 0:023X12 ÿ 0:011X22 ÿ 0:017X3 � 0:035X42

� 0:029X1�X2ÿ 0:01X1�X3ÿ 0:001X1�X4

ÿ 0:006X2�X3ÿ 0:004X2�X4ÿ 0:002X3�X4

�R2 � 0:91;Sy;x � 0:0616�

�7�

The design matrix and calculated results of rheologicalparameters (m; n) are given in Table 3. The analysis ofvariance results (Table 4) showed that the lack of ®t wasnot signi®cant for m and n (p > 0:05), and regressionmodels were signi®cant for m and n (p > 0:05). In addi-tion, the standard residual errors for m and n regressionequations were 0.0693 and 0.0616, respectively, this shouldbe accepted in practical application. Hence, it indicatedthat the ®tted model was adequate. However, it was easilyfound that the e�ects of some regression coe�cients on mand n were not signi®cant (p>0.05). In order to improvethe accuracy of the models, the non-signi®cant terms wereremoved and Eqs. (6) and (7) were simpli®ed as follows:

m � 0:579� 0:195X1ÿ 0:118X2� 0:051X3ÿ 0:02X4

� 0:047X12 � 0:027X22 ÿ 0:046X42 ÿ 0:055X1�X2

�R2 � 0:94;Sy;x � 0:0664��8�

n � 0:455ÿ 0:114X1� 0:082X2ÿ 0:05X3

ÿ 0:023X12 ÿ 0:017X32 � 0:035X42 � 0:029X1�X2

�R2 � 0:91;Sy;x � 0:0532��9�

And from Eq. (5) (Table 2), the ®nal form of therelationships were obtained as follows:

m � ÿ0:183� 0:195Cÿ 0:0079T� 0:051pHÿ 0:0028

t� 0:047�Cÿ 4�2 � 1:2�10ÿ 4�Tÿ 50�2 ÿ 8:4�10ÿ 4

�tÿ 20�2 ÿ 0:0037�Cÿ 4��Tÿ 50��R2 � 0:94;Sy;x � 0:0664�

�10�

n � 1:057ÿ 0:114C� 0:055Tÿ 0:05pHÿ 0:023�Cÿ 4�2ÿ 0:017�pHÿ 6�2 � 0:035�tÿ 20�2ÿ 0:002�Tÿ 50��Cÿ 4��R2 � 0:91;Sy;x � 0:0532�

�11�3.3. E�ects of concentration and temperature on m and n

Fig. 3 indicates the e�ects of concentration and tem-perature on consistency coe�cient m and ¯ow behavior

index n (at pH=6, t=20 min). It is clear from the ®gurethat m increased with the concentration and decreasedwith temperature, and the e�ect was opposite with n.But the extent of increase or decrease at di�erent tem-peratures or concentrations were di�erent because ofthe interaction between temperature and concentration(Table 4).

3.4. E�ects of pH and cook time on m and n

Fig. 4 indicates the e�ects of pH and cook time onconsistency coe�cient m and ¯ow behavior index n (atC=4, T=50�C). It can be easily seen that the e�ect ofpH value on m or n is linear, and cook time non-linear.Moreover, the highest m and the lowest n existed withinthe experimental range. To obtain this value, we could

Fig. 3. E�ects of concentration and temperature on consistency coef-

®ciency, m, and ¯ow behavior index, n, of tapioca starch solutions.


di�erentiate Eqs. (10) and (11) with t and equate themto zero:

@m

@t� ÿ0:0028ÿ 16:8�10ÿ4�tÿ 20� � 0; t � 18:3�min�

@n

@t� 0:07�tÿ 20� � 0; t � 20�min�

Hence, the optimum cook times were 18 min to getthe highest value of consistency coe�cient and 20 minto get the lowest value of ¯ow behavior index, respec-tively.

3.5. Comparison of the predicted m and n values withexperimental values

The pooled data for experimental m and n vs thosepredicted by Eqs (10) and (11) are shown in Fig. 5. Theregression coe�cient R2 was 0.96 and 0.94, respectively.The ®gures indicated that there was good agreementbetween experimental values and theory values of m andn predicted by models [Eqs. (10) and (11)].

4. Conclusions

The study indicated that the ¯ow behavior of tapiocastarch solutions was adequately described by the power-law model. The second order response models welldescribed the e�ects of concentration, temperature, pHvalue and cook time on the associated rheologicalproperties (m and n). There existed signi®cant interac-tion between concentration and temperature. The high-est consistency coe�cient, m, was obtained after an 18min cook time and the lowest ¯ow behavior index, n,was obtained after a 20 min cook.Fig. 4. E�ects of pH and cook time on consistency coe�ciency, m,

and ¯ow behavior index, n, of tapioca starch solutions.

Fig. 5. Plots for experimental vs calculated consistency coe�ciency, m, and ¯ow behavior index, n, of tapioca starch solutions.


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Rheology of Tapioca Starch