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Rheology of tapioca starch
Food Research International 32 (1999) 319±325
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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 to four factors: temperature, 20±80 C; concentration, 2±6%; pH, 4±8 and cooking time, 5±35 min. All test solutions showed powerlaw ¯ow behavior. A second order composite design was used to investigate the eects of concentration, temperature, pH value and cook time on rheological property parameters (consistency coecient, m, and ¯ow behavior index, n), and develop second order multiple 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 are dependent on the ¯uid viscosity and density. Calculation of thermal treatment times for processing of liquid foods containing particulates is complex because the residence time distribution (RTD) of particulates and carrier ¯uid are in¯uenced by concentration and the type of carrier ¯uid as well as other process parameters (time, temperature, pressure, and the system con®guration). Data on rheological characteristics, relative velocity between ¯uid and particles and ¯uid to particle heat transfer coecients are needed for optimizing the heat exchanger and holding tube designs in aseptic processing of liquid foods containing particulates (Dail & Stee, 1990a,b; Ramaswamy, Abdelrahin, Simpson & Smith, 1995). Starches are commonly added to popular foods such as soups and sauces to increase their consistency and improve mouth-feel characteristics. The thickening activity of starches results from the swelling of starch granules occurring at gelatinization temperatures (Self, Wilkin, Morley & Bailey, 1990). Recently, modi®ed cross-linked starches * Corresponding author. Tel.: +1-514-398-7919; fax:+1-514-3987977. E-mail address [email protected] (H.S. Ramaswamy) 1 Visiting Professor, Department of food science, Zhejiand University, Hangzhou, People's Republic of China.
have been used to simulate carrier ¯uids in aseptic processing of liquid foods containing particulates (Abdelrahim, Ramaswamy & Van de Voort, 1995; Harrod, 1989a,b,c). Tapioca starch is widely used in delicately ¯avored puddings, pastry ®llings and baby food products (Whistler, Bemiller & Paschall, 1984). Of non-cereal starches, tapioca has ranked ®rst in order of importance in North America (Kerr, 1950). There have been many research reports on the rheological properties of starch solutions (Bhattacharya & Bhat, 1997; Bhattacharya & Bhattacharya, 1994, 1996; Biliaderis, 1991; Dail & Stee, 1990a,b; Harrod, 1989a,b,c; Ramaswamy, Busak, Abbatemarco & Sablani, 1995; Sandhya & Bhattacharya, 1995; Taylor, 1979), but no published information is available on the rheological modeling of tapioca starch solutions. Further, the majority of reported experimental data on rheological properties focuses on the eects of temperature and concentration, and little on those of pH value and cook time. The objective of this work was, therefore, to study the eect of concentration (2±6%), temperature (20±80 C), pH (4±8) and cook time (5±35 min) on the rheological properties of tapioca starch solutions and develop predicting models for the rheological parameters. 2. Materials and methods Tapioca starch was obtained from a local market (modi®ed waxy starch, powdered form, produced by Yat Loong Company, Hong Kong, China, packed and
0963-9969/99/$20.00 # 1999 Published by Elsevier Science Ltd. All rights reserved. PII: S0963-9969(99)00090-3
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C.R. Chen, H.S. Ramaswamy / Food Research International 32 (1999) 319±325
distributed in Canada). The pH value of water was initially adjusted by adding acid (citric) or NaOH. Appropriate amounts of starch and water were mixed thoroughly and brought to boiling in a steam-jacketed kettle. The mixture was then allowed to slowly simmer at 100 C for selected time intervals (cook time from 5 to 35 min) under atmospheric conditions. The solution was covered during cooking to minimize loss of moisture during cooking. The lost moisture (about 5±10% by weight) was added back at the end to maintain the concentration level. Rheological measurements (shear rate±shear stress data) were made using a rotational viscometer (Haake Model RV20; Haake Mess-Technik, Karlsrulhe, Germany), equipped with an M-05 OSC measuring head and MVI (radius of the rotor, Rb , 20.04 mm; height, h, 60 mm, radius of the cylindrical cup, Rc , 21 mm) rotor assembly interfaced to a microcomputer for control and data acquisition. The sample compartment was kept at a constant temperature 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 sheared at a programmed rate linearly increasing from 0 to 200 sÿ1 in 10 min. Shear stress±shear rate data were collected continuously at 12 s intervals throughout the test. Flow curves (rheograms) were evaluated by the instrument operating software (Haake RV20 version 2.3) using the following models. 1: Power law model : m n
X2 T ÿ 50=15;
X3 P ÿ 6;
X4 t ÿ 20=7:5
5
Table 1 Experimental factors and levels Factor
Concentration temperature pH Cook time C (%) T ( C) value P t (min)
Coded ÿ2 variable (Xi) ÿ1 0 1 2
2
20
4
5
3 4 5 6
35 50 65 80
5 6 7 8
12.5 20 27.5 35
1
where is the shear stress (Pa), is the shear rate (sÿ1), m is the consistency coecient (Pasn), and n is the ¯ow behavior index (dimensionless). 2: HerschelÿBulkley model : 0 m n
X1 C ÿ 4;
Fig. 1. Comparison of ¯ow curves of three starch solutions: tapioca, maize and potato at a 4% concentration level.
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 Casson viscosity, respectively. A shear analysis test as recommended in Stee (1992) was used to assess the validity of using the power-law model for test data. A second order central composite design (Gacula & Singh, 1984; Piggott,1986) was used in order to develop predictive models of rheological parameters. The experimental factors and levels are shown in Table 1. The ®tted response model is: Y b0 bi Xi bii X2i bij Xi Xj i 1ÿ4;
j 1ÿ4;
i 6 j
4
The relationships between coded variables and practical variables(Table 1) were as follows:
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.
C.R. Chen, H.S. Ramaswamy / Food Research International 32 (1999) 319±325
3. Results and discussion
321
The curves for sweet potato and tapioca were experimentally obtained at a 4% concentration after a 20 min cook time. The maize starch data are from Ramaswamy, Basak et al. (1995) also at a 4% starch concentration level. From Fig. 1, it was found that the shear stress for tapioca starch solution was much higher than those for
3.1. Rheological characterization of tapioca starch Fig. 1 shows the ¯ow curves for tapioca, sweet potato and maize starch solutions under the same conditions.
Table 2 Comparison of dierent models for the rheology of tapioca starch solutions at dierent temperatures (T), concentrations (C), pH values and cook times (t)a Typical conditions
Model
m k1
n
T=10 C, C=4%, pH=7, t=20 min
Powder lawb Herschel±Bulkleyc Cassond Power lawb Hersche±Bulkleyc Cassond Power lawb Herschel±Bulkleyc Cassond Power lawb Herschel±Bulkleyc Cassond
1.02 1.08 0.97 0.87 0.86 0.84 0.64 0.639 0.621 0.168 0.167 0.159
0.417 0.413 0.843 0.691 0.684 1.401 0.602 0.701 1.422 0.778 0.780 0.1692
T=20 C, C=4%, pH=7, t=20 min T=20 C, C=4%, pH=7, t=40 min T=20 C, C=4%, pH=7, t=20 min
a b c d
R2
o ko
0.98 0.95 0.96 0.99 0.97 0.97 0.98 0.96 0.98 0.97 0.96 0.97
0.95 0.92 0.49 0.42 0.41 0.38 0.10 0.19
The number of data points regressed is 50. Power law model: m n . Herschel±Bulkely model: 0 m n . Casson model; 0:5 k0 0:5 k1 n 0:5 .
Table 3 Second order design matrix and calculation results of rheology parameters: consistency coecient, 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 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
ÿ1 ÿ1 ÿ1 ÿ1 ÿ1 ÿ1 ÿ1 ÿ1 1 1 1 1 1 1 1 1 ÿ2 2 0 0 0 0 0 0 0 0 0 0 0 0 0
ÿ1 ÿ1 ÿ1 ÿ1 1 1 1 1 ÿ1 ÿ1 ÿ1 ÿ1 1 1 1 1 0 0 ÿ2 2 0 0 0 0 0 0 0 0 0 0 0
ÿ1 ÿ1 1 1 ÿ1 ÿ1 1 1 ÿ1 ÿ1 1 1 ÿ1 ÿ1 1 1 0 0 0 0 ÿ2 2 0 0 0 0 0 0 0 0 0
ÿ1 1 ÿ1 1 ÿ1 1 ÿ1 1 ÿ1 1 ÿ1 1 ÿ1 1 ÿ ÿ1 0 0 0 0 0 0 ÿ2 2 0 0 0 0 0 0 0
1 1 1 1 ÿ1 ÿ1 ÿ1 ÿ1 ÿ1 ÿ1 ÿ2 ÿ1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 ÿ1 ÿ1 1 1 ÿ1 ÿ1 ÿ1 ÿ1 1 1 ÿ1 ÿ1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 ÿ1 1 ÿ1 1 ÿ1 1 ÿ1 ÿ1 1 ÿ1 1 ÿ1 1 ÿ1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 ÿ1 ÿ1 ÿ1 ÿ1 1 1 1 1 1 ÿ1 ÿ1 ÿ1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 ÿ1 1 ÿ1 ÿ1 1 ÿ1 1 1 ÿ1 1 ÿ1 ÿ1 1 ÿ1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 ÿ1 ÿ1 1 1 ÿ1 ÿ1 1 1 ÿ1 ÿ1 1 1 ÿ1 ÿ1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 4 4 0 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 4 4 0 0 0 0 0 0 0
0.423 0.38 0.531 0.470 0.321 0.301 0.387 0.360 1.043 0.883 1.109 0.950 0.632 0.611 0.721 0.703 0.38 0.98 0.88 0.336 0.321 0.613 0.35 0.33 0.558 0.549 0.63 0.661 0.583 0.559 0.513
0.512 0.522 0.49 0.495 0.613 0.625 0.587 0.608 0.201 0.231 0.181 0.195 0.471 0.465 0.389 0.372 0.602 0.214 0.289 0.62 0.651 0.211 0.615 0.626 0.471 0.469 0.458 0.471 0.423 0.498 0.514
322
C.R. Chen, H.S. Ramaswamy / Food Research International 32 (1999) 319±325
the other two starch solutions at the same shear rate. Tapioca starch solutions thus had much higher viscosity than the other two starch solutions which is one of the reasons for selecting tapioca sample in this study. Typical ¯ow curves for tapioca starch suspensions under dierent test conditions are shown in Fig. 2. A comparison of dierent rheological models as shown in Table 2 for describing the ¯ow behavior of starch suspensions under typical conditions indicated slightly better R2 of 0.97±0.99 with the power law model. The power law model generally gave a higher R2 and showed a better ®t for data points under most other circumstances as well. Shear rate corrections to the experimental data were applied, for a range of test conditions, as outlined in Stee (1992) and the power law coecients were recalculated. The recalculated values of m and n did not dier much from those calculated from the software (most were within 2% of the software calculated value while in one case it was 7% higher). Hence, the software calculated values were retained and used 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 to describe the eects of temperature, concentration, pH and cook time by one composite model. In literature, the Arrhenius model has been frequently used to model
the eects of temperature, while the eect of concentration has been described by either an exponential or a power relationship (Ramaswamy & Basak, 1991). However, Abdelrahim et al. (1995) found the Arrhenius model to be less desirable for describing the temperature dependence of power law parameters for starch especially at the low concentration levels because the associated coecients of determination were generally less than 0.7. The alternative is a Turian approach taking into account the eects of both temperature and concentration on consistency coecient and ¯ow behavior index (Ramaswamy & Basak, 1991). However, none of the above studies take into account the eects of pH and cook time on rheological properties. In this study, m and n were related to temperature, concentration, pH and cook time by a multiple regression analysis. The following predictive equations involving temperature, concentration, pH and cook time were developed using a second order response methodology: m 0:579 0:195X1 ÿ 0:118X2 0:051X3 ÿ 0:02X4 0:047X12 ÿ 0:027X22 ÿ 0:011X32 ÿ 0:046X42 ÿ 0:055X1 X2 ÿ 0:0006X1 X3 ÿ 0:0129X1 X4 ÿ 0:0015X2 X3 0:021X2 X4 ÿ 0:001X3 X4
6
R2 0:95; Sy;x 0:0693
Table 4 Analysis of variance for regression models Source of variance
DF
m (Pasn)
n
SS
MS
F Ratio
SS
MS
F Ratio
Total Model
30 14
1.613 1.530
0.1093
21.06a
0.669 0.609
0.0435
8.38a
Linear b1 b2 b3 b4
1 1 1 1
0.913 0.336 0.062 0.009
0.913 0.336 0.062 0.009
175.98a 64.76a 11.95a 1.73c
0.310 0.162 0.060 0.0
0.310 0.162 0.060 0.0
59.75a 31.23a 11.56a 0.0
Quadratic b11 b22 b33 b44
1 1 1 1
0.064 0.021 0.004 0.062
0.064 0.021 0.004 0.062
12.336a 4.048c 0.77 11.951a
0.016 0.003 0.008 0.035
0.016 0.003 0.008 0.035
3.084c 0.579 1.540c 6.746b
Interaction b12 b13 b14 b23 b24 b34
1 1 1 1 1 1
0.049 0.0 0.0003 0.0 0.007 0.0
0.049 0.0 0.003 0.0 0.007 0.0
9.455a 0.0 0.57 0.0 1.349 0.0
0.013 0.001 0.0 0.001 0.0 0.0
0.013 0.001 0.0 0.001 0.0 0.0
2.50c 0.193 0.0 0.193 0.0 0.0
16 10 6
0.083 0.075 0.008
0.0048 0.0075 0.00013
5.625
0.06 0.054 0.006
0.0038 0.0054 0.001
5.40
Error Lake of ®t Experimental a b c
p40.01. p40.005. p40.1.
C.R. Chen, H.S. Ramaswamy / Food Research International 32 (1999) 319±325
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n 0:455 ÿ 0:114X1 0:082 ÿ 0:05X3 0:02X4 ÿ 0:023X12 ÿ 0:011X22 ÿ 0:017X3 0:035X42 0:029X1 X2 ÿ 0:01X1 X3 ÿ 0:001X1 X4
7
ÿ 0:006X2 X3 ÿ 0:004X2 X4 ÿ 0:002X3 X4 R2 0:91; Sy;x 0:0616 The design matrix and calculated results of rheological parameters (m; n) are given in Table 3. The analysis of variance results (Table 4) showed that the lack of ®t was not signi®cant for m and n (p > 0:05), and regression models were signi®cant for m and n (p > 0:05). In addition, the standard residual errors for m and n regression equations were 0.0693 and 0.0616, respectively, this should be accepted in practical application. Hence, it indicated that the ®tted model was adequate. However, it was easily found that the eects of some regression coecients on m and n were not signi®cant (p>0.05). In order to improve the accuracy of the models, the non-signi®cant terms were removed and Eqs. (6) and (7) were simpli®ed as follows: m 0:579 0:195X1 ÿ 0:118X2 0:051X3 ÿ 0:02X4 0:047X12 0:027X22 ÿ 0:046X42 ÿ 0:055X1 X2 R2 0:94; Sy;x 0:0664 8 n 0:455 ÿ 0:114X1 0:082X2 ÿ 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 the relationships were obtained as follows: m ÿ0:183 0:195C ÿ 0:0079T 0:051pH ÿ 0:0028
Fig. 3. Eects of concentration and temperature on consistency coef®ciency, m, and ¯ow behavior index, n, of tapioca starch solutions.
t 0:047 C ÿ 42 1:2 10 ÿ 4 T ÿ 502 ÿ 8:4 10 ÿ 4 t ÿ 202 ÿ 0:0037 C ÿ 4 T ÿ 50 2
R 0:94; Sy;x 0:0664 10 n 1:057 ÿ 0:114C 0:055T ÿ 0:05pH ÿ 0:023 C ÿ 42 ÿ 0:017 pH ÿ 62 0:035 t ÿ 202 ÿ 0:002 T ÿ 50 C ÿ 4
index n (at pH=6, t=20 min). It is clear from the ®gure that m increased with the concentration and decreased with temperature, and the eect was opposite with n. But the extent of increase or decrease at dierent temperatures or concentrations were dierent because of the interaction between temperature and concentration (Table 4). 3.4. Eects of pH and cook time on m and n
R2 0:91; Sy;x 0:0532 11 3.3. Eects of concentration and temperature on m and n Fig. 3 indicates the eects of concentration and temperature on consistency coecient m and ¯ow behavior
Fig. 4 indicates the eects of pH and cook time on consistency coecient m and ¯ow behavior index n (at C=4, T=50 C). It can be easily seen that the eect of pH value on m or n is linear, and cook time non-linear. Moreover, the highest m and the lowest n existed within the experimental range. To obtain this value, we could
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C.R. Chen, H.S. Ramaswamy / Food Research International 32 (1999) 319±325
dierentiate Eqs. (10) and (11) with t and equate them to zero: @m ÿ0:0028 ÿ 16:8 10ÿ4 t ÿ 20 0; @t @n 0:07 t ÿ 20 0; @t
t 18:3 min
t 20 min
Hence, the optimum cook times were 18 min to get the highest value of consistency coecient and 20 min to get the lowest value of ¯ow behavior index, respectively. 3.5. Comparison of the predicted m and n values with experimental values The pooled data for experimental m and n vs those predicted by Eqs (10) and (11) are shown in Fig. 5. The regression coecient R2 was 0.96 and 0.94, respectively. The ®gures indicated that there was good agreement between experimental values and theory values of m and n predicted by models [Eqs. (10) and (11)]. 4. Conclusions
Fig. 4. Eects of pH and cook time on consistency coeciency, m, and ¯ow behavior index, n, of tapioca starch solutions.
The study indicated that the ¯ow behavior of tapioca starch solutions was adequately described by the powerlaw model. The second order response models well described the eects of concentration, temperature, pH value and cook time on the associated rheological properties (m and n). There existed signi®cant interaction between concentration and temperature. The highest consistency coecient, m, was obtained after an 18 min cook time and the lowest ¯ow behavior index, n, was obtained after a 20 min cook.
Fig. 5. Plots for experimental vs calculated consistency coeciency, m, and ¯ow behavior index, n, of tapioca starch solutions.
C.R. Chen, H.S. Ramaswamy / Food Research International 32 (1999) 319±325
References Abedlrahim, K. A., Ramaswamy, H. S., & Van de Voort, F. R. (1995). Rheological properties of starch solutions under aseptic processing temperatures. Food Research International, 28, 473±480. Bhattacharya, S., & Bhattacharya, S. (1994). Flow behavior of cooked maize ¯our suspensions and applicability of mathematical models. Journal of Food Process Engineering, 17, 263±278. Bhattacharya, S., & Bhattacharya, S. (1996). Rheology of cooked debranned maize ¯our suspension. Journal of Food Engineering, 27, 97±105. Bhattacharya, S., & Bhat, K. K. (1997). Steady shear rheology of riceblackgram suspensions and suitability of rheological models. Journal of Food Engineering, 32, 241±250. Biliaderis, C. G. (1991). Structure and interactions of starch with food constituents. Canadian Journal of Physiology and Pharmacology, 69, 60±78. Dail, R. V., & Stee, J. F. (1990a). Rhelolgical characterization of cross-linked waxy maize starch solutions under low acid aseptic processing conditions using tube viscometry techniques. Journal of Food Science, 55, 1660±1665. Dail, R. V., & Stee, J. F. (1990b). Dilatancy in starch solutions under low acid aseptic processing conditions. Journal of Food Science, 55, 1764±1765. Gacula, M. C., & Singh, J. et al. (1984). Statistical Methods in Food and Consumer Research. NY: Academic Press, Inc. Harrod, M. (1989). Modelling of ¯ow properties of starch pastes prepared by dierent procedures. Journal of Food Process Engineering, 11, 257±275. Harrod, M. (1989b). Apparent concentration: a method to predict the
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¯ow properties of viscous foods for process applications. Journal of Food Process Engineering, 11, 277±296. Harrod, M. (1989c). Time-dependent ¯ow behavior of starch pastes, with food process applications. Journal of Food Process Engineering, 11, 297±309. Kerr, R. W. (1950). Chemistry and industry of starch. New York: Academic Press Inc. Piggott, J. R. (1986). Statistical procedures in food research. London and New York: Elsevier Applied Science. Ramaswamy, H. S., Abdelrahim, K. A., Simpson, B. K., & Smith, J. B. (1995a). Residence time distribution (RTD) in aseptic processing of particulate foods: a review. Food Research International, 28, 291±310. Ramaswamy, H. S., Basak, S., Abbatemarco, C., & Sablani, S.S (1995b). Rheological properties of starch as in¯uenced by thermal processing in an agitating retort. Journal of Food Engineering, 25(3), 441±454. Ramaswamy, H. S., & Basak, S. (1991). Rheology of stirred yogurt. J. Texture Studies, 22, 231±284. Sandhya, M. R., & Bhattacharya, S. (1995). Rheology of rice-¯our pastes: relationship of paste breakdown to rice quality, and a simpli®ed Brabender viscograph test. Journal of Texture Studies, 26(5), 587±598. Self, K. P., Wilkin, T. J., Morley, M. J., & Bailey, C. (1990). Rheological and heat transfer characteristics of starch water suspensions during cooking. Journal of Food Engineering, 11, 291±316. Stee, J. F. (1992). Rheological Methods in Food Process Engineering. East Lancing MI: Freeman Press. Taylor, N. W. (1979). Rheology and water swelling of carboxymethyl starch gels (Corn). Journal of Applied Ploymer Science, 24(9), 2031± 2040. Whistler, R. L., Bemiller, J. N. & Paschall, E. F. (1984). Starch: chemistry and technology. Academic Press, Inc.
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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 to four factors: temperature, 20±80 C; concentration, 2±6%; pH, 4±8 and cooking time, 5±35 min. All test solutions showed powerlaw ¯ow behavior. A second order composite design was used to investigate the eects of concentration, temperature, pH value and cook time on rheological property parameters (consistency coecient, m, and ¯ow behavior index, n), and develop second order multiple 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 are dependent on the ¯uid viscosity and density. Calculation of thermal treatment times for processing of liquid foods containing particulates is complex because the residence time distribution (RTD) of particulates and carrier ¯uid are in¯uenced by concentration and the type of carrier ¯uid as well as other process parameters (time, temperature, pressure, and the system con®guration). Data on rheological characteristics, relative velocity between ¯uid and particles and ¯uid to particle heat transfer coecients are needed for optimizing the heat exchanger and holding tube designs in aseptic processing of liquid foods containing particulates (Dail & Stee, 1990a,b; Ramaswamy, Abdelrahin, Simpson & Smith, 1995). Starches are commonly added to popular foods such as soups and sauces to increase their consistency and improve mouth-feel characteristics. The thickening activity of starches results from the swelling of starch granules occurring at gelatinization temperatures (Self, Wilkin, Morley & Bailey, 1990). Recently, modi®ed cross-linked starches * Corresponding author. Tel.: +1-514-398-7919; fax:+1-514-3987977. E-mail address [email protected] (H.S. Ramaswamy) 1 Visiting Professor, Department of food science, Zhejiand University, Hangzhou, People's Republic of China.
have been used to simulate carrier ¯uids in aseptic processing of liquid foods containing particulates (Abdelrahim, Ramaswamy & Van de Voort, 1995; Harrod, 1989a,b,c). Tapioca starch is widely used in delicately ¯avored puddings, pastry ®llings and baby food products (Whistler, Bemiller & Paschall, 1984). Of non-cereal starches, tapioca has ranked ®rst in order of importance in North America (Kerr, 1950). There have been many research reports on the rheological properties of starch solutions (Bhattacharya & Bhat, 1997; Bhattacharya & Bhattacharya, 1994, 1996; Biliaderis, 1991; Dail & Stee, 1990a,b; Harrod, 1989a,b,c; Ramaswamy, Busak, Abbatemarco & Sablani, 1995; Sandhya & Bhattacharya, 1995; Taylor, 1979), but no published information is available on the rheological modeling of tapioca starch solutions. Further, the majority of reported experimental data on rheological properties focuses on the eects of temperature and concentration, and little on those of pH value and cook time. The objective of this work was, therefore, to study the eect of concentration (2±6%), temperature (20±80 C), pH (4±8) and cook time (5±35 min) on the rheological properties of tapioca starch solutions and develop predicting models for the rheological parameters. 2. Materials and methods Tapioca starch was obtained from a local market (modi®ed waxy starch, powdered form, produced by Yat Loong Company, Hong Kong, China, packed and
0963-9969/99/$20.00 # 1999 Published by Elsevier Science Ltd. All rights reserved. PII: S0963-9969(99)00090-3
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C.R. Chen, H.S. Ramaswamy / Food Research International 32 (1999) 319±325
distributed in Canada). The pH value of water was initially adjusted by adding acid (citric) or NaOH. Appropriate amounts of starch and water were mixed thoroughly and brought to boiling in a steam-jacketed kettle. The mixture was then allowed to slowly simmer at 100 C for selected time intervals (cook time from 5 to 35 min) under atmospheric conditions. The solution was covered during cooking to minimize loss of moisture during cooking. The lost moisture (about 5±10% by weight) was added back at the end to maintain the concentration level. Rheological measurements (shear rate±shear stress data) were made using a rotational viscometer (Haake Model RV20; Haake Mess-Technik, Karlsrulhe, Germany), equipped with an M-05 OSC measuring head and MVI (radius of the rotor, Rb , 20.04 mm; height, h, 60 mm, radius of the cylindrical cup, Rc , 21 mm) rotor assembly interfaced to a microcomputer for control and data acquisition. The sample compartment was kept at a constant temperature 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 sheared at a programmed rate linearly increasing from 0 to 200 sÿ1 in 10 min. Shear stress±shear rate data were collected continuously at 12 s intervals throughout the test. Flow curves (rheograms) were evaluated by the instrument operating software (Haake RV20 version 2.3) using the following models. 1: Power law model : m n
X2 T ÿ 50=15;
X3 P ÿ 6;
X4 t ÿ 20=7:5
5
Table 1 Experimental factors and levels Factor
Concentration temperature pH Cook time C (%) T ( C) value P t (min)
Coded ÿ2 variable (Xi) ÿ1 0 1 2
2
20
4
5
3 4 5 6
35 50 65 80
5 6 7 8
12.5 20 27.5 35
1
where is the shear stress (Pa), is the shear rate (sÿ1), m is the consistency coecient (Pasn), and n is the ¯ow behavior index (dimensionless). 2: HerschelÿBulkley model : 0 m n
X1 C ÿ 4;
Fig. 1. Comparison of ¯ow curves of three starch solutions: tapioca, maize and potato at a 4% concentration level.
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 Casson viscosity, respectively. A shear analysis test as recommended in Stee (1992) was used to assess the validity of using the power-law model for test data. A second order central composite design (Gacula & Singh, 1984; Piggott,1986) was used in order to develop predictive models of rheological parameters. The experimental factors and levels are shown in Table 1. The ®tted response model is: Y b0 bi Xi bii X2i bij Xi Xj i 1ÿ4;
j 1ÿ4;
i 6 j
4
The relationships between coded variables and practical variables(Table 1) were as follows:
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.
C.R. Chen, H.S. Ramaswamy / Food Research International 32 (1999) 319±325
3. Results and discussion
321
The curves for sweet potato and tapioca were experimentally obtained at a 4% concentration after a 20 min cook time. The maize starch data are from Ramaswamy, Basak et al. (1995) also at a 4% starch concentration level. From Fig. 1, it was found that the shear stress for tapioca starch solution was much higher than those for
3.1. Rheological characterization of tapioca starch Fig. 1 shows the ¯ow curves for tapioca, sweet potato and maize starch solutions under the same conditions.
Table 2 Comparison of dierent models for the rheology of tapioca starch solutions at dierent temperatures (T), concentrations (C), pH values and cook times (t)a Typical conditions
Model
m k1
n
T=10 C, C=4%, pH=7, t=20 min
Powder lawb Herschel±Bulkleyc Cassond Power lawb Hersche±Bulkleyc Cassond Power lawb Herschel±Bulkleyc Cassond Power lawb Herschel±Bulkleyc Cassond
1.02 1.08 0.97 0.87 0.86 0.84 0.64 0.639 0.621 0.168 0.167 0.159
0.417 0.413 0.843 0.691 0.684 1.401 0.602 0.701 1.422 0.778 0.780 0.1692
T=20 C, C=4%, pH=7, t=20 min T=20 C, C=4%, pH=7, t=40 min T=20 C, C=4%, pH=7, t=20 min
a b c d
R2
o ko
0.98 0.95 0.96 0.99 0.97 0.97 0.98 0.96 0.98 0.97 0.96 0.97
0.95 0.92 0.49 0.42 0.41 0.38 0.10 0.19
The number of data points regressed is 50. Power law model: m n . Herschel±Bulkely model: 0 m n . Casson model; 0:5 k0 0:5 k1 n 0:5 .
Table 3 Second order design matrix and calculation results of rheology parameters: consistency coecient, 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 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
ÿ1 ÿ1 ÿ1 ÿ1 ÿ1 ÿ1 ÿ1 ÿ1 1 1 1 1 1 1 1 1 ÿ2 2 0 0 0 0 0 0 0 0 0 0 0 0 0
ÿ1 ÿ1 ÿ1 ÿ1 1 1 1 1 ÿ1 ÿ1 ÿ1 ÿ1 1 1 1 1 0 0 ÿ2 2 0 0 0 0 0 0 0 0 0 0 0
ÿ1 ÿ1 1 1 ÿ1 ÿ1 1 1 ÿ1 ÿ1 1 1 ÿ1 ÿ1 1 1 0 0 0 0 ÿ2 2 0 0 0 0 0 0 0 0 0
ÿ1 1 ÿ1 1 ÿ1 1 ÿ1 1 ÿ1 1 ÿ1 1 ÿ1 1 ÿ ÿ1 0 0 0 0 0 0 ÿ2 2 0 0 0 0 0 0 0
1 1 1 1 ÿ1 ÿ1 ÿ1 ÿ1 ÿ1 ÿ1 ÿ2 ÿ1 1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 ÿ1 ÿ1 1 1 ÿ1 ÿ1 ÿ1 ÿ1 1 1 ÿ1 ÿ1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 ÿ1 1 ÿ1 1 ÿ1 1 ÿ1 ÿ1 1 ÿ1 1 ÿ1 1 ÿ1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 ÿ1 ÿ1 ÿ1 ÿ1 1 1 1 1 1 ÿ1 ÿ1 ÿ1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 ÿ1 1 ÿ1 ÿ1 1 ÿ1 1 1 ÿ1 1 ÿ1 ÿ1 1 ÿ1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 ÿ1 ÿ1 1 1 ÿ1 ÿ1 1 1 ÿ1 ÿ1 1 1 ÿ1 ÿ1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 4 4 0 0 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 4 4 0 0 0 0 0 0 0 0 0
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 0 0 0 0 0 0 4 4 0 0 0 0 0 0 0
0.423 0.38 0.531 0.470 0.321 0.301 0.387 0.360 1.043 0.883 1.109 0.950 0.632 0.611 0.721 0.703 0.38 0.98 0.88 0.336 0.321 0.613 0.35 0.33 0.558 0.549 0.63 0.661 0.583 0.559 0.513
0.512 0.522 0.49 0.495 0.613 0.625 0.587 0.608 0.201 0.231 0.181 0.195 0.471 0.465 0.389 0.372 0.602 0.214 0.289 0.62 0.651 0.211 0.615 0.626 0.471 0.469 0.458 0.471 0.423 0.498 0.514
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C.R. Chen, H.S. Ramaswamy / Food Research International 32 (1999) 319±325
the other two starch solutions at the same shear rate. Tapioca starch solutions thus had much higher viscosity than the other two starch solutions which is one of the reasons for selecting tapioca sample in this study. Typical ¯ow curves for tapioca starch suspensions under dierent test conditions are shown in Fig. 2. A comparison of dierent rheological models as shown in Table 2 for describing the ¯ow behavior of starch suspensions under typical conditions indicated slightly better R2 of 0.97±0.99 with the power law model. The power law model generally gave a higher R2 and showed a better ®t for data points under most other circumstances as well. Shear rate corrections to the experimental data were applied, for a range of test conditions, as outlined in Stee (1992) and the power law coecients were recalculated. The recalculated values of m and n did not dier much from those calculated from the software (most were within 2% of the software calculated value while in one case it was 7% higher). Hence, the software calculated values were retained and used 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 to describe the eects of temperature, concentration, pH and cook time by one composite model. In literature, the Arrhenius model has been frequently used to model
the eects of temperature, while the eect of concentration has been described by either an exponential or a power relationship (Ramaswamy & Basak, 1991). However, Abdelrahim et al. (1995) found the Arrhenius model to be less desirable for describing the temperature dependence of power law parameters for starch especially at the low concentration levels because the associated coecients of determination were generally less than 0.7. The alternative is a Turian approach taking into account the eects of both temperature and concentration on consistency coecient and ¯ow behavior index (Ramaswamy & Basak, 1991). However, none of the above studies take into account the eects of pH and cook time on rheological properties. In this study, m and n were related to temperature, concentration, pH and cook time by a multiple regression analysis. The following predictive equations involving temperature, concentration, pH and cook time were developed using a second order response methodology: m 0:579 0:195X1 ÿ 0:118X2 0:051X3 ÿ 0:02X4 0:047X12 ÿ 0:027X22 ÿ 0:011X32 ÿ 0:046X42 ÿ 0:055X1 X2 ÿ 0:0006X1 X3 ÿ 0:0129X1 X4 ÿ 0:0015X2 X3 0:021X2 X4 ÿ 0:001X3 X4
6
R2 0:95; Sy;x 0:0693
Table 4 Analysis of variance for regression models Source of variance
DF
m (Pasn)
n
SS
MS
F Ratio
SS
MS
F Ratio
Total Model
30 14
1.613 1.530
0.1093
21.06a
0.669 0.609
0.0435
8.38a
Linear b1 b2 b3 b4
1 1 1 1
0.913 0.336 0.062 0.009
0.913 0.336 0.062 0.009
175.98a 64.76a 11.95a 1.73c
0.310 0.162 0.060 0.0
0.310 0.162 0.060 0.0
59.75a 31.23a 11.56a 0.0
Quadratic b11 b22 b33 b44
1 1 1 1
0.064 0.021 0.004 0.062
0.064 0.021 0.004 0.062
12.336a 4.048c 0.77 11.951a
0.016 0.003 0.008 0.035
0.016 0.003 0.008 0.035
3.084c 0.579 1.540c 6.746b
Interaction b12 b13 b14 b23 b24 b34
1 1 1 1 1 1
0.049 0.0 0.0003 0.0 0.007 0.0
0.049 0.0 0.003 0.0 0.007 0.0
9.455a 0.0 0.57 0.0 1.349 0.0
0.013 0.001 0.0 0.001 0.0 0.0
0.013 0.001 0.0 0.001 0.0 0.0
2.50c 0.193 0.0 0.193 0.0 0.0
16 10 6
0.083 0.075 0.008
0.0048 0.0075 0.00013
5.625
0.06 0.054 0.006
0.0038 0.0054 0.001
5.40
Error Lake of ®t Experimental a b c
p40.01. p40.005. p40.1.
C.R. Chen, H.S. Ramaswamy / Food Research International 32 (1999) 319±325
323
n 0:455 ÿ 0:114X1 0:082 ÿ 0:05X3 0:02X4 ÿ 0:023X12 ÿ 0:011X22 ÿ 0:017X3 0:035X42 0:029X1 X2 ÿ 0:01X1 X3 ÿ 0:001X1 X4
7
ÿ 0:006X2 X3 ÿ 0:004X2 X4 ÿ 0:002X3 X4 R2 0:91; Sy;x 0:0616 The design matrix and calculated results of rheological parameters (m; n) are given in Table 3. The analysis of variance results (Table 4) showed that the lack of ®t was not signi®cant for m and n (p > 0:05), and regression models were signi®cant for m and n (p > 0:05). In addition, the standard residual errors for m and n regression equations were 0.0693 and 0.0616, respectively, this should be accepted in practical application. Hence, it indicated that the ®tted model was adequate. However, it was easily found that the eects of some regression coecients on m and n were not signi®cant (p>0.05). In order to improve the accuracy of the models, the non-signi®cant terms were removed and Eqs. (6) and (7) were simpli®ed as follows: m 0:579 0:195X1 ÿ 0:118X2 0:051X3 ÿ 0:02X4 0:047X12 0:027X22 ÿ 0:046X42 ÿ 0:055X1 X2 R2 0:94; Sy;x 0:0664 8 n 0:455 ÿ 0:114X1 0:082X2 ÿ 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 the relationships were obtained as follows: m ÿ0:183 0:195C ÿ 0:0079T 0:051pH ÿ 0:0028
Fig. 3. Eects of concentration and temperature on consistency coef®ciency, m, and ¯ow behavior index, n, of tapioca starch solutions.
t 0:047 C ÿ 42 1:2 10 ÿ 4 T ÿ 502 ÿ 8:4 10 ÿ 4 t ÿ 202 ÿ 0:0037 C ÿ 4 T ÿ 50 2
R 0:94; Sy;x 0:0664 10 n 1:057 ÿ 0:114C 0:055T ÿ 0:05pH ÿ 0:023 C ÿ 42 ÿ 0:017 pH ÿ 62 0:035 t ÿ 202 ÿ 0:002 T ÿ 50 C ÿ 4
index n (at pH=6, t=20 min). It is clear from the ®gure that m increased with the concentration and decreased with temperature, and the eect was opposite with n. But the extent of increase or decrease at dierent temperatures or concentrations were dierent because of the interaction between temperature and concentration (Table 4). 3.4. Eects of pH and cook time on m and n
R2 0:91; Sy;x 0:0532 11 3.3. Eects of concentration and temperature on m and n Fig. 3 indicates the eects of concentration and temperature on consistency coecient m and ¯ow behavior
Fig. 4 indicates the eects of pH and cook time on consistency coecient m and ¯ow behavior index n (at C=4, T=50 C). It can be easily seen that the eect of pH value on m or n is linear, and cook time non-linear. Moreover, the highest m and the lowest n existed within the experimental range. To obtain this value, we could
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C.R. Chen, H.S. Ramaswamy / Food Research International 32 (1999) 319±325
dierentiate Eqs. (10) and (11) with t and equate them to zero: @m ÿ0:0028 ÿ 16:8 10ÿ4 t ÿ 20 0; @t @n 0:07 t ÿ 20 0; @t
t 18:3 min
t 20 min
Hence, the optimum cook times were 18 min to get the highest value of consistency coecient and 20 min to get the lowest value of ¯ow behavior index, respectively. 3.5. Comparison of the predicted m and n values with experimental values The pooled data for experimental m and n vs those predicted by Eqs (10) and (11) are shown in Fig. 5. The regression coecient R2 was 0.96 and 0.94, respectively. The ®gures indicated that there was good agreement between experimental values and theory values of m and n predicted by models [Eqs. (10) and (11)]. 4. Conclusions
Fig. 4. Eects of pH and cook time on consistency coeciency, m, and ¯ow behavior index, n, of tapioca starch solutions.
The study indicated that the ¯ow behavior of tapioca starch solutions was adequately described by the powerlaw model. The second order response models well described the eects of concentration, temperature, pH value and cook time on the associated rheological properties (m and n). There existed signi®cant interaction between concentration and temperature. The highest consistency coecient, m, was obtained after an 18 min cook time and the lowest ¯ow behavior index, n, was obtained after a 20 min cook.
Fig. 5. Plots for experimental vs calculated consistency coeciency, m, and ¯ow behavior index, n, of tapioca starch solutions.
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