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Research Note

Journal of Food Engineering 21(1996) 203-209 Copyright 0 1995 Elsevier Science Limited Printed in Great Britain. All rights reserved

0260-8774/96 $15.00 + 0.00 0260-8774(94)00092-l

Rheological Models for Xanthan Gum

Zhang Xuewu, Liu Xin, Gu Dexiang, Zhou MO Yonghong

Wei, Xie Tong &

Food Engineering Research Center, Zhongshan University, Guangzhou, China

(Received 2 May 19Y4; revised version received 8 November 1994; accepted 3 qecember 1994)

ABSTRACT

The rheological behaviour of xanthan gum was determined at various temperatures (20-100C) and concentrations (0.3-1.3%), and was found to be most adequately described by a power-law model. The effect of temperature on the viscosity followed an Arrhenius relationship, whereas the ef$ect of concentration followed an exponential relationship. A number of models to predict the viscosity as a function of shear rate, concentration and temperature are presented. The models developed had an excellent fit and would be useful for manufacture and applications of xanthan gum.

NOTATION

Al A2 Bt B2 B3 c E, Kl K2

K3

K4

Constant in eqn (3) (dimensionless) Constant in eqn (4) (dimensionless) Constant in eqn (5) (dimensionless) Constant in eqn (5) (dimensionless) Constant in eqn (5) (dimensionless) Concentration of solids (%) Activation energy for flow (kcal (g mol)) ) Constant in eqn (6) (K) Constant in eqn (6) (dimensionless) Constant in eqn (7) (K-l) Constant in eqn (7) (dimensionless)

204 Zhang Xuewu et al.

KS Constant in eqn (8) (dimensionless) K6 Constant in eqn (8) (K-l) K Consistency index

;4 Flow behaviour index Gas constant (kcal (g mol)- K-)

T Temperature (K)

Shear rate (s-l) Viscosity (CPS) Constant in eqn (2) (CPS) Constant in eqn (3) (CPS) Constant in eqn (4) (CPS) Constant in eqn (5) (CPS) Constant in eqn (6) (CPS) Constant in eqn (7) (CPS) Constant in eqn (8) (CPS)

INTRODUCTION

Xanthan gum is a microbiological polysaccharide, made from fermentation of Xanthomonas campestris. It is widely used in food, cosmetics and medicine, etc., because of its physical, chemical and functional properties.

Li Shiyan et al. (1992) first studied the effect of shear rate, temperature and concentration on the viscosity of xanthan gum; however, no rheological model was developed. A rheological model would be useful to predict the range of shear rate, concentration and temperature suitable for preparation of xanthan gum dispersions with viscosities which permit industrial handling in agitation tanks, colloid mills and spray driers. Furthermore, a viscosity model can also be useful in studying and predicting the effects of process conditions on end-product quality attributes.

The objective of this study is to develop models which adequately describe the effect of temperature and concentration on the viscosity of xanthan gum.

EXPERIMENTAL

Commercial xanthan gum was imported from USA and served to develop the viscosity model. Selected concentrations (0*3-1.3%) were dissolved by agitation in a water bath at 60C for lo-20 min, after which the samples were cooled to ambient temperature and any foam was removed from the surface of the solutions before making viscosity measurements.

Rheological measurements were carried out using a Brookfield LVT RV viscometer. The temperature was controlled within f O.lC using a circulating wash bath. The shear rate was increased continuously from 0 to 2 s- giving five readings. Altogether five temperatures (20-100C) and six concentrations (0.3-l-3%) were studied, by adding water of the same temperature as xanthan gum solutions to eliminate evaporation of water at temperatures higher than about 60C the supplements of water kept the

Rheological models for xanthan gum 205

weight of solutions of xanthan gum constant before and after evaporation. Regression analysis was carried out using the least-squares method.

RESULTS AND DISCUSSION

Effect of shear rate

The effect of shear rate on the viscosity of xanthan gum solutions may be described by the following power-law model:

q=Kj- (1) where K is the consistency index and it is the flow behaviour index.

Figure 1 shows the effect of shear rate on the viscosity of xanthan gum according to eqn (1). The viscosity decreases as the shear rate increases, the consistency index tends to increase with the concentration of solutions, with the values as follows: O-3340, 05421, 0.7663, 1.2413, l-6875 and 2.5785 corresponding to 0.3%, O-5%, 0.7%, 0.9%, 1.1% and 1.3%, respectively, whereas the flow index (n - 1) changes slightly, average -0.9954.

Effect of temperature

The effect of temperature on the viscosity of xanthan gum solutions may be described by an Arrhenius-type equation (Towler, 1974):

q=ulo exp(E,/RT)

where Q, is a constant, E, is the activation energy for flow, T is the absolute temperature and R is the gas constant.

18 r

16

14

12

3 e 10

0 s 8 F

6

*

2

0

LP I . :c= 0.3%

0 :c= 0.5% . :c= 0.7%

. 0 :c= 0.9%

. :c= 1.1%

A :C= 1.3%

&ii&+

.

.

0 0.5 1 .o 2.0

Shear rate (s-l)

Fig. 1. Effect of shear rate on viscosity of xanthan gum at various concentrations.

206 Zhang Xuewu et al.

Figure 2 shows the effect of temperature on the viscosity of xanthan gum according to eqn (2). The viscosity decreases as the temperature increases.

Effect of concentration

Generally, the effect of concentration can be described by either an exponential or a power relationship (Rao, 1986), as given by eqns (3) and (4), respectively:

ul=ql exp(A,C) (3)

r=V2(C)A (4)

where C is the concentration in percentage solids and ql, Q, A, and A2 are constants. The two models can fit our experimental result better. Figure 3 presents the viscosity versus concentration plots with the data fitted to eqn (3) for various temperatures.

The combined effect of shear rate and concentration

According to eqn (l), parameters K and IZ are functions of concentration, by computing, the following relations are suitable:

K=0*1901 exp(2.0154C)

n - 1 = -0-9476 - 0.0598C

Substituting for eqn (1): rl=0.1901 exp(2.0154C)j(-0.9476--.0598C)

. : c= 0.3%

0 : c= 0.5%

. :c= 0.7%

0 :c= 0.9%

* :c= 1.1%

A :C- 1.3%

01 293 313 333 353 373

Temperature (K)

Fig. 2. Effect of temperature on viscosity of xanthan gum at various concentrations.

Rheological models for xanthan gum 207

30 _ A : T = 293K

. : T = 313K

. : T = 353K

0 0.3 0.5 0.7 0.9 1.1 1.3

Concentration (%)

Fig. 3. Effect of concentration on viscosity of xanthan gum at various temperatures.

i.e.

y~=rj~ exp(B1C)j(B+E3c) (5)

Thus a single model involving the effect of shear rate and concentration is obtained. The fitting of the result is better.

The combined effects of temperature and concentration

Based upon eqn (2) E, and Q, are both functions of concentration; they can be described as below:

q0=34*0385 exp(2.4247C)

E,=0.5795-0.1723C

Incorporating into eqn (2) a model involving the effect of concentration and temperature on viscosity is obtained:

q = 34.0385 exp (2*4247C + (673.84 - 200.35 C)lT)

i.e.

tl=q4 exp(E,lRT+K1CIT+K2C) (6) Similarly, according to eqns (3) and (4) ql, A,, q2, A2 are all functions of temperature; computed results are given below:

q1 =36*7951 exp(557.8345/T)

A, = 1*8531+ 0.00075 T

q2= 363.005 1 exp (494.7305/T)

A2=0.9862+0.0001T

Substituting into eqns (3) and (4), respectively:

y=36.7951 exp(O.O0075CT+ 1.8531C)

208

35 r

Zhang Xuewu et al.

5

0

Fig. 4. Combined effects of temperature and concentration on viscosity of xanthan gum.

i.e.

yl=q5 exp(E,/RT+K,CT+K,C) (7) and

i.e.

yl=y16 exp(E,/RT)CK5+KbT (8)

Thus three models involving the effect of concentration and temperature on viscosity are set up [(6)-(8)]. The common point is that the three models all have the factor exp(E,/RT). The fitting error is O-2613, 0.4742 and 0.3412 for eqns (6)-(8), respectively, so eqn (6) is best. Figure 4 illustrates the combined effects of temperature and concentration on viscosity as predicted in eqn (6).

In addition to temperature and concentration, the viscosity of xanthan gum can be affected by other factors such as pH, suspended insoluble solids, soluble ionic substances, etc. But considering these factors is beyond the scope of this study. The model, however, will be useful for the manufacture and applications of xanthan gum.

ACKNOWLEDGEMENT

The authors thank the National Natural Science Foundation of China for its financial support.

Rheological models for xanthan gum 209

REFERENCES

Li Shiyan et al. (1992). Studies on the purification and concentration of xanthan gum fermentation broth. Food & Fermentation Industries, 4, 43-6.

Rao, M. A. (1986). Rheological properties of fluid foods. In Engineering Properties qf Foods, eds M. A. Rao &. S. S. H. Rizivi. Marcel Dekker, New York, pp. l-47.

Towler, C. (1974). Rheology of casein solutions. N.Z. J. Dairy Sci. Technol., 9. 155-60.