use of nonlinear differential viscoelastic models to predict the rheological properties of gluten...

USE OF NONLINEAR DIFFERENTIAL VISCOELASTIC MODELS TO PREDICT THE RHEOLOGICAL PROPERTIES

OF GLUTEN DOUGH

M. DHANASEKHARAN’. C.F. WANG2 and J.L. KOKINI’

Depamnent of Food Science Center for Advanced Food Technology

Cook College, Rutgers Universiry New Brunswick. NJ 08901-8520

Accepted for Publication May 3, 2001

ABSTRACT

Nonlinear viscoelastic models of the differential type, such as the Phan- Thien Tanner model, White-Metzner model and Giesekus model were used to predict the steady shear, oscillatory shear and transient shear propenies of gluten dough. The predictions were compared with new data and the experimental resuits of Wang and Kokini (1995b). The Phan-Thien Tanner model and the Giesekus model were used in eight modes to fit the relaxation modulus accurately. The White-Metzner model gave the best prediction for the steady shear propellies as it used a Bird-Carreau dependence for the shear viscosity. The Phan-Thien Tanner model and the Giesekus model predicted the transient shear viscosity and the transient first normal stress comcient better than the White-Metzner model. A consistent prediction of all the experimental data could not be obtained using a single model.

INTRODUCTION

Gluten is considered to be a concentrated dispersion of gliadins and glutenins (Eliasson 1989). According to Bloksma (1990), Gliadins contain intramolecular disulfide bonds, breaking of which causes the unfolding of the protein molecule. Glutenins consist of polypeptide subunits linked together by intermolecular disulfide bonds into long unbranched or linear chain molecules. Hydrated glutenin is a tough, elastic material while hydrated gliadin is a viscous

’ Currently with: Fluent Inc.. 10 Cavendish Court, Centerra Resource Park, Lebanon, NH 03766 Currently with: RMS Technology Center, Nabisco Inc.. 200 Deforest Avenue, P.O. Box 1944, East Hanover, NJ 07936

’ Author to whom all correspondence should be addressed. TEL: (732) 932 8306 x340; FAX: (732) 932 8970; E-mail: [email protected]

Journal of Food Process Engineering 24 (2001) 193-216. AN Rights Reserved. OCopyrighr 2001 by Food & Nutrition Press, Inc., Trumbull, Connecticut. 193

194 M. DHANASEKHAMN. C.F. WANG and J.L. KOKINI

liquid. This suggests that a mixture of the two is essential to give dough the viscoelastic properties that are associated with good breadmaking performance. The rheology of gluten therefore can be very complex.

Graveland and Henderson (1987) suggest that gliadins act as a diluent that function to reduce the stiffness of gluten. The viscoelastic behavior of gluten therefore depends on the gliadin to glutenin ratio. Bernardin (1978) suggested a fibril-fibril interaction model during dough mixing based on the concepts of Bernardin (1975) and Ewart (1972) that gliadin and glutenin have the ability to form fibrous structures. The fibrils exhibited elastic recovery and viscous flow. Bohlin and Carlson (198 1) interpreted the rheological behavior of gluten using the theory of cooperative flow. The observed macroscopic flow is regarded as a consequence of cooperative rearrangements of a large number of subunits. Gluten was shown to exhibit two flow processes: A primary process with a relaxation time of about 1 s occurring in a fibrillar structure and a secondary process with a relaxation time of about 500 s occurring in a lamellar superstruc- ture. Crosslinking stops the flow in the fibrillar structure and then the flow in the lamellar structure becomes more important.

Given the above discussed complexity, trying to build a constitutive model for gluten from molecular and structural arguments is a challenging task. There are many kinetic theories in expressing either liquid or solid type of flows. Among those theories the network theories which are fundamentally based on the entanglement and the cooperativeness of molecular motion for polymer melts and concentrated solutions.

Stress relaxation studies from Funt Bar-David and Lerchenthal (1975) show a complete decline to zero in the stress. A complete relaxation of stress is typical of liquids and it might be concluded that gluten behaves as a viscoelastic liquid. Also Mita and Matsumoto (1984) reported oscillatory data with some investigations showing the tan 6 values with 6 = 71" which indicates a predominance of viscous behavior in gluten.

The most fundamental difference between solids and melts is the molecular scale of the relaxation processes (Matsuoka 1992). By observing the oscillatory and steady flow in two simple mesomorphic model systems, Bohlin and Carlson (1981) found that the flow unit coordination number z is equal to the structural coordination number. The coordination number therefore serves as an index in distinguishing the liquid and solid. An analysis of the coordination number of gluten dough with different moisture contents is discussed later in the paper.

Following the above arguments based on molecular structure of gluten most researchers have used flow models based on the network theory to characterize gluten and wheat flour doughs alike.

Bagley et al. (1988) studied uniaxial compression of hard wheat flour dough using the upper convected Maxwell model. Using a single relaxation time, they showed good agreement between experimental and calculated results.

NONLINEAR DIFFERENTIAL VISCOELASTIC MODELS 195

However, the rheological parameters had to be varied with compression rates to get best fits, which reflects a broad relaxation time distribution of dough.

Dus and Kokini (1990) used a 5-parameter Bird-Carreau model to predict steady shear and oscillatory shear properties of hard wheat flour dough. The model was successful in predicting steady shear viscosity and small amplitude oscillatory properties but showed significant deviation from primary normal stress coefficient data. Wang and Kokini (1995a) used Bird-Carreau model to simulate the rheological properties of gluten dough. The small amplitude oscillatory shear properties were successfully predicted while the primary normal stress coefficient was overpredicted.

Wang and Kokini (1995b) examined the ability of the Wagner model to predict transient shear properties and uniaxial and biaxial extensional rheological properties of gluten doughs. The Wagner model used a generalized Maxwell model for the linear time dependent component to predict transient shear properties. They found that a damping function with two exponential terms was suitable to simulate nonlinear shear properties. They were also able to predict the uniaxial and biaxial extensional viscosities with a second damping function to account for extensional strain dependence of gluten doughs.

Phan-Thien et af. (1997) proposed a constitutive model for flour-water dough consisting of a rubber-like and viscoelastic response to predict oscillatory and viscometric data. The authors mention that dough is solid-like and therefore flow models may not be relevant. The discussion at the beginning of this section indicate the complex molecular nature of gluten and that the viscoelastic properties of gluten is dependent on a variety of factors including glutenin to gliadin ratio. Therefore it is difficult and not clear to identify the exact molecular mechanisms which control dough rheology . However, the current state of knowledge in gluten rheology indicates that gluten is a liquid-like material and flow theories have been used successfully in the past.

More recently, Bagley et al. (1998) raised concerns on the experimental and conceptual problems in the measurement and characterization of the rheological properties of wheat flour doughs. They observed huge fluctuations in the experimental data for doughs not overmixed. Overmixed doughs gave consistent results but their use is limited. Phan-Thien and Safari-Ardi (1998) reported dynamic oscillatory and stress relaxation data on Australian strong flour-water dough. They derived relaxation spectra from both dynamic and relaxation data, and found them to be consistent with each other.

Dhanasekharan et al. (1999) used the Phan-Thien Tanner, White-Metner model and the Giesekus model to study whole wheat flour doughs. The Phan- mien Tanner model gave good zero shear viscosity prediction, but overpredicted the shear viscosity at higher shear rates and the transient and extensional properties. The Giesekus-hnov model gave similar predictions to the Phan- Thien Tanner model, but the extensional viscosity prediction showed extension

196 M. DHANASEKHARAN, C.F. WANG and J.L. KOKINI

thickening. Using high values of the mobility factor, extension thinning behavior was observed but the predictions were not satisfactory. The White-Metzner model gave good predictions of the steady shear viscosity and the first normal stress coefficient but it was unable to predict the uniaxial extensional viscosity as it exhibited asymptotic behavior in the tested extensional rates. It also predicted the transient shear properties with moderate accuracy in the transient phase, but very well at higher times, compared to the Phan-Thien Tanner model and the Giesekus-Leonov model.

The objective of this work is to build on previous studies which attempt using flow theories to model doughs by testing the validity of the Phan-Thien- Tanner, the Giesekus, and the White-Metzner models to predict the steady shear and transient shear properties of gluten dough. This study will provide insight into the ability of the models to predict the rheological properties of gluten doughs.

THEORY

The differential viscoelastic constitutive equations selected in this study describe the total stress tensor T as the sum of the viscoelastic component, T, and the purely Newtonian component, T2 as: T = T, +T2, where Tz = 2r],D, where D is the strain rate tensor. The models studied in this research are the Giesekus model, the White-Metzner model and the Phan-Thien-Tanner models. The models are discussed below:

Giesekus Model

The model (Giesekus 1982) considers polymer molecules as unbranched or branched chains of structural elements, which can be viewed as “beads”, joined either by elastic “springs” or rigid “rods” and which are additionally subjected to “Brownian Motion” forces. The constitutive equation has the following form:

With a purely Newtonian component T, = 2qzD. When a > 0 the model always predicts shear-thinning behavior. The term

involving a is the “mobility factor” that is associated with anisotropic Brownian motion and anisotropic hydrodynamic drag on the constituent polymer molecules. The material functions for the Giesekus model were obtained numerically.


White-Metzner Model

The White-Metzner model is derived from the network theory of polymers (White and Metzner 1963). The viscoelastic differential constitutive model takes the following form:

(2) V

T, +A(Y)T] =2rl , ( Y P

Where q , (q ) is obtained from the experimental shear viscosity curve, and the function A(+) is obtained from the experimental first normal stress difference curve. The shear viscosity of the model is given by:

(3) rl = tl, + (?l0-q.J (1 + A V Y 2 . 2 1 (nv-1Y'2

The first normal stress coefficient is given by:

$ , = h A

where X is the relaxation time function given by:

2 (4-1112 A(P)=A.,(l +A*)

The transient shear properties are given by: rl+=q(l-e-(t-tJ/*)

(4)

Phan-Thien-Tanner Model

Phan-Thien and Tanner (1977) assumed specific forms for the creation and destruction rates of the network junctions and derived a constitutive equation containing two free parameters E and 4. The constitutive model takes the following form:

ex p[ e-tr(T1) bl + A[(l-;);] + fill = 2qD

198 M. DHANASEKHARAN. C.F. WANG and J.L. KOKINI

The parameters r] and X are the partial viscosity and relaxation time respectively, measured from the equilibrium relaxation spectrum of the fluid. They are not considered as adjustable parameters of the model. E and E are the adjustable parameters of the model. The parameter 5 can be obtained using the dynamic viscosity-shear viscosity shift according to:

The shear viscosity for the model is given by:

where the summation to n refers to the number of modes. The first normal stress coefficient was obtained as:

The transient shear properties for the Phan-Thien Tanner model were obtained numerically.

MATERIALS AND METHODS

Identifying a linear viscoelastic range is a challenge with many food materials. In particular wheat flour doughs have been the subject of many studies (Hibberd and Wallace 1966; Dus and Kokini 1990; Janssen 1992; Wang and Kokini 1995; Phan-Thien er al. 1997). For wheat flour doughs all researchers agree that wheat flour doughs exhibit linear behavior until a strain of O(O.001). However, there is a disagreement among researchers for Gluten. Janssen (1992) reported that a clear region of linear viscoelasticity for gluten doughs could not be identified. Wang and Kokini (1995) reported a linear viscoelastic strain limit of O(O.l). Lindborg (1995) reported that the linear viscoelastic strain limit for gluten doughs is about the same as that of wheat flour doughs. Therefore in an attempt to evaluate the linear viscoelastic range for gluten doughs we conducted strain sweeps for varying gap widths and different testing frequencies. The Rheometrics ARES was used in a dynamic mode and parallel plate geometry with 25 mm plates to conduct the strain sweep experiments.


Preparation of Gluten Dough

Gluten powder obtained from Sigma Chemical Co. was mixed with the necessary amount of distilled water and well mixed for 10 min to make gluten dough at moisture contents of 52.596, 5 5 % and 57.5%. A Brabender farinograph with a 50 g mixing bowl and a rotation speed of 63 rpm was used to obtain different moisture gluten doughs. After mixing, the sample was stored in a sealed bag and let to relax overnight. Strain sweep measurements were conducted at 25C and 60C.

Oscillatory Measurements

Small amplitude oscillatory measurements were conducted using the ARES provided by Rheometrics Inc. Strain sweeps from 0.01 % strain to 100% strain were conducted to determine the region of linear viscoelasticity. A parallel-plate testing fixture with a diameter of 25 mm was used. The strain sweeps were conducted at four different gap heights, 0.554 mm, 1 mm, 1.5 mm, 2 mm, and 3 mm. At each gap height, the strain sweeps were conducted at different frequencies of a radls, 2r radls, 4 r radls, 8r radls, 12r radls, 16r radls, and 20r rad/s. We also conducted a strain sweep at 2 mm gap and a testing frequency of 10 radls to compare with the results of Wang and Kokini (1995b).

Measurement of Bagley Factors to Establish Steady Shear Flow

The Instron capillary rheometer was used to measure the Bagley correction factors. A set of capillaries with the same diameter (0.052") but different lengths with LID of 5 , 10, .15, 20, 30 and 40 was used. Entrance pressure drops at different shear rates was obtained and calculated by extrapolating the pressure drop to LID = 0. The Bagley correction factor e, which is the LID value at zero AP, is empirically obtained by extrapolating the Bagley plot (Force Vs LID) to the x-axis.

Other Data Used for Model Predictions

The data published by Wang and Kokini (1995b) was chosen to test the differential viscoelastic models. Wang and Kokini (1995a) conducted shear stress relaxation measurements using the Rheometrics Mechanical Spectrometer (RMS- 800) using parallel disk geometry with 25 mm diameter and 2 mm gap. Shear viscosity measurements and first normal stress difference measurements were made using parallel plate geometry with the RMS-800 for the shear rate range 10" - lo-* s-I. Measurements above this shear rate were not possible due to sample rolling underneath the plates. To access higher shear rates, an Instron Capillary Rheometer 3211 was used and experiments in the range of 2.5 - 1400 s-' were conducted. Wall slip was minimized using a capillary of


1.524 mm diameter and 16.67 L/D ratio. The zero shear viscosity was measured using the Rheometrics Stress Rheometer (RSR) with parallel plate geometry with a diameter of 50 mm and 2 mm gap. Transient measurements were made using the transient test mode in the above described steady measurement at a fixed shear rate over a predefined time range. Oscillatory measurements were also conducted using RMS-800 with a parallel plate fixture of diameter of 25 mm and 2 mm gap.

When using differential models, the number of differential equations is equal to the number of modes. It was therefore necessary to optimize the number of modes, which can be used to fit the data.

The linear relaxation modulus is given by: II

G(t) = G,e-VA' i=1

Where n is the number of relaxation times (modes). We found that with 8 relaxation times (modes) we could predict the linear shear relaxation modulus with almost no loss of accuracy relative to the 12 relaxation times used by Wang and Kokini (1995b).

The error in the model predictions was estimated using the s u m of squares as follows:

b - 2 - c k x p - Y p r d 2 (13)

Where yerp is the experimental value and yPd is the corresponding predicted value from the model, and n is the number of data points.

n

RESULTS AND DISCUSSION

The strain sweeps obtained at different gap heights and testing frequency showed that the strain sweep is dependent on gap height and the testing frequency. The dependence on gap height is strong when we have small gap heights like 0.554 mm or 1 mm. At small gap heights the dough takes a few hours to relax. The instrument was insensitive below strains of 0.17%. We did not observe any linear region at 0.554 mm gap height at all the tested frequencies. The data showed noise at low strains due to limits on the sensitivity of the measuring instrument. However, we were able to obtain results for 1 mm gap and a testing frequency of OSHz, which showed the onset of nonlinearity in the strain of the order of 0.001 (Fig. 1). On the other hand, high gap widths such as 3 mm showed the onset of nonlinear viscoelasticity at a strain of the order of 0.01 for testing frequency greater than 2Hz (Fig. 2). For testing

NONLINEAR DIFFERENTIAL VISCOELASTIC MODELS 20 1

frequencies of 1Hz and 0.5 Hz, the onset occurred at a strain of 0.1. Higher gap widths may cause slippage during measurements and therefore can be a source of experimental error. The results of the strain sweep were identical for gap widths of 1.5 mm and 2 mm. Most researchers used a gap width of 2 mm for conducting strain sweeps and frequency sweeps. Therefore small gap widths (less than 1.5 mm) and higher gap widths (greater than 2 mm) induce experimental errors and therefore not suitable for oscillatory measurements of gluten dough. The results from 1.5 mm and 2 mm gap width show that the onset of nonlinear viscoelasticity occurs at a strain, which is dependent on the testing frequency. At low testing frequencies such as 10 rad/s, the linear viscoelastic strain limit is 0.1, which is consistent with Wang and Kokini (1995b) as shown in Fig. 3a and Fig. 3b. At high testing frequencies such as 10 Hz, the strain limit shifts to the order of 0.001 (Fig. 4). Therefore it is clear that the onset of nonlinear viscoelasticity for gluten is a function of the testing frequency.

For the current work, which is aiming to find suitable differential models to fit the material functions of steady and transient shear properties we choose 10% strain at a testing frequency of 10 rad/s as the onset of nonlinear viscoelasticity consistent with Wang and Kokini (1995b).

-

lo* f -

-4 t - b

* * * * A * *

'a m

10.' 10 ' 1oO 10' Id Slrah [%]

FIG. 1 . DYNAMIC STRAIN SWEEP OF GLUTEN Parallel plate fucture gap = 1 nun. Testing frequency is T rad/s.

9

Y ' f


+ % -o_ b

Strain [%]

FIG. 2. DYNAMIC STRAIN SWEEP OF GLUTEN Parallel plate fixture gap = 3 mm. Testing frequency is 87r rad/s.

The most important fundamental difference between solids and melts is the molecular scale of the relaxation processes (Matsuoka 1992). By observing the oscillatory and steady flow in two simple mesomorphic model system, Bohlin and Carlson (1981) found that the flow unit coordination number z equal to the structural coordination number. An analysis of the coordination number of gluten dough with different moisture contents is shown in Table 1. As seen in Table 1, the value of z falls between 3 and 5 indicating that gluten dough is a liquid-like viscoelastic substance.

Increasing moisture content results in a larger z value. Higher moisture content will increase the mobility of gluten molecules and thus increase the chances to form better-developed network, consequently the cooperativity is more significant and thus increase the coordination value.

The storage modulus of gluten dough at 25C is higher than that at 60C for all moisture contents except the one with 57.5% moisture at frequency smaller than 1 rad/s (Fig. 5) . However, with the same moisture content, the coordination number z of gluten at 60C is larger than that of gluten at 25C for all moisture studied. This suggests that gluten dough may undergo thermal transition at 60C and therefore increases the coordination number by increasing

+= - b

fas 1 I

G' (52.5%. 25C) 0 G' (6z6% 6OCJ A 0" (62.5%, 26C) A G" (52.6% 6OC)

q' (62.6#, 2SC) 0 ll* (62.6% 6OC)

lo4 - * ( Pa. s) 0 0 . 0 0 . .

0 P P Q Q Q P Q ,

A A A A A A A

c. c" (Pa) (

'' l o 3 -

CF -E b

11

l o 2


. . . . . . .~. a 0 0 0 0 0 0 0

' I I


slope*

z**

Strain [%I FIG. 4. DYNAMIC STRAIN SWEEP OF GLUTEN

Parallel plate fixture gap = 2 mm. Testing frequency is 20r radls.

J

52.5%. 52.5), 55%, 558, 57 .5c , 57.5c,

25.C 60°C 25.C 6 0.C 25.c 60.C

0 .269 0.215 0.236 0.213 0.227 0.187

3.718 4.654 4 . 2 4 1 4 . 6 0 1 4 .409 5.341

TABLE 1 . SLOPE VALUE AND THE COORDINATION NUMBER FOR GLUTEN DOUGH WITH

DIFFERENT MOISTURE CONTENTS AT 25C AND 6OC

I moisture content and temperature 1 I I of gluten doushs

* Slope of log G' vs log o ** Coordination number z = Mope


10)

GI (rlI)

I 1

0 62.6%.26.C 0 62.69b.6dC A 56%,26’C

0 67.6%,25% 67.5%, 60%

A SIW.(IO*C

0

0 0

the crosslink density. From the state diagrams of glutenin and gliadin previously developed in our laboratory (Cocero and Kokini 1991; Madeka and Kokini 1994), for higher moisture content of glutenin and gliadin, it is known that the thermal reaction zone starts around 65C and 70C, respectively. It is not difficult to understand that in the border of thermal reaction zone, gluten dough may have experienced a slight thermal reaction at 60C and thus results in a higher density of crosslinks. However, from the magnitude of the modulus, it can be seen that the temperature softening effect is still more significant than the crosslinking effect since the modulus at 60C is lower than the modulus at 25C.

Figure 6 shows the prediction of the shear relaxation modulus using 8 modes along with the experimental data. The error parameter is 6’ = 0.0002 for the fit. The chosen relaxation times and the corresponding moduli are shown in Table 2.

l.OE+04 -

- n 5 l.OE+03 = (3

.-4

l.OE+OZ 7

0 Wang and Kokini(l995b' -8 element Maxwell Fit

0

1 3 I332 5 I 1x103 I

No. Of modes GI (Pa) 1 17.5 2 150 n

449.1 497.7 939.3 2,824.8 1 x 10-

&(Sec) 1 x 10' I x 10"

I 30,@0.0

The Bagley correction factor e, which is the L/D value at zero AP is empirically obtained by extrapolating the Bagley plot (Fig. 7) to the x-axis. The Bagley correction factors are used in obtaining corrected shear viscosity to


reduce the error due to entrance effects. The values obtained at different shear rates are shown in Table 3. From Table 3, the Bagley correction factors obtained at different shear rates are not the same. Similar results have been reported for Soy dough (Jasberg et al. 1981). If we consider the largest e value and calculate the value of eD/2 for the shear viscosity measured using the Instron Capillary rheometer with L/D = 16.67 and D = 1.524 mm we have:

eD/2 = (11.75 x 1.524 mm) / 2 = 8.9535.

Therefore the effective length of the capillary is

L+eD/2 = 25.41 + 8.95 = 34.36 mm.

In other words 65% of the capillary length is available for steady shear flow and this is a measure of existence of steady shear flow in the capillary rheometer. This is in contrast to the large values of e reported by Bagley ef al. (1998) calculated from the data of Kieffer et al. (1982) who reported end correction values, e = 109.5 for gluten.

Force

1575

I350

I125

"lotr 675

JSO

225

0 - 0 6 10 I 6 20 26 30 35 40

UD FIG. 7. FORCES GENERATED BY GLUTEN DOUGH AT VARIOUS L/D

Entrance force is obtained at L/D = 0.


Differential Model Giesekus White Metzner

TABLE 3. THE ENTRANCE PRESSURE DROPS AND THE BAGLEY CORRECTION FACTOR (e) AT

DIFFERENT SHEAR RATES FOR GLUTEN DOUGH

Model Parameters a = 0.001 no = 6.15 x lo6 Pa. s; qm = 10 Pa. s, k,, = 3 x 10.' S,

shear rate ( l / o ) I '" 1 4 ~ 13 ~ 40 ~ 133 400 ~ 13331 5 . 2 2 6 . 8 1 9.95 17.4 24 .2 40.8

(I .om Pa)

11.75 8.26 8 . 3 3 10.06 9 . 3 2 10.57

Phan-Thien Tanner

Table 4 shows the model parameters for the different models that gave the best prediction of the observed data. These parameters were obtained by following the recommendations of the authors of the models (Phan-Thien and Tanner 1977; White and Metzner 1963; Giesekus 1982).

~lv = n,. = 0.25; & = 1 x lo5 s; A, = 3 x 10' s 6 = 2 x 10.'; E = 0.01

The predictions and their comparison of the shear viscosity with the models are shown in Fig. 8. The Giesekus model and Phan-Thien Tanner model underpredicted the zero shear viscosity but gave a good prediction in the shear thinning regime. At high shear rates, these models overpredicted the infinite shear viscosity. The White-Metzner model gave the best prediction of shear viscosity data both in the zero viscosity regime and the shear thinning regime (Table 5) . The White-Metzner model uses a Bird-Carreau type model to predict the shear viscosity. The Bird-Carreau type model has a power law parameter to predict the shear viscosity in the shear thinning regime, and also a zero shear viscosity term, which enables good prediction in the constant viscosity regime at low shear rates.

NONLINEAR DIFFERENTIAL VISCOELASTIC MODELS

I PTT I White-Metzner

209

Ciesekus

1 .OE+O7

1 .OE+06

A

@ .OE+05 a P, .- 22 LO .OE+04 8 5 LO

5 .OE+03 r tn

l.OE+OZ

l.OE+Ol

-------- .. ..._.___

- PTT - PTT

- . . . . - Giesekus 0 Wang and Koklnl( 1996b)

White-Metzner --- 4

1 0 Wang and Koklnl( 1996b) ,

- . . . . - Giesekus White-Metzner ---

4

1.OE-07 1.OE-06 1.OE-03 1.OE-01 l.OE+Ol l.OE+03

Shear Rate (Us)

FIG. 8 . COMPARISON OF SHEAR VISCOSITY DATA OF 55% MOISTURE GLUTEN DOUGH AT 25C WITH THE PREDICTIONS OF DIFFERENTIAL MODELS

TABLE 5 . ERROR PARAMETER a2 FOR THE PREDICTIONS BY THE

DIFFERENTIAL MODELS


Figure 9 shows the predictions of the first n o d stress coefficient by the models. The comparison of the model predictions with experimental data here are difficult because the experimental data is only available at three shear rates. Nevertheless the predictions obtained using each model are very close to the experimental data. The White-Memer model gave the best prediction (Table 5).

l.OE+14 T

n̂ I.OE+12

0 E I.OE+lO

UI U

0 0 .- 5 I.OE+08 0

I I.OE+06

v)

2 I.OE+M z 8

I.OE+O2 LL

PTT

Giesekus White-Mebner

0 Wang and Kokini (1995b) .-.--- - - - White-Mebner - - -

l.OE+OO 4 1.OE-07 1.OE-05 l.OE-03 1.OE-01 l.OE+Ol 1.OE+03

Shear Rate (lls)

FIG. 9. COMPARISON OF FIRST NORMAL STRESS COEFFICIENT DATA OF 55% MOISTURE GLUTEN DOUGH AT 25C WITH THE PREDICTIONS OF

DIFFERENTIAL MODELS

The small amplitude oscillatory shear properties for Phan-Thien-Tanner and Giesekus are same as the equations for Maxwell-B model. The moduli, relaxation time pairs used, are the ones in Table 2. The predictions are very close to the experimental values as shown in Fig. 10. One of the drawbacks of the White-Metmer model is that the small amplitude oscillatory shear properties are not defined for White-Metzner model.


1 .OE+12

1 .OE+ 10

- l.OE+08

5 l.OE+06 3

N In A

> e b A

l.OE+04

' l.OE+02 't

l.OE+OO

l.OE-02

-n' (PTTlGiesekus)

1.OE-07 1,OE-05 1.OE-03 l.OE-01 l.OE+Ol l.OEt03

Frequency (lls)

FIG. 10. COMPARISON OF DYNAMIC VISCOSITY (n') AND THE OUT-OF-PHASE COMPONENT OF COMPLEX VISCOSITY DIVIDED BY FREQUENCY (n"/o) AS A

FUNCTION OF FREQUENCY OF 55% GLUTEN DOUGH AT 25C WITH THE PREDICTIONS OF DIFFERENTIAL MODELS

Figures 11 and 12 show the prediction of transient shear properties at a shear rate of 0.01 s-'. The Giesekus Model and Phan-Thien Tanner model gave good predictions of the transient shear viscosity and transient first normal stress coefficient in the transient region of 0 to 500 s. The steady values predicted by the Phan-Thien Tanner and Giesekus models are higher than observed values. At large times, the White-Metmer model approached a steady value in close agreement with observed values for the first normal stress coefficient, but showed higher steady values for the transient shear viscosity.


B.OE+OS

4.OE+OS A

In (1

% 2 3.OE+05

5

In

In 8

0 2.OE+O5 S rn * E Q .- t l.OE+OI

I=

O.OE+OO

. ._ . -- . - .- /

/ 1

-Giesekus .....

PTT - Wang and Kokinl(1995b)

White-M etzner - - -

-Giesekus .....

PTT - Wang and Kokinl(1995b)

White-M etzner - - -

0 600 1000 1500 2000 2500 3000 Time ( 8 )

FIG. 11. COMPARISON OF TRANSIENT SHEAR VISCOSITY DATA OF 55 % MOISTURE GLUTEN DOUGH AT 25C WITH THE PREDICTIONS OF DIFFERENTIAL MODELS

CONCLUSIONS

The White-Metzner and Phan-Thien and Tanner models are derived using Lodge-Y amamoto network theory, which assumes the polymer molecules (Gluten molecules in this case) form a network by strong local attractions along the chains. These junctions are assumed to break off and reform continually in a nonaffne fashion during flow. Gluten dough has been demonstrated (Ewart 1972) to form transient networks with continuous break off and formation of junctions. Cocero (1993) describes gluten structure to form temporary entanglements. Therefore it is no surprise that Phan-Thien-Tanner model and White-Metzner predicts closely most of the properties of gluten dough.

None of the models studied here have considered all the factors affecting gluten rheology. Therefore a single model that can predict all the observed rheological properties of gluten dough could not be obtained. Some of the factors affecting gluten rheology are water content, temperature, and even


5.OE+09

4.OE+09

3.OE+09

2.OE+09

I.OE+09

O.OE+OO

PTT - ...... --- White-Metzner Giesekus /

0 Wang and Kokini(l995b) ,

I

0 500 1000 1500 Time ( 5 )

FIG. 12. COMPARISON OF TRANSIENT FIRST NORMAL STRESS COEFFICIENT DATA OF 55 % MOISTURE GLUTEN DOUGH AT 25C WITH THE PREDICTIONS OF

DIFFERENTIAL MODELS

protein variety. For example large differences in the rheological properties of the gluten from bread and durum wheat have been reported in several studies (Doguchi and Hlynka 1967; Matsuo 1978). Therefore future work may need to develop constitutive models for wheat flour doughs that take into account at least some of the above factors.

ACKNOWLEDGMENTS

This is publication No. D-10544-13-01 of the New Jersey Agricultural Experiment Station supported by State funds and the Center for Advanced Food Technology (CAFT). The Center for Advanced Food Technology is a New Jersey Commission on Science and Technology Center.


NOMENCLATURE

D Strain Rate Tensor G(t) Linear relaxation modulus function (Pa) N Number of modes T Extra Stress Tensor TI T, i / Shear Rate (s-') (Y Mobility factor h Relaxation time (s) q Viscosity (Pa. s) 6 Error function E , 4 Adjustable parameters of the Phan-Thien Tanner model q+

+, qi Partial viscosity (Pa. s)

Viscoelastic component of the Extra Stress Tensor Newtonian component of the Extra Stress tensor

Transient shear viscosity (Pa. s) First normal stress coefficient (Pa.s2) Transient first normal strain coefficient (Pa. s2)

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use of nonlinear differential viscoelastic models to predict the rheological properties of gluten...

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