Review paper
A review of dough rheological models used in numerical applications
S. M. Hosseinalipour*, A. Tohidi and M. Shokrpour
Department of mechanical engineering, Iran University of Science & Technology, Tehran, Iran.
Article info: Abstract Received: 14/07/2011 The motivation for this work is to propose a first thorough review of dough Accepted: 17/01/2012 rheological models used in numerical applications. Although many models have Online: 03/03/2012 been developed to describe dough rheological characteristics, few of them are employed by researchers in numerical applications. This article reviews them in Keywords: detail and attempts to provide new insight into the use of dough rheological Dough, models. Rheological Models Rheology.
Nomenclature
Relative increase in viscosity due to Pa.sec A Apparent viscosity, gelatinization, dimensionless
1 b Index of moisture content effects on viscosity, Shear rate, sec dimensionless Rate of deformation tensor Strain history, dimensionless D K 11sec k ReactionArchive transmission coefficient, of Time SID-temperature history, K.sec a
MC Moisture content, dry basis, decimal Yield stress, Pa 0 MC Reference moisture content, dry basis, decimal u Velocity, ms/ r m Fluid consistency coefficients, dimensionless Stress tensor n Flow behavior index, dimensionless E Free energy of activation, cal/g mol v 1.987cal / g mol K Pa R Universal gas constant, Stress, Index of molecular weight effects on viscosity, Relaxation time, sec dimensionless 1. Introduction *Corresponding author Email address: [email protected] www.SID.ir129 JCARME S. M. Hosseinalipour et al. Vol. 1, No. 2, March 2012
Bread is the most important daily meal of Thien-Tanner model [1,12,13]. In these studies people in the world. Furthermore, improving they often employed the Brabender Farinograph the quality of bread baked products and the to predict the measured rheological behavior of development of relevant apparatuses completely wheat flour dough at different moisture depend upon a comprehensive knowledge of contents. dough rheology. Therefore, it is essential to However, the limited application of their results gain a deep knowledge of dough behavior and and difficulties encountered in correlation to ensure the accuracy of the measured between the quality of the baked products and rheological data. However, finding a values obtained from them complicate the task constitutive model that has all accurate of characterizing the flow behavior of dough. molecular and structural arguments to simulate In 1954, Cunningham and Hlynka [14] tried to the linear and non-linear properties of wheat characterize the linear viscoelastic properties of flour dough is a tough challenge due to the dough using distribution of relaxation times. In complicated nature of wheat flour doughs 0. order to characterize the viscoelastic properties The challenge is due to the fact that once water, of flour dough, Bagley and Christianson [15] wheat flour dough and small amount of used the BKZ elastic fluid theory. Thereafter, ingredients such as salt, yeast, preservatives, the upper convected Maxwell model was used etc. are combined, a cohesive viscoelastic by Bagley et al.[16]. Till 1990, the aim of substance is produced called dough. All of studies had been to simulate the rheological these ingredients can considerably change the properties of wheat flour dough without rheological properties of the dough during considering its non linear behavior. Dus and mixing, and make it rheologically complex. In Kokini [6], therefore, tried to describe the fact, the combination of these ingredients steady state shear viscosity and oscillatory produces a three dimensional network called shear properties of hard flour dough using the gluten which has a crucial role in complex five-parameter Bird-Carreau model. Bagley viscoelastic behavior of wheat flour dough 0. [17] used of the upper-convected Maxwell Despite these complexities, the rheology of model to explain the dough behavior in biaxial wheat flour dough has been an important of extension flow. scientific researches topics. Over the years, Before 1995, less attention was paid to the several efforts have been made to measurements of uniaxial and biaxial experimentally and theoretically evaluate dough extensional rheological properties of wheat properties that affect its flow behavior. In this flour doughs in the strain rates region [12]. approach, Schofield and Scott Blair [2-5] might Therefore, Wang and Kokini [11], showed that be considered as pioneer researchers who one can profit by using the Wagner model to studied the flow behavior of the wheat flour predict transient shear properties and uniaxial doughs. They also demonstrated that dough and biaxial extensional rheological properties of behaves both like a Hookean solid and also like gluten doughs and also to simulate nonlinear a Newtonian liquid. shear properties. Dhanasekharan and Kokini In order to provideArchive information on the [13] usedof the Phan SID-Thien Tanner model as a rheological properties of wheat flour dough, the more realistic model describing dough-like measurement of dough material properties has fluids for 3-D numerical modeling of been obtained using empirical instruments such viscoelastic flow in a single screw extrusion as Farinograph, Alveograph, Extensigraph and and then analyzed the effect of viscoelasticity Mixograph [6-8] and capillary rheometry (shear considering a stationary screw and rotating and extensional viscosities for dough) [9,10]. barrel. Phan-Thien and Safari-Ardi [18] derived Kokini et al. have attempted to simulate and relaxation spectra from both dynamic and compare dough-like rheological materials using relaxation data for Australian strong flour-water the Bird Carreau model [6, 8], the Wagner dough and reported dynamic oscillatory and model [11], the White-Mezner model, the stress relaxation data [1,19]. Giesekus-Leonov model [1,12] and the Phan-
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Till that time, most of the reported models dough behavior in such a single screw extruder. simulating the rheological properties of wheat In this study, in order to take into account the flour doughs or their protein components had variations in the rheology of wheat flour dough, been either linear differential viscoelastic the Mackey and Ofoli viscosity model was models like the generalized Maxwell models or applied. With regards to attempts to examine nonlinear integral viscoelastic models such as the mixing ability of single and double screw the Bird-Carreau and Wagner models [19]. mixers, significantly Kokini et al. [23,24,26,27] Using the Phan-Thien Tanner, White-Metzner examined the effects of shear thinning and model and the Giesekus model applied by differential viscoelasticity on dough mixing Dhanasekharan et al. [12] to study whole wheat behavior. flour doughs, Dhanasekharan et al. 0 compared For the first time, Binding et al. [28] examined the validity of these models to predict the the combination of numerical and experimental steady shear and transient shear properties of studies of dough kneading in a partially filled gluten dough. Using the theory of rubber cylindrical mixer, with either one or two elasticity, Leonard et al. [19] studied the eccentric stirrers. The numerical procedure rheology of wheat flour doughs at large utilized a parallel numerical method based on a extensional strains and reported an intermediate finite element semi implicit time-stepping behavior between rubber elasticity and plastic Taylor-Galerkin/pressure-correction scheme. flow for dough. The same approach was then employed In order to evaluate the constitutive eqations [29,30,31] to analyze the wetting and peeling of introduced by Phan-Thien et al. [20], the large- dough like material on solid surfaces strain oscillatory shear flow of flour dough was considering the free surfaces, kinematics and studied by Phan-Thien et al. [21]. Their results stress fields produced by variations of stirrers’ indicated that a model with a shear-rate speed and changing geometry mixer. For fluid dependent viscosity alone is inadequate to rheology, Carreau–Yasuda, constant viscosity describe the response of flour dough since the Oldroyd-B and two shear-thinning Phan- material response is significantly non-linear Thien/Tanner constitutive models were which is mainly due to the strain softening employed. Velocity profiles and relevant behavior of the material. Furthermore, in order peeling stress were calculated using laser scatter to be able to differentiate between different technology, Laser Doppler Anemometry (LDA) flour types, tests at large-strain deformations and a video capture technique. Results revealed are required. good agreements between the numerical and Although, the literature has explored numerous experimental studies. papers dealing with both theoretical and It is not feasible here to even attempt to review experimental methods of characterizing dough many of efforts that have been made to explore like materials, there are only a few scattered both theoretical and experimental ways of references devoted to evaluating the application characterizing and evaluating dough; however, of reported constitutive equations of wheat Bagley [9], Kokini [19] and Phan-Thien et al. flour dough inArchive numerical simulations. In [21]of have cited SID some useful references. characterizing dough behavior and its effects on Despite all these attempts, there is still a great different flow patterns, the most notable works need to understand the necessary constitutive belong to Kokini et al. [13, 22, 23, 24 and 26] equations to accurately describe wheat flour and Phan-Thien et al. [18, 21, 25 and 26]. A dough behavior. According to the author’s numerical modeling of viscoelastic flow in a knowledge, there is no work in the literature single screw extrusion conducted by that has reviewed the rheological models used Dhanasekharan and Kokini [13] can be in numerical applications of dough like considered as one of the earliest dough materials. Therefore, this study aims to review numerical simulations. Thereafter, Connelly the constitutive equations applied in numerical and Kokini [23] conducted a simultaneous simulations of dough flow behavior during, scale-up of mixing and heat transfer analysis of approximately, the period 1987-2007. The
www.SID.ir131 JCARME S. M. Hosseinalipour et al. Vol. 1, No. 2, March 2012 review represents all parameter values of these current computational technology and available rheological models. software tools [19]. Only a selection of the viscosity models applied 2. Dough rheological model in numerical applications is given here; more complete descriptions of such models and The characterization of a non-Newtonian, fundamental knowledge of non Newtonian steady state, incompressible flow, is provided models are available in many references [33- by the conservation of mass and momentum 44]. equations, respectively. (1) .0u 2. 1. The power law (Ostwald de Waele) model
(2) .0 The relationship between shear stress and shear
rate for a shear-thinning fluid can often be The stress tensor σ is defined by Eq. (3), where approximated by a straight line over a limited a constitutive equations or rheological model is range of shear rate (or stress). For this part of required to define the deviatoric stress tensor . the flow curve, an expression of the following In constitutive models, the deviatoric stress form is applicable: tensor is described as the sum of the (6) m n 1 viscoelastic component , and the purely m n Where and are the fluid consistency Newtonian component 2 (Eq. (4)). coefficient and the flow behavior index respectively. The apparent viscosity for the so- pI (3) called power-law (or Ostwald de Waele) fluid is (4) thus given by Eq. (7) [38]. 12 yx n1 m()xy (7) Where 2 is given by Eq. (5) where D is the yx rate of deformation tensor. The power-law models are the preferred 2 D (5) 22 rheological model due to their ability to predict velocity and pressure distributions in uniform Among all attempts that have been made to flows [19] and the simplest representation of formulate the constitutive equations, those for shear thinning behavior [38]. However, their viscoelastic materials have encountered application in the process engineering difficulties due to their considerable encounters following shortcomings: nonlinearity [32]. In characterizing dough a. These models should be applied over only a rheological behavior, more powerful models are limited range of shear rates and therefore the linear differential viscoelastic models like the fitted values of m and n will depend on the generalized Maxwell models, nonlinear integral range of shear rates [38]. viscoelastic models sucArchiveh as the Bird-Carreau of SID b. They are not able to predict zero and infinite and Wagner models and nonlinear differential shear viscosities [38]. models. The latter is of the particular interest in c. The dimensions of the flow consistency numerical simulations, which is used for coefficient, m, depend on the numerical value process design, optimization and scale-up. [19] of n and therefore the m values must not be However, till 2000, due to high computational compared when the n values differ [38]. costs and lack of advanced software, there was d. They are seldom able to provide accurate a scarcity of work in viscoelastic flow analysis predictions of measurements of important in extruder channels. However, nowadays, operating parameters such as Specific complicated calculations are possible using the Mechanical Energy (SME) and Residence Time Distribution (RTD) [19].
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The Upper Convected Maxwell model is a 2. 2. Maxwell model generalization of the Maxwell material for the case of large deformations using the Upper Certainly, the most striking feature connected convected time derivative. The model was with the deformation of a viscoelastic substance proposed by James G. Oldroyd [47] and is is its simultaneous display of 'fluid-like' and represented by Eq. (10). 'solid-like' characteristics [38]. Consequently, the idea of a linear combination of elastic and 2 D (10) viscous properties by using mechanical analogues involving springs (elastic component) and dash pots (viscous action) has is the stress tensor; is the relaxation time; affected the early efforts in quantitative description of viscoelastic behavior [38]. is the upper convected time derivative of Like other viscoelastic materials, dough was stress tensor; is the material viscosity at primarily characterized in terms of a simple D Maxwell model [8]. As shown in Fig. 1, the steady simple shear and is the tensor of the deformation rate. Maxwell model can be represented by a purely elastic spring and a purely viscous damper The convected derivative and the rate of connected in series, with the individual strain deformation tensor are defined by: 1 2 rates of and respectively. This model D T follows the following Eq. (8) [38]. [uu .] [. ] Dt
(11) dd .(uu ) ( )T . .( u ) 12 (8) t 12dt dt 1 D[( uu ) ( )T ] (12) Combining above equation with the Hooke's 2 law of elasticity and Newton's law of viscosity, one can obtain: Using the upper convected Maxwell model, Bagley et al. [16] tried to interpret the results of extensional deformation of viscoelastic dough. (9) Their study showed that the upper convected Maxwell model is particularly convenient for an In which is the stress tensor, total strain initial analysis of a constant crosshead speed rate tensor, is the time derivative of , is experiment on dough, and the governing the viscosity of the dashpot (viscose) fluid and differential equations can be easily solved numerically [16]. ( /)G is the relaxation time, which is a characteristic of the fluid. An important feature 2. 3. Oldroyd-B of the MaxwellArchive model is its predominantly of SID fluid-like response. A more solid-like behavior Another form of viscoelastic model is Oldroyd- is obtained by considering the Voigt model B model [32]: which is represented by the parallel arrangement of a spring and a dashpot, as 1 112( 1dd 2 ) 0 shown in Fig. 2. (13) Subsequent research showed that dough possesses complex viscoelastic properties that d is the rate of deformation tensor, 0 is the can only be represented by a generalized Maxwell model which includes a distribution of shear viscosity, 1 is the relaxation time and 2 relaxation times (Fig. 3) [8, 14, 45, and 46]. is the second relaxation parameter (retardation
www.SID.ir133 JCARME S. M. Hosseinalipour et al. Vol. 1, No. 2, March 2012 time [33]). As it was previously (Eq. (11)) Since the magnitudes of 1700 of food polymer described is upper convected derivative. dispersions with concentrations of practical interest are usually very low in magnitude, they 0 1) 1 the model simplifies to a second-order are difficult to determine experimentally. fluid with a vanishing second normal stress Therefore, to avoid consequent errors in coefficient [33]. estimation of the other rheological parameters 0 2) 2 the model reduces to the convected in Eqs. (14) and (15), is usually neglected Maxwell model [33]. [49,50].
3) 12 the model reduces to a Newtonian fluid with viscosity 1 [33]. 2 (1 ) n1 D 0 2. 4. Cross and Carreau model (16)
The cross model [48] is a four parameter model In general, the model of Cross has been used in which is written as [34]: studies in Europe and that of Carreau in North America.
2. 5. Bird-Carreau model 0 1( )m The Bird-Carreau model [51] is a nonlinear c (14) extension of the generalized Maxwell model. It 0 uses four empirical constants ( 1 , 1 , 2 and 2 N [1 ( ) ] 2 ) and the zero shear rate viscosity, 0 . Two c (15) constants, 1 and 1 are typically obtained where c and c are time constants related to the relaxation times of the polymer in solution from a logarithmic plot of vs. and the
Archive of SID
Fig. 1. Schematic of Fig. 2. Schematic of the Fig. 3. Schematic of the the Maxwell model. Voigt model. generalized Maxwell model.
and m and N are dimensionless exponents.
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These models are appropriate for liquid-like other two constants 2 and 2 are obtained materials; they may yield the right behavior in a ' from a logarithmic plot of vs. [52]. ( is specific type of flow, but they are not appropriate in all types of deformations [21]. ' the viscosity function, is the dynamic More complete description of this model is viscosity and is the frequency) [53]. provided in many publications especially in The Bird-Carreau prediction for is [52, 53]. [51] and [52]. The Bird-Carreau-Yasuda model is more complex and has the advantage of predicting both Newtonian and pseudo plastic behavior of 1 2 polymers, as well as the transition region and 1( 1 ) contains five parameters. Mathematically the (17) Bird-Carreau-Yasuda model can be expressed At large shear rates the above equation is as follows [54]: approximated by [53]: 1 (1 11 ) / (2 ) an( 1) / a 0 1 (18) [1 ( ) ] (24) Z ( )1 1 1 2 sin(1 ) 0 1 2 1 where is shear viscosity,0 is the zero-shear-
2 1 () 11 1 (19) rate viscosity, is the infinite-shear-rate 1 viscosity, is the time constant, is the shear 0 (20) rate, and n is the power law index. In the 1 original Bird-Carreau model the constant a 1 equals to 2. In many cases the infinite-shear- Zk()1 (21) 1 rate viscosity is negligible, reducing Eq. (24) to ' a three parameter model [54]. The Bird-Carreau prediction for is [53]: Dus and Kokini [6] simulated the nonlinear ' viscoelastic properties of wheat-flour dough (22) with the Bird-Carreau model. Although, this 1( )2 1 2 model showed significant deviation from ' and at high frequencies is approximated by primary normal stress coefficient data, it was [53]: adequate to predict steady shear viscosity and small amplitude oscillatory properties. (22 )(1 12 ) / ' 0 2 Thereafter, Wang and Kokini [8] investigated Z( )1 12 the applicability of the Bird-Carreau model in 1 2 sin( 21 ) 2 2 predicting steady shear viscosity and primary 2 Archive (23) normalof stress SID coefficient data of gluten dough as a function of water content at two temperatures. The results reported that the small The Bird-Carreau model approximates the amplitude oscillatory shear properties could be polymeric material as a loosely held structure successfully simulated using the Bird-Carreau where temporary network junctions are constitutive model. However, the primary continuously formed and then destroyed during normal stress coefficient was overpredicted. shear. This structural concept appears to be 2. 6. Giesekus-Leonov model quite appropriate for wheat-flour dough since wheat gluten is a high molecular weight Giesekus [55] proposed a constitutive model biological polymer whose components have based on a concept of configuration-dependent been demonstrated to form entanglements [8].
www.SID.ir135 JCARME S. M. Hosseinalipour et al. Vol. 1, No. 2, March 2012 molecular mobility. According to this model, this approach, the model proposed by Phan the viscoelastic component of the extra stress Thien and Tanner [20,18,26] was claimed to tensor is represented by Eq. (25) with four correctly describe the nonlinear behavior of viscoelastic fluids, especially viscoelastic 1 2 parameters , , and . Due to the highly properties of wheat flour doughs [56]. The nonlinear nature of the model equations, all of original Phan-Thien Tanner equations was the properties need to be obtained numerically written using both of the following [12]. modifications simultaneously: the Gordon Schowalter derivative and the segment kinetics 11 1 term [35]. It employs specific forms for the I ij ij ij ij 2 1 ij (25) creation and destruction rates of the network 1 junctions in the network theory of Lodge and The parameter is the dimensionless Giesekus Yamamoto [56]. model mobility factor and controls the Although the Phan-Thien Tanner model extensional viscosity and the ratio of second overpredicts the shear viscosity at higher shear rates and the transient and extensional normal stress difference to the first one. 0 properties, it accurately predicts the zero shear represents shear thinning behavior [12]. viscosity 0 and seems to be suitable for numerical simulations of wheat flour doughs. 2. 7. White-Metzner model It is worth noting that, compared to the integral
models such as the Bird-Carreau and Wagner Modification of the viscosity and relaxation models, the differential models such as the parameter as a function of the shear rate, Phan-Thien Tanner model provide robust leads to the White-Metzner model. This model numerical algorithms [56] and exhibits good exhibits shear thinning, not because of behavior in FEM simulations [23]. The nonaffine motion, but because the relaxation is interested reader is referred to [35] for more accelerated at high strain rates, where the accurate comparison between the Wagner relaxation is faster than any deformation [32] model (as integral model) and the PTT model. (The use of molecular considerations based on In the PTT model, the extra stress tensor is nonaffine Network Theories will result in the considered as the sum of the viscoelastic PIT model [32] which will be discussed in the component1 next section). , and the purely Newtonian In this model the viscoelastic component of the component 2 (Eq. (27)) [12]. extra stress tensor is given by Eq. (26) [12]. (27) 12 In which 2 is given by Eq. (28) where D is the 11 2 (26) ij ij 1 ij strain rate tensor. 2 D (28) The functions 1 and can be obtained from 22 ArchiveThe finalof form ofSID the PTT model for the the experimental shear viscosity curve and the experimental first normal stress curve, viscoelastic component1 is expressed by Eq. respectively. Constant, Power law, and Bird- (29) [12]. Carreau types can be considered for these two functions [12].
exptr ( ) (1 ) 2 D (29) 2. 8. Phan-Thien-Tanner model 11 1 1 22
The literature describes many attempts to improve the Upper Convected Model [35]. In
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D Osswald and Hernández-Ortiz [33] provided a [uu .] [. T ] Dt (30) valuable general form of viscoelastic models represented in Eq. (32). and are the adjustable parameters and and are the partial viscosity and relaxation Y { . . } {.} [ ] time respectively which can be measured from 1 (1) 2 3 0 4 ( 2) the equilibrium relaxation spectrum of the fluid (32) [12]. The operators and are the upper where (1) is the first contravariant convected convected derivative (Eq. (11)) and lower time derivative of the deviatoric stress tensor convected derivative (Eq. (30)), respectively. and represents rates of change with respect to a The Phan-Thien Tanner model can be solved convected coordinate system that moves and using a single relaxation time or multiple deforms with the fluid. All constants are relaxation times, similar to the Giesekus model defined in Table. 1 for various viscoelastic [12]. models commonly used to simulate dough like materials. The convected derivative of the 2. 9. Mackey & Ofoli model deviatoric stress tensor is defined by Eq. (33).
D T Modifying the model of Morgan et al. [56], (1) [(uu ) . .( )] Mackey et al. [57] proposed a model for the Dt (33) viscosity of starch-based products related in Eq. (31). Similar summaries of viscoelastic models using general forms can be found in other references = + ̇ [36]. ̇
3. Models and parameters used in numerical { [( / ) + ( − )]} applications 1 + [1 − (− )] {1 − (− )} Vergnes and Villemaire [58] investigated the (31) effects of temperature, moisture content and intensity of the treatment on the rheological This model provides accurate results for behavior of a molten maize starch in a low predicting the viscosity of relatively pure hydrated phase. In this approach, they applied a starches such as potato flour [57] and corn power law model with an exponential starch [7] and does not account for non starch dependence on temperature, water content and components. However, Mackey and Ofoli [7] mechanical energy provided to the product evaluated the viscosity of whole wheat flour before measurement. Moreover, they introduced a dependence on temperature and doughs (which contains significant levels of m non starch components) at low to intermediate water content for the pseudoplasticity index , moisture content.Archive They incorporate the effects whichof has beenSID observed in different papers of shear rate, temperature, moisture content, [59, 60] but never quantified. They have also time-temperature history, and strain history. summarized different expressions that had been Due to the presence of flour components such reported before 1987 in the literature to as bran, protein, and lipids, (which the model describe the rheological behaviour of starchy does not account for) the accuracy of products in three simplified expressions [58]: rheological modeling for whole wheat flour was m1 (34) K not nearly as good as had been observed in E m1 previous studies of corn starch and potato flour. K0 exp( )expMC (35) RT Kexp( bT ) exp MC m1 (36) 0
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Table 1. Definition of constants in Eq. (32)[33].
Model Parameters
Constitutive Model Y 1 2 3 4 Generalized 1 0 0 0 0 Newtonian Upper Convected 1 0 0 0 Maxwell 1 White-Metzner 1 0 0 0 1() 1 Pahn-Thien Tanner -1 exp( ( / )tr ) 0 0 0 2
Pahn-Thien Tanner -2 1 (/0 )tr
Giesekus 1 1 0 (10 /) 0
characteristics and formation of this complex Eq. (35) has been used by Fletcher et al. [61] material. Since rheometers do not provide the and Senouci et al. [62] to characterize maize necessary information for all important grits, and by Cervone and Harper [60] in the rheological properties, constitutive equations case of pregelatinised maize flour. Eq. (36) are ultimate tools for effective control of particularly has been used by Yacu [59] on process. wheat starch [58]. Vergnes and Villemaire [58] The development of valuable models for showed that in comparing the results obtained, complex dough behavior and the search for the main difficulty comes from the variety of appropriate constitutive equations to describe products. Table. 2 shows the scatter of the this complex behavior have been a high priority predicted parameters characterizing the of most scientific researches. However, viscosity over a wide range, even for equal understanding the mechanical behavior of products. Moreover, they claimed that their wheat flour dough is a formidable challenge. results are the first to take into account the Consequently, due to high computational costs, influence of thermomechanical history on there has been a scarcity of work in numerical viscosity. Facilitating the progress achieved simulation of the flow behavior of the wheat over the years, more researches have been flour dough, particularly in the numerical carried out. simulation of the viscoelastic flow analysis in In order to summarize this paper and also to the relevant dough preparation apparatuses. provide a useful and complete collection of Perhaps Vergnes and Villemaire’s [58] effort models, their relevantArchive parameters and can beof considered SID as the pioneer researches applications which simplifies furthere access, a conducted in categorizing and comparing large number of constitutive equations reported models for starchy products, generally, employed for the simulation of dough like and for wheat dough, particularly. In this study, materials are summarized in Table 2. the authors try to provide a useful collection of models which simplifies further access of 4. Conclusions researchers. This approach can be developed in the near future by studying the rheological Understanding the complex behavior of dough- behavior of other starchy products. like materials and interpreting it as one general equation require a vast knowledge of the
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References Cereal Chemistry. 67(3) , pp. 221-226. (1990 b). [1] Dhanasekharan, K. M. Wang, C. F. and [8] Wang C. F. and Kokini J. L. "Prediction Kokini, J. L. "Use of Nonlinear of the Nonlinear Viscoelastic Properties Differential Viscoelastic Models to of Gluten Doughs.", Journal of Food Predict the Rheological Properties of Engineering , pp. 297-309. (1994). Gluten Dough.", Journal of Food [9] Bagley, E. B. Dintzis, F. R. and Process Engineering , Vol. 24, pp. 193- Chakrabarti, C. "Experimental and 216. (2001). Conceptual Problems in the Rheological [2] Schofield, R. K. and Scott Blair, G. W. Characterization of Wheat Flour "The Relationship Between Viscosity, Doughs.", Rheol Acta., Vol. (37), pp. Elasticity and Plastic Strength of Soft 556-565. (1998). Materials as Illustrated by Some [10] Singh, N. and Smith, A. C. "Rheological Mechanical Properties of Flour Doughs.", Behavior of Different Cereals Using I. Proceedings of the Royal Society of Capillary Rheometry.", Journal of Food London, Series A, Vol. 138 , pp. 707- Engineering , Vol. 39, pp. 203-209. 719. (1932). (1999). [3] Schofield, R. K. and Scott Blair, G. W. [11] Wang, C. F. and Kokini J. L. "Simulation "The Relationship Between Viscosity, of the Nonlinear Rheological Properties Elasticity and Plastic Strength of Soft of Gluten Dough Using the Wagner Materials as Illustrated by Some Constitutive Model.", Journal of Mechanical Properties of Flour Doughs.", Rheology , Vol. 39(6), pp. 1465-1463. II. Proceedings of the Royal Society of (1995 b). London. Series A, Vol. 139 , pp. 557- [12] Dhanasekharan, .K. M., Huang, H. and 566. (1933a). Kokini, J. L. "Comparison of Observed [4] Schofield, R. K. and Scott Blair, G. W. Rheological Properties of Hard Wheat "The Relationship Between Viscosity, Flour Dough with Predictions of the Elasticity and Plastic Strength of Soft Giesekus-Leonov, White-Metzner and Materials as Illustrated by Some Phan-Thien Tanner Models.", Journal of Mechanical Properties of Flour Doughs.", Texture Studies , Vol. 30, pp. 603-623. III. Proceedings of the Royal Society of (1999). London. Series A, Vol. 141 , pp. 72-85. [13] Dhanasekharan, .K. M. and Kokini, J. L. (1933b). "Viscoelastic Flow Modeling in The [5] Schofield, R. K. and Scott Blair, G. W. Extrusion of a Dough-Like Fluid.", "The Relationship Between Viscosity, Journal of Food Process Engineering , Elasticity and Plastic Strength of Soft Vol. 23, pp. 237-247. (2000). Materials as Illustrated by Some [14] Cunningham, J. R. and Hlynka, I. Mechanical Properties of Flour Doughs.", "Relaxation Time Spectrum of Dough IV. ProceedingsArchive of the Royal Society of ofand theSID Influence of Temperature, Rest, London. Series A, Vol. 160 , pp. 87–94. and Water Content.", Journal of Applied (1937). Physics , Vol. 25, pp. 1075-1081. (1954). [6] Dus, S. J. and Kokini, J. L. "Prediction of [15] Bagley, E. B. and Christianson, D. D., the Nonlinear Viscoelastic Properties of "Stress Relaxation of Chemically Hard Wheat Flour Dough Using the Bird- Leavened Dough-Data Reduction Using Carrea Constitutive Model.", Journal of the BKZ Elastic Fluid Theory.", The Rheology , Vol. 34(7), pp. 1069-1084. Society of Rheology , Vol. 31(5), pp. (1990). 405-413 . (1987). [7] Mackey, K. L. and Ofoli, R. Y. [16] Bagley, E. B., Christianson, D. D. and "Rheology of Low- to Intermediate- Martindale, J. A., "Uniaxial Compression Moisture Whole Wheat Flour Doughs.", of a Hard Wheat Flour Dough: Data
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Analysis Using the Upper Convected Finite Element Method Simulation with Maxwell Model.", Journal of Texture Particle Tracking.”, Journal of Food Studies , Vol. 19, pp. 289-305. (1998). Engineering , Vol. 79, pp. 956-969. [17] Bagley, E. "Food Extrusion Science and (2007). Technology",. New York, Marcel [26] Phan-Thien, N. and Tanner, R. I. “A New Dekker, (1992). Constitutive Equations Derived from [18] Phan-Thien, N. and Safari-Ardi, M. Network Theory.”, Journal of non- "Linear Viscoelastic Properties of Flour– Newtonian Fluid Mechanics. , Vol. 2 , Water Doughs at Different Water pp. 353-365. (1977). Concentrations.", Journal of Non- [27] Connelly, R. K. and Kokini, J. L. “The Newtonian Fluid Mech , Vol. 74, pp. Effect of Shear Thinning and Differential 137-150. (1998). Viscoelasticity on Mixing in a Model 2D [19] Leonard, A. L. Cisneros, F. and J. L. Mixer as Determined using FEM with Kokini “Use of the Rubber Elasticity Particle Tracking.”, Journal of Non- Theory to Characterize the Viscoelastic Newtonian Fluid Mechanics , Vol. 123, Properties of Wheat Flour Doughs.”, pp. 1-17. (2004). American Association of Cereal [28] Binding, D. M., Couch, M. A., Sujatha, Chemists, Inc. , Vol. 76(2), pp. 243-248. K. S. and Webster, M. F. “Experimental (1999). and Numerical Simulation of Dough [20] Phan-Thien, N. Safari-Ardi, M. and Kneading in Filled Geometries.”, Morales-Patifio, “A. Oscillatory and Journal of Food Engineering , Vol. 58, Simple Shear Flows of a Flour-Water pp. 111-123. (2003). Dough: a Constitutive Model.”, Rheol [29] Sujatha, K. Ding, D. and Webster, M. F. Acta , Vol. 36, pp. 38-48. (1997). “Modelling of Dough Mixing with Free [21] Phan-Thien, N., Newberry, M. and Surfaces in Two and Three Tanner, R.I. “Non-Linear Oscillatory Dimensions.”, Sixth International Flow of a Soft Solid-Like Viscoelastic Conference on Computational Modelling Material.”, Journal of Non-Newtonian of Free and Moving Boundary Problems Fluid Mech. , Vol. 92, pp. 67-80. (2000). (pp. 102-111). Lemnos, Greece: Brebbia [22] Dhanasekharan, .K. M. and Kokini, J. L. CA, Sarler B (eds). (2001). “Design and Scaling of Wheat Dough [30] Sujatha, K. S. Webster, M. F. Binding, Extrusion by Numerical.”, Journal of D.M. and Couch, M.A. “Modelling and Food Engineering , Vol. 60, pp. 421-430, Experimental Studies of Rotating Flows (2003). in Part-Filled Vessels: Wetting and [23] Connelly, R. K. and Kokini, J. L. “2-D Peeling.”, Journal of Food Engineering , Numerical Simulation of Differential Vol. 57, pp. 6-79. (2003). Viscoelastic Fluids in a Single-Screw [31] Balouch, A. and Webster, M. F. Continuous Mixer: Application of “Distributed Parallel Computation for Viscoelastic FiniteArchive Element Methods.”, Complexof RotationalSID Flows of Non- Advances in Polymer Technology , Vol. Newtonian Fluids.”, International 22(1), pp. 22-41. (2003). Journal for Numerical Methods in [24] Connelly, R. K. and Kokini, J. L. “3D Fluids, Vol. 43, pp. 1301-1328. (2003). Numerical Simulation of The Flow of [32] Loh, K. W. L, Tay, A. A. O and Teoh, Viscous Newtonian and Shear Thinning S.H. “Effect of Constitutive Models on Fluids in a Twin Sigma Blade Mixer.”, the Numerical Simulation of Viscoelastic Advances in Polymer Technology , Vol. Flow at an Entry Region.”, Polymer 25(3), pp. 182-194. (2006). Engineering and Science, Midauust [25] Connelly, R. K. and Kokini, J. L. 1996, , Vol. 15(36), pp. 1990 -2000. “Examination of The Mixing Ability of (1996). Single and Twin Screw Mixers Using 2D
140 www.SID.ir JCARME A review of dough . . . Vol. 1, No. 2, March 2012
[33] Osswald, T.A. and Hernández-Ortiz, J.P. Can. J. Technol. , Vol. 31, pp. 98-108. “Polymer Processing Modelling and (1953). Simulation.” Munich: Hanser Publishers. [46] Barney II,J.E., Pollock, H.B. and Bolze, (2006). C.C. “A Study of the Relationship [34] Rao, M. “Rheology of Fluid and Semi Between Viscoelastic Properties and the Solid Foods, Principels and Chemical Nature of Wheat Gluten and applications.” Maryland: Aspen Glutenin.”, Cereal Chemistry , Vol. 42, Publishers, (1999). pp. 215-235. (1965). [35] Piau, J. M. and Agassant, J. F. “Rheology [47] Oldroyd, J. “On the Formulation of for Polymer Melt Processing.”, Rheological Equations of State.”, Amsterdam, Lausanne, New York, Proceedings of The Royal Society A: Oxford, Shannon, Tokyo: Elsevier. Mathematical, Physical and Engineering (1996). Sciences , 200(1063), 523-521. (1950). [36] Barnes, H. A. Hutton, J. F. and Waiters [48] Cross, M. “Rheology of Non-Newtonian K.F.R.S. “An Introduction to Rheology.”, Fluids: A New Flow Equation for Amsterdam, London, New York, Tokyo : Pseudoplastic Systems.”, Journal of Elsevier, (1989). Colloid Science , Vol. 20, pp. 417–437. [37] Brennan, J. “Food Processing (1965). Handbook.”, Weinheim: Wiley-VCH. [49] Abdel-Khalik, S.I., Hassager, O. and (2006). Bird. R.B. “Prediction of Melt Elasticity [38] Chhabra, R.P. and Richardson, J.F. “Non- from Vscosity Data.”, Polymer Eng and Newtonian Flow in the Process Sci. , Vol. 14, pp. 859-867. (1974). Industries.” Oxford: Butterworth- [50] Lopes da Silva, J. A. L., Goncalves, M. Heinemann, (1999). P. and Rao, M. A. “Rheological [39] Schramm, G. “Practical Approach to Properties of High-Methoxyl Pectin and Rheology and Rheometry.”, Karlsruhe: Locust Bean Gum Solutions in Steady Gebrueder HAAKE Gmbh. (1998). Shear.”, J Food Sci. , Vol. 57, pp. 443- [40] Braun, D. B. and Rosen, M. R. “Rheoligy 448, (1992). Modifiers Handbook, Practical Use and [51] Bird, R. B. and Carreau, P. J. “A Non- Applications.” New York: William Linear Viscoelastic Model for Plymer Andrew Publishing. (2000). Solutions and Melts.”, Chemical [41] Skelland, A. “Non-Newtonian Flow and Engineering Science , Vol. 23, pp. 427- Heat Transfer.”, New York: Wiley. 434, (1968). (1967). [52] Bird, R. B., Hassager, O. and Armstrong, [42] Wilkinson, W. “Non-Newtonian Fluids R. C. “Dynamics of Polymeric Liquids: Fluid Mechanics, Mixing and Heat Fluid Mechanics.”, Wiley-Interscience Transfer.”, London: Pergamon Press. publication. (1977). (1960). [53] Kokini, J. L. Bistany, K. L. and Mills, P. [43] Schowalter,Archive W. “Mechanics of Non- ofL. " PredictingSID Steady Shear and Dynamic Newtonian Fluids.”, Oxford: Pergamon Viscoelastic Properties of Guar and Press, (1978). Carrageenan Using the Bird-Carreau [44] Siginer, D. A. De Kee, D. and Chhabra, Constitutive Model. ", Journal of Food R.P. “Advances in the Flow and Science , Vol. 49, pp. 1569-1576. (1984). Rheology of Non-Newtonian Fluids.”, [54] Naranjo, A. del Pilar Noriega, M., Amsterdam: Elsevier. (1999). Osswald, T., Roldan-Alzate, A. and [45] Cunningham, C. J. Hlynka, I. and Diego Sierra, "Plastics Testing and Anderson, J.A. “An Improved Characterization: Industrial Relaxometer for Viscoelastic Substances Applications.", Munich: Hanser Gardner. Applied to the Study of Wheat Dough.”, (2008).
www.SID.ir141 JCARME S. M. Hosseinalipour et al. Vol. 1, No. 2, March 2012
[55] Giesekus, H. "A Simple Constitutive [65] Breuillet, C. Yildiz, E, CUQ, B. and Equation for Polymeric Fluids Based on Kokini, J. L. "Study of the Anomalous the Concept of Deformation Dependent Capillary", Journal of Texture Studies, Tensorial Mobility. ", Journal of Non- Vol. 33, pp. 315-340, (2002). Newtonian Fluid Mechanics , Vol. 11, [66] Ding, D. and Webster, M. F. "Three- pp. 69-109. (1982). Dimensional Numerical Simulation of [56] Morgan, R. G. Steffe, J. F. and Ofoli, R. Dough Kneading", XIII Int. Cong. on Y. "A Generalized Viscosity Model for Rheol., British Society of Rheology, Vol. Extrusion of Protein Doughs. ", Journal 2, pp. 318-20.(2000). of Process Engineering , Vol. 2, pp. 57- 78. (1989). [57] Mackey, K. L. Ofoli, R. Y. Morgan, R. G. and Steffe, J. F. "Rheological Modeling of Potato Flour During Extrusion Cooking. ", Journal of Food Process Engineering , Vol. 12, pp. 1-11. (1989). [58] Vergnes, B. and Villemaire, J. P. "Rheological Behaviour of Low Moisture Molten Maize Starch. ", Rheologiea Acta , pp. 570-576. (1987). [59] Yacu, W. "Modeling a Twin Screw Co- Rotating Extruder.", Journal of Food Process Engineering , Vol. 8, pp. 1-21. (1985). [60] Cervone, N. W. and Harper, J. M. "Viscosity of an Intermediate Moisture Dough.", Journal of Food Process Engineering , Vol. 2, pp. 83-95. (1978). [61] Fletcher, S. I., McMaster, T. J. Richmond, P. and Smith, A. C. "Rheology and Extrusion of Maize Grits. ", Chem. Eng. Communications , Vol. 32, pp. 239-262. (1985). [62] Senouci A. and Smith A.C. "Analysis of a Corotating Twin Screw Extruder.", In: Cuisson-Extrusion, Ed. INRA, Paris, (1986). [63] Wang C. F. and ArchiveKokini J. L. "Prediction of SID of the Nonlinear Viscoelastic Properties of Gluten Doughs.", Journal of Food Engineering , pp. 297-309, (1995 a). [64] Prakash, S. Karwe, M. V. and Kokini, J. L. "Measurement of Velocity Distribution in the Brabender Farinograph as a Model Mixer, using laser-doppler anemometry.", Journal of Food Process Engineering , Vol. 22, pp. 435-452. (1999).
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