Chapter 15
Measurement and Interpretation of Batter Rheological Properties Hulya Dogan Department of Grain Science and Industry Kansas State University Manhattan, Kansas, U.S.A. Jozef L. Kokini Department of Food Science and Human Nutrition University of Illinois at Urbana-Champaign Champaign, Illinois, U.S.A.
Overview Throughout this book, the reader finds references to physicochemical properties of batters and their significance in transporting, coating, and frying. The fundamental rheological characterization of batter designed for coating is an area of great importance and potentiality. Therefore, in this chapter we have attempted to explain the basic rheological principles related to batter systems. Further, we included discussion of current research on the rheology of cake batters systems, which bear an appreciable rheological similarity to food-coating batter systems. Thus, the methodology and functional explanations used for cake batters are also applicable to food coatings and may provide guidelines for future investigations. Rheology is the science of the deformation and flow of matter. Rheological properties define the relationship between stress and strain or strain rate in different types of shear and extensional flows. The rheological characterization of foods provides important information for food scientists regarding ingredient selection strategies that assist with the design, improvement, and optimization of their products; the selection and optimization of their manufacturing processes; and the design of packaging and storage strategies. Changes in rheological properties of material reveal changes in the material’s molecular structure, and therefore rheological measurements can provide a means of monitoring changes in product structure during a process. When subjected to an applied force, all materials deform in characteristic ways. If the material is a fluid, it deforms continuously. The strain and shear rate provide a measure of the rate of deformation imposed upon the material. If the material is a solid, it eventually reaches an equilibrium displacement, which can be quantified through the concept of strain. In this instance, strain becomes a measure of relative displacement. 263
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The specific relationship between the applied stress (force divided by area) and the resulting strain or strain rate results in a rheological property. A rheological measurement is conducted on a given material by imposing a well-defined stress and measuring the resulting strain or strain rate, or by imposing a well-defined strain or strain rate and then measuring the stress developed. The relationship between these physical events leads to different kinds of rheological properties. Rheological properties can be expressed empirically in terms of material functions that relate specific components of stress to specific components of strain rate or in terms of constitutive models that relate all components of stress to all components of strain or strain rate. Figure 15.1 shows how a force or a deformation imposed upon a given material is transformed to obtain a material function or constitutive model (Darby1976). STEADY-SHEAR RHEOLOGY OF FLUID AND SEMISOLID FOODS Simple shear is one of the most useful types of deformation for rheological measurements of fluid materials. The definitions of shear stress and shear rate in simple shear flow are shown in Figure 15.2. The steady-shear rheology of fluids is classified according to the shape of the curve of shear stress versus shear rate. The most common flow curves are shown in Figure 15.3. The flow curve for a Newtonian fluid is a straight line through the origin, where the slope of the line is equal to a Newtonian viscosity, μ. The mathematical relationship for this sort of material is Newtonian model
(1)
where is shear stress and is shear rate. When the relationship between shear stress and shear rate is nonlinear, the resulting curves represent nonNewtonian behavior. For dilatant or shear-thickening fluids, the viscosity is an increasing function of the shear rate, whereas for pseudoplastic or shear-
Fig. 15.1. Physical and mathematical relation between force, deformation, and material properties. (Reprinted, with permission, from Darby 1976)
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thinning fluids, the viscosity is a decreasing function of the shear rate. The flow curves of Bingham plastic and of Herschel-Bulkley fluids have a positive intercept, referred to as the yield stress, 0, which is the minimum shear stress necessary to initiate flow. It is mainly attributed to strong interparticle interactions in the three-dimensional structure of the material that are capable of resisting deformation at small shear rates (Dzuy and Boger 1983). Bingham plastic fluids have linear flow curves with a yield stress, whereas HerschelBulkley fluids are nonlinear materials with yield behavior. The most commonly used empirical models to define the shear dependency of fluid materials are Generalized model (power-law model),
k n
(2)
Bingham plastic,
0
(3)
where k is consistency index (Pa.s), τ0 is yield stress, and n is flow behavior index. Pseudoplastic fluids (n<1) display decreasing viscosity with an increasing shear rate. This type of behavior is also called shear-thinning. Dilatant fluids (n>1) are characterized by increasing viscosity with an increase in shear rate. Dilatancy is also referred to as shear-thickening. Generalized model with yield stress (Herschel-Bulkley model),
0 k n
Fig. 15.2. Steady simple shear flow. A = area, F = force tangentially applied to surface A, v = velocity, t = time.
Fig. 15.3. Classification of fluid flow behavior.
(4)
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Fig. 15.4. Qualitative behavior of shear stress () and shear rate ( )for thixotropic and rheopectic materials.
For n = 1 and yield stress 0 = 0, the flow characteristics of Herschel-Bulkley fluids are those of a Newtonian fluid. The viscosity of some materials is not only dependent upon shear rate but depends also on the time they are subjected to shear. If the viscosity decreases with time under conditions of constant shear rate, the material is called thixotropic; if it increases with time, the material is rheopectic (Fig. 15.4). Simple shear flow, or viscometric flow, serves as the basis for many rheological measurement techniques (Bird et al 1987). The stress tensor in simple shear flow has two non-zero terms: 12 and 21. Three shear-ratedependent material functions are used to describe material properties in simple shear flow. Viscosity (), the first normal stress coefficient (ψ1), and the second normal stress coefficient (ψ2) are given in eqs. 5, 6, and 7. 12
Viscosity,
First normal stress coefficient,
1
11 22
N1 2
(6)
Second normal stress coefficient,
2
22 33 N 2 2 2
(7)
(5) 2
Among the viscometric functions, viscosity is the most important parameter for a food material. In the case of a Newtonian fluid, both the first and second normal stress coefficients are zero, and the material is fully described by a constant viscosity over all shear rates studied.
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Fig. 15.5. Normal stress function ( 12 ) as a function of shear rate ( ). (Reprinted, with permission, from Middleman 1975)
An important phenomenon for non-Newtonian materials is the development of normal stresses that relate to elasticity in the fluid. First normal stress data for a wide variety of food materials are available (Dickie and Kokini 1982, Lai and Kokini 1992, Wang and Kokini 1995). Normal stresses (N1 and N2) appear to be a power function of the shear rate. They are usually converted into material functions by dividing the normal stress differences by the square of the shear rate. The limiting behavior of this function at low shear rates is ψ12, which is a parameter like the Newtonian viscosity observed with many nonNewtonian materials at very low shear rates (Middleman 1968). This limiting first normal stress coefficient is constant as a function of shear rate in the lowshear-rate region. A typical primary normal stress function as a function of shear rate is shown in Figure 15.5. Normal stresses are responsible for the extrudate swell phenomenon observed with polymeric systems. Well-known practical examples demonstrating the presence of normal stresses are the Weissenberg or rod climbing effect and the die swell effect. Although the exact molecular origin of normal stresses is not well understood, they are considered to be the result of the elastic properties of viscoelastic fluids (Darby 1976) and are a measure of the elasticity of the fluids. TRANSIENT SHEAR STRESS DEVELOPMENT With many semisolid food materials, shear stresses overshoot at inception of steady-shear flow (Kokini and Plutchok 1987). These overshoots can range anywhere from 30 to 300% of their steady-state value, depending on the particular shear rate and material used. These stresses are of particular importance in the start-up of processes and in terms of affecting properties such as spreadability and thickness (Dickie and Kokini 1983) and also in the start-up of flow equipment. Transient shear stresses have been observed in a wide variety of materials. An example is given in the case of peanut butter in Figure 15.6. In this figure, simulation of the transient shear stress using the Bird-Leider equation is observed (Leider and Bird 1974). This model can be written as follows: Bird-Leider model,
xy m n 1 b t 1 e t / an
(8)
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where xy is shear stress; m and n are limiting viscous power-law parameters; is shear rate; t is time; a and b are adjustable parameters; and the time constant is m / 2m 1 / n n (9) with m' and n' being first normal stress power-law parameters. This equation converges to the power-law model observed with many food materials (Rao 1977). Cereal doughs and thick batters would also be expected to portray transient shear stress overshoots at inception of steady flow. VISCOELASTIC PROPERTIES OF FOOD MATERIALS Ideal solid and ideal liquid materials represent the extremes of rheological behavior. An ideal solid material deforms instantaneously when a load is applied. It returns back to its original configuration instantaneously (complete recovery) upon removal of the load. Ideal elastic materials obey Hooke’s law,
Fig. 15.6. Shear-stress development for peanut butter at 25°C, and a comparison of experimental data, with Bird-Leider model predictions. = shear stress. (Reprinted, with permission, from Kokini and Plutchok 1987)
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where the stress () is directly proportional to the strain (γ). The proportionality constant is called the modulus. An ideal fluid deforms at a constant rate under an applied stress, and the material does not regain its original configuration when the load is removed. The flow of a simple viscous material is described by Newton’s law, where the shear stress () is directly proportional the shear rate ( ). Most food materials exhibit characteristics of both elastic and viscous behavior and are called viscoelastic. Cereal doughs and batters are viscoelastic (Baird 1981). For a purely viscous material, applied stresses are solely a function of the rate of strain. For purely elastic materials, stresses are solely a function of the applied strain. The stress response of a viscoelastic material, on the other hand, is a function of both strain and strain rate, and such materials have both viscous and elastic properties. Furthermore, the response of the material also depends on the deformation history. The difference between viscous and elastic materials becomes most obvious in time-dependent experiments. The most commonly used experiments to determine the rheological properties of a viscoelastic material are creep and recoil, stress relaxation, and oscillatory tests (Fig. 15.7). In the creep and recoil test, a constant stress, 0, is applied for a finite time and then removed, and the resulting deformation is observed as a function of time, γ(t). In an ideal elastic material, the applied force is proportional to the resulting deformation, and the material recovers completely when the force is removed. The rheological property of interest is the ratio of strain to stress as a function of time, which is referred to as the creep compliance, J(t). The compliance has units of Pa–1, and it describes how compliant a material is. The greater the compliance, the easier it is to deform the material.
Fig. 15.7. Comparative response of linear viscous, elastic, and viscoelastic material. = shear stress, = strain, = shear rate, t = time. (Reproduced, with permission, from Darby 1976)