Rheological properties stress-strain relationship

The main reasons for studying rheology (stress-strain relationships) in this chapter are (1) to determine the suitability of materials to serve specific applications and (2) to relate the results to polymer structure and form. Studying structure-property relationships allows a better understanding of the observed results on a molecular level resulting in a more knowledgeable approach to the design of materials. 

Many lipid-based foods show time-dependent rheological behavior and a combination of these, for example, viscous-elastic and viscous-plastic. In general, lipids, from a rheological point of view, can be classified as Newtonian and non-Newtonian, as depicted in Figure 4.1. To characterize lipid properties, such as Newtonian and non-Newtonian behavior, several approaches can be taken and the stress-strain relationships obtained. 

A thermodynamic model was recently proposed to calculate the solubility of small molecules in assy polymers. This model is based on the assumption that the densiQr of the polymer matrix can be considered as a proper order parameter for the nonequilibrium state of the system (7). In this chapter, the fundamental principles of the model are reviewed and the relation of the model to the rheological properties of the polymeric matrix is developed. In particular, a unique relation between the equilibrium and non-equilibrium properties of the polymer-penetrant mixture can be obtained on the basis of a simple model for the stress-strain relationship. 

If you step back and think about it, the mechanical and rheological properties of many solids and liquids can be modeled fairly well by just two simple laws, Hooke s law and Newton s law. Both of these are what we call linear models, the stress is proportional to the strain or rate of strain. If we examine viscoelastic properties like creep, the variation of strain with time appears decidedly non-linear (see Figure 13-75). Nevertheless, it is possible to model this non-linear time dependence by the assumption of a linear relationship between stress and strain. By this we mean that if, for example, we measure the strain as a function of time in a creep experiment, then for a given time period (say 1 hour) the strain measured when the applied stress is 2o would be twice the strain measured when the stress was o. 

FIGURE 10.1 Rheological properties of an ideal solid (a) depicts the rheological representation of an ideal solid, whereas (b) displays the relationship between stress, strain, and time for an ideal solid. 

In reality we find a superposition of elastic and viscous effects in the strain-stress relationship. In 3D-rheology properties of a given system turned out to be described by the combination of... 

The measurement of rheological properties for non-Newtonian, lipid-based food systems, such as dilatant, pseudoplastic, and plastic, as depicted in Figure 4.1, are much more difficult. There are several measurement methods that may involve the ratio of shear stress and rate of shear, and also the relationship of stress to time under constant strain (i.e., relaxation) and the relationship of strain to time under constant stress (i.e., creep). In relaxation measurements, a material, by principle, is subjected to a sudden deformation, which is held constant and in many food systems structure, the stress will decay with time. The point at which the stress has decayed to some percentage of the original value is called the relaxation time. When the strain is removed at time tg, the stress returns to zero (Figure 4.8). In creep experi-... 

Rheology is the study of flow of matter and deformation and these techniques are based on their stress and strain relationship and show behavior intermediate between that of solids and liquids. The rheological measurements of foodstuffs can be based on either empirical or fundamental methods. In the empirical test, the properties of a material are related to a simple system such as Newtonian fluids or Hookian solids. The Warner-Bratzler technique is an empirical test for evaluating the texture of food materials. Empirical tests are easy to perform as any convenient geometry of the sample can be used. The relationship measures the way in which rheological properties (viscosity, elastic modulus) vary under a... 

Let us now turn to the relationship between stresses and strains. We have already addressed this in Chapter 3 where we discussed a very broad spectrum of rheological properties found in various systems, namely, elasticity, plasticity, viscosity, and their numerous combinations. Some of the significant limitations that we adapted include a consideration of a single stressed state of a uniform shear and of near steady-state processes. Here, we will limit ourselves to a discussion of a single rheological behavior, that is, elasticity, and will focus on the particular peculiarities and generalizations pertinent to this field. 

Since stress is homogeneous within the material, the strain rate is necessarily homogeneous, too, when steady conditions are reached, as a consequence of the constitutive equation (equation [7.16]). The rheological properties of a material subjected to the effect of shear stress ate readily determined using the relationship between the shear stress and the displacement of a wall. 

Figure 30 shows the various rheological behaviors in terms of shear stress-shear rate relationship. In this case, the modulus is not a constant but must be represented by a more complex material function (of shear stress or shear strain). The form of the material function would depend on the nature of the material, and those constant parameters which would appear in any analytical expression for this function then become the rheological properties of the material. 

Knowledge of the rheological properties of food pastes, slurries and sauces, such as ketchup, mayonnaise and salad creams, is important both for quality assurance and for optimizing industrial flow and mixing processes. Unfortunately, many food slurries and pastes are opaque and do not lend themselves to flow studies with conventional techniques such as laser Doppler anemometry. Moreover, conventional rheological measurements are model-dependent in that it is necessary to fit the data by assuming a function relationship between the stress and strain (or strain rate) and to assume a set of boundary conditions (such as slip or stick) at the fluid-container... 

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