Constitutive equations Carreau model

There are numerous other GNF models, such as the Casson model (used in food rheology), the Ellis, the Powell-Eyring model, and the Reiner-Pillippoff model. These are reviewed in the literature. In Appendix A we list the parameters of the Power Law, the Carreau, and the Cross constitutive equations for common polymers evaluated using oscillatory and capillary flow viscometry. 

Constitutive equations were applied to simulate viscoelasticity of concentrated food polymer dispersions. Some fundamental and empirical models have been discussed in Section V. Among them, the Bird-Carreau constitutive model [Eqs. (89-94)] have been used for food polymer dispersions (Kokini et ai, 1984 Kokini and Plutchok, 1987b Plutchok and Kokini, 1986). 

This relation can be derived from several phenomenological models and also from molecular theory. According to the constitutive equation of Bird and Carreau, it holds for finite 7 even though equations 67 and 74 are limited to small 7. With large deformations or large strain rates, other nonlinear phenomena will... 

In this chapter we have developed the general constitutive equation for a viscous liquid. We found that by using the rate of deformation or strain rate tensor 2D, we can write Newton s viscosity law properly in three dimensions. By making the coefficient of 2D dependent on invariants of 2D, we can derive models like the power law. Cross, and Carreau. We also showed how to introduce a three-dimensional yield stress to describe plastic materials with models like those Bingham and Casson. We saw two ways to describe the temperature dependence of viscosity and the importance of shear heating. 

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