Some Simplified Equations from the Theory of Mixtures

Abstract

This chapter presents an overview of some simplified equations from the theory of mixtures. The theory of mixtures is based on an idea that is both obvious and appealing. A mixture is modeled as a number; a number of continuous bodies superposed in space. The form of the balance equations for each of the bodies is then taken to be essentially the same as for an isolated body. This chapter presents two sets of constitutive equations based on the formulation of the thermodynamics of mixtures. The peculiar virtue of these models is that they are quite simple; they involve only coefficients that should be experimentally accessible. But the observation about them that is most significant is that although they are linear constitutive equations, the equations of motion in both cases turn out to be nonlinear and it is at least very plausible that any more complicated constitutive model should lead to similar nonlinearities. A mixture of incompressible viscous fluids is considered in the chapter. Flow of an incompressible viscous fluid through a rigid porous medium is described in the chapter.