Non-Linear Diffusion - Non-linear diffusion II. Constitutive equations for mixtures of isotropic fluids

Abstract

In the preceding paper I (Adkins 1963) a theory for the diffusion and flow of fluid mixtures was formulated based upon hydrodynamical considerations. It was assumed that the mechanical properties of each constituent of the mixture could be described by means of constitutive equations for the stresses occurring in the equations of motion for that constituent, while the effect of the other components could be accounted for by the nature of the body forces in these equations. In the present work, some of the restrictions previously imposed upon the constitutive equations for the stresses and the body forces are removed. It is assumed that the stresses for a given constituent may depend upon velocity and acceleration gradients for all components of the mixture and that the body forces depend upon relative velocities and accelerations and upon velocity gradients. Invariance requirements are discussed, attention being confined to mixtures of isotropic fluids.