A Phenomenological Theory of Diffusion in Multiphase Mixtures

This paper is devoted to a micromorphic description of multiphase mixtures whose behavior is influenced by the temperature rate as well. A brief discussion of the equations of balance of mixtures of micromorphic continua is given. Then we make the constitutive assumptions for the appropriate undetermined quantities in the equations, bearing in mind that the classical diffusion equation is of parabolic character and consequently predicts an infinite speed of propagation. This fact calls for the formulation of a generalized thermodynamics of the mixture. Attention is payed to constitutive equations of rate type. A general entropy principle is applied to discuss restrictions on the constitutive equations. We study the algebraic conditions on the possibility of local dissipation of energy and of temperature changes without heat flow. From these criteria, we derive the appropriate energy equation and investigate the existence of finite speeds or propagation of second-order discontinuities in temperature.