DIFFUSION EQUATIONS FOR A MIXTURE OF AN ELASTIC FLUID AND AN ELASTIC SOLID.

A mechanical theory is formulated for the diffusion of an elastic fluid through an isotropic elastic solid. It is assumed that each point of the mixture is occupied simultaneously by both constituents in given proportions. The motion of each constituent is governed by the usual equations of motion and continuity. The mechanical properties of each component are specified by means of constitutive equations for the stresses. Diffusion effects are accounted for by means of a body force acting on each constituent which depends upon the composition, the elasticity of the solid and the relative motion of the substances in the mixture. This approach makes it possible to derive coupled diffusion equations for both constituents. Uncoupling of the equations is accomplished within the framework of a linearized theory by adopting particular motions for the mixture. The result is compared with classical diffusion equations derived by intuitive modifications to the empirical Fick's law.