Applications of the theory of interacting continua to the diffusion of a fluid through a non-linear elastic media

Abstract

The theory of interacting continua is applied to the problem of diffusiion of a fluid through a non-linear elastic layer and a hollow sphere. Using methods which are by now standard in continuum mechanics expressions and restrictions are derived from a thermodynamic standpoint for the partial stresses for the fluid and solid and the diffusive body force. In order to obtain detailed solutions to specific boundary value problems a choice of a particular form for the free energy function for the mixture is made based on statistical theory. To simplify the problem, we assume that the fluid in question is ideal. The difficulties inherent to a clear definition of the boundary conditions for the partial stresses are overcome by the use of the Flory-Huggins equation. Two specific examples are considered. The first is the problem of diffusion through a stretched layer and second is diffusion through a spherical shell. Results of the numerical solution enable the construction of the pressure difference-flux relations, which have been shown to be in good agreement with experimental data.