Non-Linear Diffusion III. Diffusion through Isotropic Highly Elastic Solids - J. E. Adkins (Philosophical transactions of the Royal Society of London. Series A: Mathematical, physical, and engineering sciences, 1964)
A theory is formulated for the diffusion of fluids through highly elastic materials. This forms an extension of earlier work (Adkins 1963 a, b) on flows of mixtures of fluids, but attention is here confined to the diffusion of a single fluid through the solid. It is assumed that each point of the region of space concerned may be occupied simultaneously by the fluid and solid, and the motion of each constituent is governed by the usual equations of motion and continuity. The mechanical properties of each substance are specified by means of constitutive equations for the stresses, and diffusion effects by means of a body force or diffusive drag acting on each component, this force being a function of the composition and relative motions of the constituents of the solid-fluid mixture. In applications, attention is confined to steady-state problems. These include the swelling of a solid due to presence of fluid, and the diffusion of a fluid through uniform plane plates or slabs subject to uniform all-round compression or extension and to a shearing deformation. It is assumed throughout that the diffusing fluid is non-Newtonian, the theory for ideal and viscous fluids emerging as special cases.