Diffusion of a fluid through a spherical elastic solid undergoing large deformations

The diffusion of a fluid through a spherical elastic solid undergoing large deformation is described in this paper. The constitutive model used is the single-constituent model for diffusion of fluids in nonlinear elastic solids, originally presented by Baek and Srinivasa [S. Baek, A.R. Srinivasa, Int. J. Nonlinear Mech. 39 (2004) 201–218] and based on a variational method and on the assumption of continuity of chemical potential across the solid–fluid interface. The balance laws for a single continuum with mass diffusion are cast in spherical coordinates, and suitable boundary conditions are posed to describe the radial diffusion of fluid through an elastic spherical shell with finite thickness. Its inner surface is adjacent to a rigid wall, either impermeable or permeable, while the outside surface is in contact with the fluid that swells the solid, diffuses through it, and exerts a hydrostatic pressure on its surface.