Unsteady diffusion of fluids through solids undergoing large deformations

In this work, firstly, based on the theory of interacting continua, we establish a general theory governing the motion of an elastic solid infused with a fluid. This general theory includes Biot's equation of wave propagation as a special case. Also, this theory describes the diffusion of an incompressible fluid through incompressible isotropic and anisotropic nonlinear elastic solids. The theory also allows for the inclusion of interactions like the effect of drag and the virtual mass effect, and generalizes most previous studies. Secondly, we develop a theory for studying unsteady diffusion problems which involve a moving singular surface. Behind this singular surface there is a mixture of a solid and a fluid, while ahead of the surface there might be a single solid or a mixture of a solid and a fluid with properties different from the mixture that is present behind the surface. Thirdly, we consider two specific applications, that is, the unsteady diffusion of an incompressible fluid through an incompressible isotropic nonlinear elastic solid thick slab and the unsteady diffusion of an incompressible fluid through an incompressible isotropic nonlinear elastic thick cylindrical annulus. Some numerical results are obtained and a phenomenon of local accumulation of fluid near the boundary where the fluid enters is predicted.