Properties of a generalized diffusion equation with a memory

A third-order partial differential equation for the concentration or chemical potential of a penetrant diffusing in a relaxing medium with a memory described by a simple Maxwell–Debye relaxation function is shown to be equivalent to generalized diffusion equations with memory terms. We establish some properties of solutions of this equation for both suddenly or adiabatically prepared initial conditions. We extend our general treatment to account for osmotic pressure effects in mechanical equilibrium which can arise due to swelling of the solvent medium in which the transport occurs.