We propose a one-dimensional model to describe the sorption of a solvent by a polymeric membrane, followed by polymer swelling and drug release. We assume that the solvent diffuses into the membrane and induces a stress driven diffusion, that causes a non-Fickian mass flux. We assume that the drug is present in two states (dissolved and undissolved) and that its transport occurs by Fickian diffusion and non-linear dissolution. Polymer swelling is tracked with a volume conservation equation. The system of
partial differential equations that define the model is numerically solved.

A qualitative analysis of the dependence of the solutions on the parameters of the model shows a complete agreement with the expected physical behavior.

CEMAT - Center for Computational and Stochastic Mathematics