A three-dimensional mathematical model for sorption/desorption by a cylindrical polymeric matrix with dispersed drug is proposed. The model is based on a system of partial differential equations coupled with boundary conditions over a moving boundary. We assume that the penetrant diffuses into a swelling matrix and causes a deformation, which induces a stressdriven diffusion and consequently a non-Fickian mass flux. A physically sound nonlinear dependence between strain and penetrant concentration is considered and introduced in a Boltzmann integral with a kernel computed from a Maxwell-Wiechert model. Numerical simulations show how the mechanistic behavior can have a role in drug delivery design.
Introduction.In this paper we study a three-dimensional model of diffusion of a solvent into a cylindrical polymeric matrix containing drug and followed by the drug release. To describe drug release from a polymeric matrix, several models have been proposed [11,12,13,15,18,25,27]. However to the best of our knowledge, the influence of the mechanical properties of a swelling polymer in the sorption of a solvent and in the desorption of drug has not yet been considered in the literature. We propose a model where we combine non-Fickian sorption of the liquid agent, non-Fickian desorption, coupled with nonlinear dissolution and polymer swelling.It is well known that the diffusion of a liquid agent into a polymeric sample cannot be completely described by Fick's classical law. The liquid strains the polymeric matrix that, while swelling, exerts a stress that acts as a barrier to the incoming fluid. To explain these phenomena several authors [2,4,5,11,22,23,24] agree that a modified flux must be considered, that is