Simulation of non-classical diffusion in polymers

Abstract

The present contribution is concerned with the computational modelling of non-classical diffusion in amorphous polymers. Special attention is paid to the limiting case of Case II diffusion. Application of the dual-phase-lag concept to Fick’s first law leads to a description of Case II behaviour. The change in material properties during the glass transition is explicitly accounted for by a concentration dependent formulation of the material parameters. The proposed model is well suited for modelling the sharp diffusion front and linear uptake kinetics associated with Case II diffusion. Application of a concentration dependent diffusion coefficient reduces the concentration gradient behind the front to a minimum. For the solution procedure, a finite element scheme in space and a finite difference method in time are applied. Three-dimensional numerical results are presented for classical Fickian and non-classical Case II diffusion. This paper adds to the basic understanding of the computational modelling of the Case II diffusion phenomenon.