The effect of a changing diffusion coefficient in super-Case II polymer-penetrant systems

In certain polymer-penetrant systems, nonlinear viscoelastic effects dominate those of Ficlcian diffusion. By introducing a dependence of the chemical potential on concentration history, this behaviour can be modelled by a memory integral. The mathematical framework presented is a moving boundary-value problem where the boundary separates the polymer into two distinct states: glassy and rubbery. In each region, a different operator holds at leading order. The problem which results is not solvable by similarity solutions, but can be solved by perturbation and integral equation techniques. By introducing a new model where the diffusion coefficient changes with phase, asymptotic solutions are obtained where sharp fronts initially move like t³/2. This ‘super-Case II’ behaviour is found in various non-Fickian polymer-penetrant systems