A MATHEMATICAL-MODEL FOR A DISSOLVING POLYMER

In certain polymer-penetrant systems nonlinear viscoelastic effects do minate those of Fickian diffusion. This behavior is often embodied in a memory integral incorporating nonlocal time effects into the dynamic s; this integral can be derived from an augmented chemical potential. The mathematical framework presented is a moving boundary-value proble m. The boundary separates the polymer into two distinct stares: glassy and rubbery, where different physical processes dominate. The moving boundary condition that results is not solvable by similarity solution s, but can be solved by perturbation and integral equation techniques. Asymptotic solutions are obtained where sharp fronts move with consta nt speed. The resultant profiles are quite similar to experimental res ults in a dissolving polymer. It is then demonstrated that such a mode l has a limit an the allowable front speed and a self-regulating mass uptake.