Constant Front Speed in Weakly Diffusive Non-Fickian Systems

In certain polymer-penetrant systems, the effects of Fickian diffusion are dominated by nonlinear viscoelastic behavior. Consequently, such systems often exhibit concentration fronts unlike those seen in classical Fickian systems. These fronts not only are sharper than in standard systems but also propagate at constant speed. The mathematical model presented is a moving boundary-value problem, where the boundary separates the polymer into two distinct states, glassy and rubbery, where different physical processes dominate. The moving boundary condition that results is not solvable by similarity solutions but can be solved by integral equation techniques. In the case under consideration, namely, one where the standard Fickian diffusion coefficient is small, asymptotic solutions where a comparatively sharp front moves with constant speed are obtained.