Physically insightful modeling of non-Fickian kinetic regimes encountered in fundamental studies of isothermal sorption of swelling agents in polymeric media

The kinetics of sorption of micromolecular swelling agents by polymeric media often deviates from normal Fickian behavior in various ways, which have to be understood and interpreted, with the aid of appropriate models, in terms of the underlying physics. One difficulty which arises in this respect is that salient aspects of the observed kinetic behavior can be mimicked by extraneous effects, in the form of significant deviation from a boundary condition or of imperfect macroscopic homogeneity of the polymer film (modeled in both cases as a surface resistance to penetrant transport). Such effects have, in fact, been invoked (notably by Hansen (2010) ) to question the significance of conclusions drawn from modeling approaches based on the effect of intrinsic bulk polymer properties, leading to delayed (viscous) swelling and to build-up and decay of differential swelling stresses. We present here a brief critical account (following the mainstream modeling line initiated by Crank) of typical results concerning various salient aspects of observed non-Fickian sorption kinetics and of the comparative possibility of achieving satisfactory general interpretation thereof, in terms of approaches based on the aforementioned extraneous, versus intrinsic bulk property, effects. We find that the latter approach has been successful so far, both computationally and physically, by establishing a close physically significant analogy between non-Fickian sorption, and (both linear and non-linear) viscoelastic mechanical deformation, behavior. The former approach, on the other hand, proves weak on both counts.