Macroscopic description of the kinetics of swelling for a cross-linked elastomer or a gel

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Abstract
We consider the diffusion of a solvent in a cross-linked polymer network and the corresponding swell- ing and deswelling. Recently, we obtained equations describing the time evolution of the concentration profile of a polymer (or solvent) in one dimension and three dimensions with radial symmetry. In this paper we discuss in detail the properties of these equations and the experimental predictions which can be inferred from them. In particular, we find that a number of features commonly regarded as a signature for anomalous or ‘‘non-Fickian’’ behavior, can in fact be found as a consequence of Fick’s law once the presence of moving boundaries is properly taken into account. We briefly discuss the problems associated in extending our treatment to a general two- or three-dimensional geometry and its possible use in interpreting the surface morphologies and fracture behavior observed in the swelling process.