Approximate solution techniques for the sorption of a finite amount of swelling solvent in a glassy polymer

• Considered a nonlinear kinetic law for the case of zero initial thickness, which significantly complicates analysis. Novel numerical technique when exponent is greater than 1 (requiring log transformation and boundary immobilisation). Asymptotic expansions small large time, as well values control parameter. This study examines one-dimensional Stefan problem describing sorption finite amount swelling solvent in glassy polymer. The polymer initially dry non-swollen state, where network dense. then injected with critical concentration solvent, causing chain relaxation to occur. A moving separating swollen rubbery from created, whose speed defined by law. form typically assumed be linear, but this nonphysical restriction, thus we consider general exponent. We present formal asymptotic expansions, both times parameter, considering heat balance integral method. These approximations are compared scheme, uses immobilisation correctly identifies appropriate starting solution.