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Desorption overshoot in polymer-penetrant systems: Asymptotic and computational results. (English) Zbl 1011.35011

Summary: Many practically relevant polymers undergoing desorption change from the rubbery (saturated) to the glassy (nearly dry) state. The dynamics of such systems cannot be described by the simple Fickian diffusion equation due to viscoelastic effects. The mathematical model solved numerically is a set of two coupled PDEs for concentration and stress. Asymptotic solutions are presented for a moving boundary-value problem for the two states in the short-time limit. The solutions exhibit desorption overshoot, where the penetrant concentration in the interior is less than that on the surface. In addition, it is shown that if the underlying time scale of the equations is ignored when postulating boundary conditions, nonphysical solutions can result.

MSC:

35B20 Perturbations in context of PDEs
35C20 Asymptotic expansions of solutions to PDEs
35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
35R35 Free boundary problems for PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74D10 Nonlinear constitutive equations for materials with memory
76M10 Finite element methods applied to problems in fluid mechanics
35C15 Integral representations of solutions to PDEs
80A22 Stefan problems, phase changes, etc.

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