Shock Formation in a Multidimensional Viscoelastic Diffusive System

Creators: Cohen, Donald S.; White, Andrew B., Jr.; Witelski, Thomas P.

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Abstract

We examine a model for non-Fickian "sorption overshoot" behavior in diffusive polymer-penetrant systems. The equations of motion proposed by Cohen and White [SIAM J. Appl. Math., 51 (1991), pp. 472–483] are solved for two-dimensional problems using matched asymptotic expansions. The phenomenon of shock formation predicted by the model is examined and contrasted with similar behavior in classical reaction-diffusion systems. Mass uptake curves produced by the model are examined and shown to compare favorably with experimental observations.

Additional Information

©1995 Society for Industrial and Applied Mathematics. Received by the editors June 26, 1993; accepted for publication (in revised form) May 27, 1994. The research of this author [D.S.C.] was supported by United States Army Research Office (Durham) contract DAAL03-89-K-0014, National Science Foundation grant DMS-9024963, Air Force Office of Scientific Research grant AFOSR-91-0045, and Department of Energy grant W-7405-ENG-36 and performed at the Center for Nonlinear Studies at Los Alamos. The research of this author [A.B.W.Jr.] was supported by United States Department of Energy contract W-7405-ENG-36. The research of this author [T.P.W.] was supported by a National Science Foundation graduate fellowship, National Science Foundation grant DMS-9024963, and Air Force Office of Scientific Research grant AFOSR-91-0045. This paper is dedicated to Joseph B. Keller on the occasion of his 70th birthday.

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