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The effect of a changing diffusion coefficient in super-Case II polymer-penetrant systems

Edwards, David A. and Cohen, Donald S. (1995) The effect of a changing diffusion coefficient in super-Case II polymer-penetrant systems. IMA Journal of Applied Mathematics, 55 (1). pp. 49-66. ISSN 0272-4960. doi:10.1093/imamat/55.1.49.

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In certain polymer-penetrant systems, nonlinear viscoelastic effects dominate those of Ficlcian diffusion. By introducing a dependence of the chemical potential on concentration history, this behaviour can be modelled by a memory integral. The mathematical framework presented is a moving boundary-value problem where the boundary separates the polymer into two distinct states: glassy and rubbery. In each region, a different operator holds at leading order. The problem which results is not solvable by similarity solutions, but can be solved by perturbation and integral equation techniques. By introducing a new model where the diffusion coefficient changes with phase, asymptotic solutions are obtained where sharp fronts initially move like t³/2. This ‘super-Case II’ behaviour is found in various non-Fickian polymer-penetrant systems.

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Additional Information:© 1995 Oxford University Press. Received: 30 December 1994; Published: 01 January 1995. This work was performed under National Science Foundation grants DMS-9024963 and DMS-9407531 and Air Force Office of Scientific Research grant AFOSR-91-0045. Additional support was provided by a National Science Foundation Graduate Fellowship, the John and Fannie Hertz Foundation, and the Theoretical Director's Office and the Center for Nonlinear Studies at Los Alamos National Laboratory. The authors wish to thank Thomas Witelski and Christopher Durning for their contributions, both direct and indirect, to this paper. Many of the calculations herein were performed using Maple and Mathematica.
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Air Force Office of Scientific Research (AFOSR)AFOSR-91-0045
NSF Graduate Research FellowshipUNSPECIFIED
John and Fannie Hertz FoundationUNSPECIFIED
Los Alamos National LaboratoryUNSPECIFIED
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Record Number:CaltechAUTHORS:20200113-131352375
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Official Citation:DAVID A. EDWARDS, DONALD S. COHEN, The effect of a changing diffusion coefficient in super-Case II polymer-penetrant systems, IMA Journal of Applied Mathematics, Volume 55, Issue 1, 1995, Pages 49–66,
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:100682
Deposited By: Tony Diaz
Deposited On:13 Jan 2020 23:33
Last Modified:16 Nov 2021 17:56

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