The effect of a changing diffusion coefficient in super-Case II polymer-penetrant systems
- Creators
- Edwards, David A.
- Cohen, Donald S.
Abstract
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.
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.Additional details
- Eprint ID
- 100682
- Resolver ID
- CaltechAUTHORS:20200113-131352375
- DMS-9024963
- NSF
- DMS-9407531
- NSF
- AFOSR-91-0045
- Air Force Office of Scientific Research (AFOSR)
- NSF Graduate Research Fellowship
- John and Fannie Hertz Foundation
- Los Alamos National Laboratory
- Created
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2020-01-13Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field