| Type of Document |
Dissertation |
| Author |
Edwards, David A.
|
| URN |
etd-09092005-155000 |
| Persistent URL |
http://resolver.caltech.edu/CaltechETD:etd-09092005-155000 |
| Title |
A model for nonlinear diffusion in polymers |
| Degree |
PhD |
| Option |
Applied and Computational Mathematics |
| Advisory Committee |
| Advisor Name |
Title |
| Donald S. Cohen |
Committee Chair |
|
| Keywords |
|
| Date of Defense |
1994-03-29 |
| Availability |
unrestricted |
Abstract
In certain polymer-penetrant sytems, the effects of Fickian diffusion are augmented by nonlinear viscoelastic behavior. Consequently, such systems often exhibit concentration fronts unlike those seen in classical Fickian systems. These fronts not only are sharper than in standard systems, but also they propagate at speeds other than that typical of Fickian diffusion. A model is presented which replicates such behavior. This model is reduced to a moving boundary-value problem where the boundary separates the polymer into two distinct states: glassy and rubbery, in each of which different physical processes dominate. An unusual condition at the moving interface, which arises from the inclusion of a viscoelastic memory term, is not solvable by similarity solutions, but can be solved by integral equation techniques. Perturbation methods are used to obtain asymptotic solutions for differing strengths of molecular diffusion and viscoelastic stress. These solutions are characterized by sharp fronts which move with constant speed; the asymptotic solutions mimic those found experimentally in polymer-penetrant systems.
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| Filename |
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Edwards_da_1994.pdf |
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