Diffusion and stress driven flow in polymers

Citation

Hayes, Catherine Kent (1990) Diffusion and stress driven flow in polymers. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/1NE9-1T14. https://resolver.caltech.edu/CaltechETD:etd-02212007-132113

Abstract

A recently proposed model for non-Fickian diffusion of penetrants into polymers is adapted and used to study a drug-delivery problem. The model modifies Fick's diffusion equation by the addition of stress-induced flux and a bimolecular reaction term. A stress evolution equation incorporating aspects of the Maxwell and Kelvin-Voigt viscoelastic stress models completes the model. The diffusivity and relaxation time in the polymer are taken as functions of the penetrant concentration. The system is first studied on a doubly infinite domain under the assumption that the penetrant's saturation concentration is small. When the diffusivity and relaxation time are taken to be constant, a perturbation analysis is used to show the form and the region of stability of traveling-wave solutions. When the diffusivity and relaxation time are taken as specified functions of the concentration, the shapes of traveling-wave solutions are predicted by perturbation analysis and found to be different when the equations are diffusion-driven than when they are stress-driven. The predictions are verified by numerical integration for specified parameter values. The system is also studied on a finite domain under the assumption that the diffusivity is large. A perturbation analysis is used to demonstrate that the concentration and stress evolve according to a Fickian diffusion equation on a short time scale. After longer time has elapsed, the concentration and stress are shown to exhibit steep fronts in a narrow region within the domain. These predictions are verified numerically. Finally, the equations are studied in the steady state and are found to predict the evolution of shocks. Work done on Fisher's equation is presented in an appendix. When the diffusivity is taken in the same nonlinear form as was used in the polymer-penetrant model, a qualitatively new solution of Fisher's equation is found, using a method which is also applied to the polymer-penetrant system

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