Mathematical modelling of diffusion in polymers
In the first part of this thesis, mathematical models describing solvent and drug diffusion in glassy polymers are investigated using both numerical and approximate methods. These models are analysed using formal asymptotic expansions based on small and large-times as well as extreme parameter values. Boundary immobilisation methods are employed to transform the moving boundary problems onto a fixed domain, where if necessary, a suitable start-up condition for the numerical scheme is derived. The models are then extended with the inclusion of advection, which is induced by the significant volume changes in the polymers as they swell, and nonlinear diffusion. In part two of this thesis, mathematical models describing two different pharmaceutical problems are derived. In Chapter 5, a model describing the pulsatile release of a drug from a thermoresponsive polymer is described. This model is investigated from both a numerical and analytic perspective and is shown to have an exact solution under a particular regime. Lastly, Chapter 6 is concerned with the derivation of a model to describe the controlled release of a chemical during the cleaning of contact lenses. Numerical and approximate solutions are described, along with a detailed experimental investigation and model validation.
- Faculty of Science and Engineering
First supervisorSarah L. Mitchell
Second supervisorStephen B.G. O'Brien
Other Funding informationSFI
Department or School
- Mathematics & Statistics