Abstract:
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.
