ボーウェン マーク

Research

Thin-film theory

Thin liquid films arise in applications throughout nature, the natural sciences, engineering and industry. The mathematical modelling of such phenomena often yields evolution equations for the interfacial film thickness in the form of (high-order) degenerate parabolic equations.

Analysis of free-boundary problems based on these equations considering, for example, rupture phenomena, moving contact lines and the effects of surface topography and driving forces upon the motion of the liquid requires a combination of analytical methods (e.g. perturbation theory, bifurcation theory, dynamical systems, self-similarity) and numerical techniques (e.g. shooting methods, boundary value solvers, ADI computations) in order to make progress.

The results of this research are also fundamental in understanding the behaviour of other degenerate parabolic partial differential equations. The mathematical methodologies are also applicable to a wide range of problems beyond the scope of thin film theory.