Flow on thin fluid sheets
Physical phenomena that combine effects on a surface and that in the bulk occur in many fields, ranging from crystal growth in chemistry and proton diffusion in biomembranes, through tyre aquaplaning and self-cleaning materials. We consider this multi-scale problem specifically for coupled bulk-surface fluid flow. Simulating these problems with traditional fluid solvers is challenging because of the different scale of the surface phenomena versus that in the bulk. Towards this end, specialized thin film flow models have been developed to accurately capture surface-level flow effects. However, it remains impossible to automatically detect the formation of thin fluid sheets and resolve the bulk/sheet coupled flow. This limits the application of thin film models. Advances made in thin film modelling have not been applied to complex flow situations where, for example, a free flowing bulk fluid can form thin films over an obstacle, or where sufficient fluid collects on a moving thin fluid sheet to obtain bulk flow. Such problems rely on bulk flow simulations with significantly finer resolutions to capture the surface-level effects, which dramatically increases computation time making full dynamic simulations unrealistic for actual applications.

The primary objective of this project is to model bulk/surface flow phenomena numerically. We will propose novel mathematical models to computationally simulate flow of thin fluid sheets on moving curved surfaces, which can predict not just the evolution of an existing film, but also their formation, collapse and break up. We will develop efficient methods to two-way couple film flow with bulk fluid flow which are able to identify regions where surface level effects are relevant, on the fly. This fellowship will build on the expertise in fluid flow and particle methods of the researcher, and that in multi scale modeling, free boundary problems and advanced discretisation adaptivity of the host.