Free surface flows of complex fluids

Abstract

This proposal sets out a research plan to investigate two classes of complex fluids. The first are viscoelastic liquids, composed of long chained molecules that impart a memory aspect to the fluid. The second are nematic liquid crystals that are composed of rod like molecules that give the liquid a directional preference (anisotropy). Both classes share properties of both liquids and solids, which makes them challenging to understand mathematically and numerically. They have a myriad of industrial applications, making their investigation timely and important. The research is to focus on a benchmark free-surface flow termed die-swell, which arises in industrial extrusion processes. A unique combination of asymptotic analysis and numerical techniques is proposed to deal with this problem in order to simulate these flows accurately. This will involve a synergy of expertise of the Bath researchers in asymptotic methods with the expertise of the São Paulo researchers (at USP and UNESP) in numerical analysis. The Bath researchers will also lend their expertise in mathematical modelling to the Brazilian Study Groups with Industry held in São Carlos with the Bath PI also running a graduate short course in Industrial Mathematics. The São Paulo researchers will contribute to the activities of the Bath Doctoral Centre SAMBa. (AU)