Nonlinear stability of viscous pressure or gravity driven multilayer flows

Multilayer flows arise whenever a physical or technological process involves
several liquids. In numerous applications the liquids are also immiscible and so when caused to flow they form sharp interfaces separating different phases. Examples include extrusion processes in manufacturing, coating processes for electronics or advanced materials, distillation columns in chemical engineering applications, as well as physiological and geological applications.
The mathematical problem is very complicated due to the unknown positions of interfaces that need to be calculated as part of the solution. This project centres on the nonlinear stability of such flows in the strongly nonlinear regime for three or more immiscible stratified fluids. Several effects will be explored including strong surface tension, textured bounding walls (either superhydrophobic or elastic), and external effects that can be used in flow control such as fluid injection/suction and applied electric fields. The project will use mathematical modelling, analysis and computations to obtain the behaviour of this class of flows.