Viscous multilayer shear flows of immiscible liquids can become unstable due to the presence of interfaces. The nonlinear patterns that emerge are complex and extreme events such as interface pinching and/or wall touching are possible. It is of interest, therefore, to develop reduced dimension and reduced parameter nonlinear models that can be used to study the dynamics and quantify solutions and allied phenomena.

In this talk, Prof Papageorgiou will describe how asymptotic analysis can be used to derive classes of equations that couple thin and thick regions and produce nonlocal PDEs. The physical origins can be free-stream shear, electric or magnetic fields etc. The particular case of two-layer viscous flows in channels will be considered in detail and comparisons of the nonlocal equations with experiments will be shown that confirm their usefulness. Finally, he will discuss models that describe multilayer extrusion processes that in many cases support slip at the interface between viscous fluids. Such slip is the viscous analogue of classical inviscid slip that leads to Kelvin-Helmholtz instability. It will be shown that the viscous case also supports short-wave instabilities, albeit not catastrophic. Nonlinear aspects will also be discussed.

Demetrios Papageorgiou is Professor of Applied Mathematics at Imperial College London. He is a Fellow of the American Physical Society and of the Institute of Mathematics and its Applications (IMA). He is Co-Editor in chief of the IMA Journal of Applied Mathematics.

More information can be found here.