Modelling, analysis and simulation of incompressible multi-fluid flows

Multi-fluid flows are omnipresent in our lives, from the fabrication of integrated circuit components in most electronics to the miniature laboratories inside medical tools, and even as a drop of rain splashes onto the wing of an aeroplane. In this thesis we use theoretical and numerical tools to investigate topics from the fascinating world of interfacial flows. The first part of this dissertation is dedicated to the study of multi-fluid systems in small scale channel geometries in the presence of electric fields. We develop the theoretical machinery to address the stabilisation (to the point of complete suppression) of the classical Rayleigh-Taylor instability under the action of an electric field acting in the plane of the liquid-liquid interface. In a related context, in many situations electric fields normal to the fluid-fluid interface may be employed in order to accurately drive instabilities towards beneficial goals. In particular, we discuss novel mechanisms to generate pumping and mixing in millimetre-sized geometries without requiring moving parts or an oncoming flow. In the second part of this thesis we turn our attention to the area of aerodynamics, thus investigating multi-fluid flows in a very different regime, dictated by high speed environments. We initially address one of the canonical problems in fluid mechanics, drop impact onto solid or liquid coated surfaces. This situation arises naturally on an aircraft in either rain or de-icing conditions. A new model for water catch on a surface is proposed, incorporating the violent splashing dynamics occurring in realistic conditions. The impingement of a large number of droplets ultimately leads to the formation of a liquid layer on the surface. We extend the powerful asymptotic framework of triple-deck theory to analyse changes in the flow separation process in the presence of an additional liquid. Flows past surface roughnesses and corners/flaps are discussed as practical examples.Open Acces