The Macroscopic Modelling of Multi-Phase Mixtures

Abstract

The usual classification of materials into solids, liquids and gases is not entirely satisfying. Those who already used a tooth-paste, made a mayonnaise or wiped muddy shoes have experienced materials with strange properties, neither completely solid nor completely liquid. There also exist liquid-like materials (paint, egg white etc...) which do not behave as ordinary liquids. A careful investigation of those soft solids or odd liquids reveals they are all made of several chemical species and that the basic blocks of material are of a supramolecular size. In fact, these complex fluids are multi-phase mixtures, the simplest example of which is a suspension of particles in a fluid.The present lectures will concern the macroscopic modelling of multi-phase mixtures. Let us insist on the two underlined terms. Macroscopic: we will not focuss on the way to get exact results concerning the flow around particles but we will select among these results, the ones which prove important when considering the mixture as a continuous medium. Modelling: the description to be given will be a simplified one, obtained after a selection of the relevant physical phenomena, and a choice of the best variables to represent them. In the first chapter we will present fluid-mechanical results, while in chapter two we will consider the possible implications of the second law of thermodynamics. In these two chapters, a certain number of (more or less) intuitive statements will be made concerning the averaging procedure. These statements will be justified in chapter three while the last chapter will insist on phenomena linked with the fluctuational kinetic energy.