The fundamental equations of gas-droplet multiphase flow

Abstract

This paper describes the derivation of an equation set for the multiphase flow of small polydispersed liquid droplets in a continuous gas-phase consisting of either a pure vapour (of the same chemical species as the liquid droplets) or a mixture of pure vapour and an inert gas. Some difficulties of previous formulations are resolved by more judicious definitions of the interphase transfer terms. The analysis includes a consistent model to represent the surface energy and entropy of the liquid droplets. Surface effects are normally neglected but must be included if consistency is to be maintained with droplet growth models in which the droplet temperature depends on its radius due to the effects of capillarity. A derivation of the equation for the rate of entropy creation due to departures from equilibrium is also presented. Entropy production in non-nucleating flows can be represented by precisely four terms, three of which are associated individually with the interphase transfer of mass, momentum and energy. The fourth term represents the entropy change due to the homogeneous nucleation of liquid droplets from the vapour and is in exact agreement with the results of classical nucleation theory. The form of the entropy creation equation allows an interpretation using the methods of linear irreversible thermodynamics and indicates that some mathematical models of droplet growth in common use, derived on an informal basis, may not be physically realistic in certain circumstances.