Surface equations for two-phase flows

Abstract

This chapter is devoted to the presentation of the fundamental equations governing the interfacial surfaces. We begin by recalling the definitions of the different kinds of interfacial areas: the global one and the local one and the existing link between them. We pursue by a presentation of the different forms of the Leibniz rule (or Reynolds transport theorem) for a surface. The interfacial area balance equation can be understood as a particular case of this Leibniz rule, except for the discontinuous phenomena like coalescence and breakup which must be added for completeness. The average equations for the void fraction and for the interfacial area are then derived and their closure issue is examined. For strongly non-spherical interfaces (e.g. for strongly deformed bubbles or droplets), the area tensors are introduced, which are a new tool to deal with the tensorial aspect of non-spherical interfaces. The interfacial area balance is then completed by an additional transport equation for the second order area tensor or for its deviator, which is named the interface anisotropy tensor.