On Diffusive Interface Models for Two Phase Fluid Flow

Two-phase flows or multi-phase flows are important in many industrialapplications, for instance, in aerospace, chemical engineering, micro-technology and so on. They have attracted studies from many engineers, geophysicists and astrophysicists. Classically, the fluids, which are macroscopically immiscible, are assumed to be separated by a sharp interface. But, in order to describe topological transitions, such as droplet formation, coalescence of several droplet or droplet breakup, we need to take into account a partial mixing on a small length scale in the models, which is called the diffusion interface models divided into Navier-Stokes-Cahn-Hilliard and Navier-Stokes-Allen-Cahn systems. This book offers our recently results on the diffusion interface models for two-phase fluid flows.