Multiphase flow

Definition

Consider a flow of matter in a region $\Omega \subseteq \R^3$. It is a multiphase flow if $m \ge 2$ distinct phases are present. At each time $t$, the region $\Omega$ is then divided into disjoint open sets $\Omega_1(t), \dots, \Omega_m(t)$ and the interfaces between them. The set $\Omega_k(t)$ is the part occupied by the $k$-th phase, and it need not be connected. A phase is a gas, a liquid, a solid, or one of several immiscible liquids. The interfaces move with the flow. In each $\Omega_k(t)$ the phase obeys its own equations of motion, for example the Navier–Stokes equations with its own density and viscosity. On the interfaces, conditions couple the phases: conservation of mass and momentum across the interface, and a jump of normal stress given by surface tension. A two-phase flow is the case $m = 2$.