Diffuse Interface (D.I.) Model for Multiphase Flows

We review the diffuse interface model for fluid flows, where all quantities, such as density and composition, are assumed to vary continuously in space. This approach is the natural extension of van der Waals' theory of critical phenomena both for one-component, two-phase fluids and for liquid binary mixtures. The equations of motion are derived, showing that the problem is well posed, as the rate of change of the total energy equals the energy dissipation. In particular, we see that a non-equilibrium, reversible body force appears in the Navier-Stokes equation, that is proportional to the gradient of the generalized chemical potential. This, so called Korteweg, force is responsible for the convective motion observed in otherwise quiescent systems during phase change. Finally, the results of several numerical simulations are described, modeling, in particular, a) mixing, b) spinodal decomposition; c) nucleation; d) heat transfer; e) liquid-vapor phase separation.