A diffuse interface model for two-phase flows with phase transition

Abstract

A thermodynamically consistent diffuse interface model is developed for two-phase flows with phase transition. Inside the liquid-vapor mixing layer, the Cahn-Hilliard equation governing the evolution of liquid/vapor species explicitly includes the phase transition between the two species. In the present model, the specific Helmholtz free energy of the binary mixing fluid as well as other thermodynamic functions consists of a classical part (ideal mixing free energy plus a double-well potential of the mass fraction) and a nonclassical part consisting of the gradient of mass fraction. The nonclassical chemical potential is defined in a manner similar to the classical chemical potential. According to the present model, there exists a (conserved) nonclassical stress tensor in the mixing fluid, which is a distributed form of the surface tension across the mixing layer. Using the principle of entropy increase, it is observed that the rate of local phase transition is proportional to the local generalized chemical potential, and a system of transport equations of the mixing fluid is derived. This system of equations can be reduced to that of Guo and Lin [“A thermodynamically consistent phase-field model for two-phase flows with thermocapillary effects,” J. Fluid Mech. 766, 226 (2015)] except for the formula on chemical potential. The present diffuse-interface model will also be reduced to the general classical sharp interface model when the mixing layer collapses to a sharp surface.