Water Evaporation and Condensation by a Phase-Field Model

We develop a phase-field model for the liquid-vapor phase transition. The model aims to describe in a thermodynamically consistent way the phase change phenomenon coupled with the macroscopic motion of the fluid. The phase field ϵ describes the liquid fraction at any point and the overall water density is a function of the phase field and the pressure. An extra gaseous substance (e.g. air) is allowed in the system and contributes to the mechanical pressure. The phase transition is described by a Ginzburg-Landau equation. The parameter that drives the transition is the partial vapor pressure, which is the relevant quantity for condensation and evaporation phenomena. Moreover, a velocity-dependent term contributes to the phase change in the transition layers where a vapor pressure gradient exists