A phase field model for liquid-vapour phase transitions

We propose a model describing the liquid-vapour phase transition according to a phase-field method. A phase variable $φ$ is introduced whose equilibrium values $φ=0$ and $φ=1$ are associated with the liquid and vapour phases. The phase field obeys Ginzburg-Landau equation and enters the constitutive relation of the density, accounting for the sudden density jump occurring at the phase transition. In this paper we concern ourselves especially with the problems arising in the phase field approach due to the existence of the critical point in the coexistence line, which entails the merging of the phases described by $φ$.