A phase-field model for liquid-vapor transitions

Starting from the mesoscopic description of the state equations for the vapor and liquid pure phases of a single chemical species, we propose a phase-field model ruling the liquid-vapor phase transition. Two different phases are separated by a thin layer, rather than a sharp interface, where the phase-field changes abruptly from 0 to 1. All thermodynamic quantities are allowed to vary inside the transition layer, including the mass density. The approach is based on an extra entropy flux which is proved to be non vanishing inside the transition layer, only. Unlike classical phase-field models, the kinetic equation for the phase variable is obtained as a consequence of thermodynamic restrictions and it depends only on the rescaled free enthalpy. The system turns out to be thermodynamically consistent and accounts for both temperature and pressure variations during the evaporation process. Few commonly accepted assumptions allow us to obtain the explicit expression of the Gibbs free enthalpy and the Clausius-Clapeyron formula. As a consequence, the customary form of the vapor pressure curve is recovered.