A phase-field model for quasi-incompressible solid-liquid transitions

By virtue of a unified thermodynamic scheme, we derive the general kinetic equation ruling the phase-field evolution in a binary quasi-incompressible mixture for both transition and separation phenomena. When diffusion effects are negligible in comparison with source and production terms, a solid-liquid phase transition induced by temperature and pressure variations is obtained. In particular, we recover the explicit expression of the liquid-pressure curve separating the solid from the liquid stability regions in the pressure-temperature plane. Consistently with physical evidence, its slope is positive (negative) for substances which compress (expand) during the freezing process.