Phase field model of solid-liquid and liquid-liquid phase transitions in flow and elastic fields in one-component systems

We construct a phase field model including hydrodynamics and elasticity in one-component systems. It can be used to investigate solid-liquid and liquid-liquid phase transitions. Upon first-order phase transition, a velocity field is induced around interfaces in the presence of a density difference between the two phases even without applied shear flow. As applications, we present simulation results on two cases of melting, where a solid domain is placed on a heated wall in one case and is suspended in a warmer liquid under shear flow in the other. We find that the solid domain moves or rotates as a whole due to elasticity, releasing latent heat. We also examine the liquid-liquid phase transition of a highly viscous domain into a less viscous liquid on a heated wall, where an inhomogeneous velocity field is induced within a projected part of the domain. In these phase transitions, the interface temperature is nearly equal to the coexisting temperature $T_{\rm cx}(p)$ away from the heated wall in the presence of heat flow in the surrounding liquid.