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We construct a phase field model including hydrodynamics and elasticity inone-component systems. It can be used to investigate solid-liquid andliquid-liquid phase transitions. Upon first-order phase transition, a velocityfield is induced around interfaces in the presence of a density differencebetween the two phases even without applied shear flow. As applications, wepresent simulation results on two cases of melting, where a solid domain isplaced on a heated wall in one case and is suspended in a warmer liquid undershear flow in the other. We find that the solid domain moves or rotates as awhole due to elasticity, releasing latent heat. We also examine theliquid-liquid phase transition of a highly viscous domain into a less viscousliquid on a heated wall, where an inhomogeneous velocity field is inducedwithin a projected part of the domain. In these phase transitions, theinterface temperature is nearly equal to the coexisting temperature $T_{\rmcx}(p)$ away from the heated wall in the presence of heat flow in thesurrounding liquid.

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