Phase-field model of solid-liquid phase transition with density difference and latent heat in velocity and elastic fields

We present a phase-field model of solid-liquid transitions with inhomogeneous temperature in one-component systems, including hydrodynamics and elasticity. Our model can describe plastic deformations at large elastic strains. We use it to investigate the melting of a solid domain, accounting for the latent heat effect, where there appears a velocity field in liquid and an elastic field in solid. We present simulation results in two dimensions for three cases of melting. First, a solid domain is placed on a heated wall, which melts mostly near the solid-liquid-wall contact region. Second, a solid domain is suspended in a warmer liquid under shear flow, which rotates as a whole because of elasticity and melts gradually. Cooling of the surrounding liquid is accelerated by convection. Third, a solid rod is under high compression in liquid, where slips appear from the solid-liquid interface, leading to a plastic deformation. Subsequently, melting starts in the plastically deformed areas, eventually resulting in the fracture of the rod into pieces. In these phase-transition processes, the interface temperature is kept nearly equal to the coexisting temperature T-cx(p) away from the heated wall, but this local equilibrium is not attained near the the contact region. We also examine a first-order liquid-liquid phase transition under heating from a boundary in one-component liquids.