Phase-Field Simulation of Solidification With Density Change

Phase-field models of solidification with convection often assume the existence of a single (mixture) velocity at any location inside the diffuse interface, and the phase-field, φ, is advected by this mixture velocity. In this paper, the advection of the phase-field is examined for a one-dimensional normal flow to a solidification front induced by a density difference between the solid and liquid. It is found that the results from a phase-field model that assumes a single velocity inside the diffuse interface are generally not in agreement with the sharp interface condition for the kinetic undercooling of the front in the presence of unequal densities, regardless of the interface width. By introducing a two-phase approach, where the solid and liquid are assumed to coexist inside the diffuse interface with different velocities, good agreement with the sharp interface condition is obtained irrespective of the density ratio between the two phases. NOMENCLATURE L latent heat of fusion per unit mass J mass flux across the interface M interface mobility S interfacial area per unit volume T temperature m T melting temperature s X existence function