We have previously developed a phase-field model of solidification that includes convection
in the melt [Physica D 135 (2000) 175]. This model represents the two phases as viscous
liquids, where the putative solid phase has a viscosity much larger than the liquid phase.
The object of this paper is to examine in detail a simplified version of the governing
equations for this phase-field model in the sharp-interface limit to derive the interfacial
conditions of the associated free-boundary problem. The importance of this analysis is that it …

We have previously developed a phase-field model of solidification that includes convection
in the melt [Anderson, McFadden and Wheeler, Physica D, 135 (2000) 175-194]. This model
represents the two phases as viscous liquids, where the putative solid phase has a viscosity
much larger than the liquid phase. The object of this paper is to examine in detail a
simplified version of the governing equations for this phase-field model in the sharp-
interface limit and derive the interfacial conditions of the associated free-boundary problem …