The Solid-Liquid Phase Interface Dynamics in an Undercooled Melt with a Solid Wall

A new boundary integral equation for the interface function of a curved solid/liquid phase interface propagating into an undercooled one-component melt is derived in the presence of a solid wall in liquid. Green's function technique is used to transform a purely thermal boundary value problem to a single integro-differential equation for the interface function in two- and three-dimensional cases. It is shown that a solid wall represents an additional source of heat and melt undercooling can be negative in the vicinity of the wall. The new boundary integral equation has a limiting transition to previously developed theory in the absence of a solid wall.