A Note on the Interface Condition in Phase Change Problems

Abstract

In this note the fundamental relations to be satisfied at the solid-liquid interface for phase-change problems are examined. The attention is focused on situations in which melting (or solidification) takes place at a discrete melting point temperature and, as a result, a solid and liquid phases are separated by a sharp interface. The interface condition appropriate for a general nonorthogonal curvilinear coordinate system has been developed. The result is suitable for studying various problems of practical interest where the formulation is terms of general nonorthogonal curvilinear coordinates is either required or convenient. A specific example wherein the relationships derived in this note have proved useful is in the wire melting, ball roll-up, and subsequent solidification aspects of ball bonding in the packaging of microelectronic semiconductor chips. Depending on the material and detailed boundary conditions, the authors have successfully tracked phase-change interfaces of different shapes. A brief description of this example has been included in this note.