One dimensional multi-phase moving boundary problems with phases of different densities

Density changes occur naturally in phase change problems. It is customary in analyzing such problems to ignore the bulk movement of material thus introduced and assume the densities to be equal. However, for one dimensional problems the complexity introduced by this bulk movement is more apparent than real. This can be demonstrated by posing the problem in local coordinates fixed in each phase. In this report we show how to define suitable moving coordinates and, using them, pose and solve a one dimensional, multi-phase Stefan problem with phases of distinct densities. This explicit solution is essentially a similarity solution in the local coordinates. However, utility of these local coordinates is not limited to problems for which similarity solutions exist. They could be used with finite element or finite difference schemes to analyze more complex problems