A large time solution of a crystal growth stefan problem

Abstract

An asymptotic large time solution has been obtained for a Stefan problem of crystal growth. The analysis presented is valid at large times when the rate of crystal growth is limited by the diffusion process in the environmental melt system so that a thermodynamic equilibrium state prevails at the interface. The first three terms of the asymptotic expansions obtained show that the leading term reduces to a similarity solution of Ghez, a counterpart of Neumann's solution in the thermal Stefan problem and that logarithmic terms start intervening at the third power of the expressions.