A phase-field model for the diffusive melting of isolated dendritic fragments

A thermal phase-field model constructed in the "thin-interface" limit and incorporating a number of advanced numerical techniques such as adaptive mesh refinement, implicit time stepping, and a multigrid solver has been used to study the isolated diffusive melting of dendritic fragments. The results of the simulations are found to be fully consistent with the experimental observation of such melting in microgravity during the Isothermal Dendrite Growth Experiment. It is found that the rate at which the ratio of semi-major to semi-minor axes changes is a function of the melt Stefan number, which may help explain why both melting at (approximately) constant ratio and melting at slowly increasing ratio have been observed.