Linear stability analysis on a spherical particle growing from a binary melt under the far-field flow

The solutions of temperature and solute fields around a spherical crystal growing from a binary melt under the far-field flow are obtained. Based on the results, a linear stability analysis on the spherical interface growing from the binary melt under the far-field flow is performed. It is found that the constitutional supercooling effect ahead of the spherical crystal interface under the far-field flow is enhanced compared with that without the flow. The growth rate of the perturbation amplitude at the up-wind side of the spherical crystal interface is larger than that at the down-wind side. The critical stability radius of the crystal interface decreases with the increasing far-field flow velocity. Under the far-field flow, the whole spherical interface becomes more unstable compared with that without the flow.