Shear stabilization of morphological instability during directional solidification

A linear stability analysis is performed on the interface formed during the directional solidification of a dilute binary alloy in the presence of a time-periodic flow. In general, the flow is generated by translating the crystal relative to the far-field flow in elliptical orbits parallel to the interface. The presence of this complex, unsteady flow can either stabilize or destabilize the system relative to the case without flow, with the result depending on the frequency and amplitude of the oscillations as well as the properties of the material. We find, however, that proper selection of the frequency and amplitude of the modulation, both physically realizable, can eliminate the possibility of morphological instability for a significant range of solute concentrations.