Instabilities In Directional Solidification Under Inclined Rotation

We investigate the stability of a binary alloy directionally solidifying at a constant rate and rotating with spin and/or precession about an inclined axis. Results show that, prior to the onset of instability, a flow is induced by the inclination and modified by the rotation, having a velocity profile like a spiral Ekman flow. The induced flow moves steadily relative to the system when the system rotates with precession only, while it changes direction periodically when the system rotates with spin (even if precession is included). Based on this flow, the effects of inclined rotation on the stability of the system are examined by linear analyses. We find that there are five mechanisms affecting the stability due to inclined rotation: the reduction of both buoyancy and the rotation vector along the height of the system are stabilizing, the gravity component along the melt/solid interface is destabilizing, and the inclination-induced flow and precession combine to play a stabilizing or a destabilizing role, depending on their relative orientation and amplitude ratio. In general, the morphological mode is slightly stabilized whereas the convective and mixed modes are significantly stabilized. For inclined precession, the instability mode moving aligned with the gravity component along the melt/solid interface is most unstable. For inclined spin, all the stability-affecting mechanisms act equally in all directions so that the stability thresholds for the instability modes moving in different directions are equal. For directional solidification applications, the present results suggest that to prevent compositional non-uniformities in the solid, inclined spin is more effective than inclined precession.