Stability of Solutal Convection in a Gravity Modulated Mushy Layer During the Solidification of Binary Alloys

The linear stability theory is used to investigate the effects of gravity modulation on solutal convection in mushy layers found in solidifying binary alloys. The gravitational field is modeled to consist of constant part and a sinusoidally varying part. The linear stability results are presented for both the synchronous and subharmonic solutions, and it is demonstrated that up to the transition point between the synchronous and subharmonic regions, increasing the frequency of vibration rapidly stabilizes the solutal convection. However, beyond the transition point, further increases in the frequency tends to destabilize convection. It is also demonstrated that the effect of increasing the ratio of the Stefan number and the solid composition (ηo) is to destabilize the solutal convection.