The morphological stability of dendritic growth from the binary alloy melt with an external flow

The morphological stability of dendritic growth from the binary alloy melt with an external flow is studied by means of the matched asymptotic expansion method and multiple variable expansion method. The uniformly valid asymptotic solution is obtained for the case of the large Schmidt number. The analytical result reveals that the stability of dendritic growth depends on a critical stability number above which dendritic growth is stable. The selection condition of dendritic growth determines the Peclet number, tip growth velocity, tip radius and oscillation frequency, which is significantly affected by the external flow. The stability mechanism of dendritic growth in the binary alloy melt with the external flow remains the same as that in pure melt. In the binary alloy melt with the external flow the solute concentration destabilizes the dendritic growth system. The numerical computation for various growth conditions demonstrates the variations of the critical stability number, tip growth velocity, tip radius, and oscillatory frequency with the undercooling, external flow and morphological number.