Hydrodynamic and morphological stability of the unidirectional solidification of a freezing binary alloy: a simple model

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Abstract
In this paper we consider the effect of a model boundary-layer flow on the hydrodynamic and morphological stability of a simple model of the solidification of a binary alloy. We conduct a linear analysis and develop asymptotic solutions for large Schmidt number and large Reynolds number. We also present numerical solutions for data appropriate to a lead–tin alloy. We show that for modes parallel to the free-stream velocity the flow is responsible for the appearance of travelling waves and, for common values of the material parameters, may stabilize the morphological stability of the interface. However the morphological stability of modes perpendicular to the free-stream velocity is unaffected by the presence of the flow. The hydrodynamic stability of the boundary layer is very weakly affected by the presence of the interface, which we attribute to the large Schmidt numbers associated with real crystal growth situations.