Abstract
Convective and interfacial instabilities during directional solidification are considered for a binary system where the coupling of the two modes of instability leads to oscillatory behavior very near the onset of instability. For a limited range of the control parameters, an oscillatory critical mode of instability is actually obtained. The directional solidification model assumes vertical growth of a binary alloy at constant velocity. Buoyant thermosolutal convection and morphological stability are treated via a stability analysis of the linearized governing equations and boundary conditions, which include the Boussinesq form of the Navier-Stokes equations for viscous flow and the required conservation laws for mass and energy in the two phases and at the solid-liquid interface. Numerical results for the stability criteria are obtained using two independent solution procedures. Detailed results are presented for the region of parameters where oscillatory behavior is obtained at or close to onset.
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Coriell, S.R., Murray, B.T., McFadden, G.B., Leonartz, K. (1994). Convective and Morphological Stability during Directional Solidification of the Succinonitrile-Acetone System. In: Brown, R.A., Davis, S.H. (eds) Free Boundaries in Viscous Flows. The IMA Volumes in Mathematics and its Applications, vol 61. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-8413-7_6
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DOI: https://doi.org/10.1007/978-1-4613-8413-7_6
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