Linear Stability Analysis of a Solidifying Ternary Alloy




Flynn, Terrance J. Jr.

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Solidification occurs frequently in many natural and industrial settings. Since producing solids from liquids impacts many aspects of daily life, it is worthwhile to understand this process. Modeling the transformation of a liquid into a solid for multicomponent systems can, among other things, provide insights into the quality of the final solid. In recent years, mathematical models describing the solidification of aqueous ternary alloys have been proposed. These models include governing equations and boundary conditions for each of the four major layers and interfaces present during the phase transition from liquid to solid. The four layers consist of a completely solid and completely liquid layer separated by two distinct mushy layers. The mushy layers are composed of both solidified material and residual liquid and are treated as reactive porous regions. Here, reactive means the amount of solid occupying the mush is influenced by the local temperature and liquid composition. Furthermore, these solute and temperature fields are coupled to the fluid velocity. Tracking the general motion of the °uid within these mushy layers then becomes important to understanding their growth. This work seeks to improve earlier models describing the change of phase in aqueous ternary alloy systems. One such improvement is the addition of equations allowing transport of heat and solute by both diffusion and convection. With these enhancements made, a base state problem and solution are identified for the new model. The linear stability of the basic solution is investigated numerically using a Chebyshev pseudospectral collocation method. Results of the analysis are given in the form of neutral stability curves which describe the base state's linear stability to infinitesimal perturbations for some specific cases.



Solidification, Ternary alloys, Linear stability, Mushy layer