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Selection Mechanisms for Multiple Similarity Solutions for Solidification and Melting



Sam R. Coriell, Geoffrey B. McFadden, R F. Sekerka


When a solid phase of uniform temperature Ts∞ and Composition Cs∞ is brought into contact with a liquid phase of uniform temperature TL∞ and composition CL∞, there exist similarity solutions for which the position X of the solid-liquid interface is proportional to the square root of time t, i.e., X = λ{root}t. Recently, we have explored situations in which there are multiple similarity solutions, e.g., three values of λ for the same far-field and initial conditions. We relax the assumption of local equilibrium by assuming a linear kinetic law in which the interface velocity is proportional to the deviation of interface temperature from the equilibrium temperature. For small time, we find a unique constant velocity solution. With local equilibrium at the interface, we examine the stability of the similarity solutions with respect to perturbations which preserve the planar geometry.
Journal of Crystal Growth


alloy melting, alloy solidification, lead-tin, multiple solutions, similarity solutions


Coriell, S. , McFadden, G. and Sekerka, R. (1999), Selection Mechanisms for Multiple Similarity Solutions for Solidification and Melting, Journal of Crystal Growth (Accessed March 4, 2024)
Created April 1, 1999, Updated February 17, 2017