Stability of dendritic arrays

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Abstract
We propose an approximate method for studying steady-state properties and linear stability of the dendritic arrays that are formed in directional solidification of alloys. Our analysis is valid at high growth rates where the primary spacing between dendrites is larger than the velocity-dependent solutal diffusion length. We compute a neutral stability boundary and find that, in the situations where we expect our results to be valid, the experimental data of Somboonsuk, Mason, and Trivedi [Metall. Trans. A 15A, 967 (1984)] lie in the stable region, well away from the boundary.