Capillary-Wave Description of Rapid Directional Solidification

Alexander L. Korzhenevskii; Richard Bausch; Rudi Schmitz

doi:10.1103/physreve.85.021605

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arXiv · 1112.4091

Capillary-Wave Description of Rapid Directional Solidification

Alexander L. Korzhenevskii·Richard Bausch·Rudi Schmitz

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Abstract

A recently introduced capillary-wave description of binary-alloy solidification is generalized to include the procedure of directional solidification. For a class of model systems a universal dispersion relation of the unstable eigenmodes of a planar steady-state solidification front is derived, which readjusts previously known stability considerations. We, moreover, establish a differential equation for oscillatory motions of a planar interface that offers a limit-cycle scenario for the formation of solute bands, and, taking into account the Mullins-Sekerka instability, of banded structures.

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Alexander L. Korzhenevskii, Richard Bausch, Rudi Schmitz. 2011-12-17. Capillary-Wave Description of Rapid Directional Solidification. https://doi.org/10.1103/physreve.85.021605

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