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Capillary-wave description of rapid directional solidification

Alexander L. Korzhenevskii

Richard Bausch

Rudi Schmitz

  • Institute for Problems of Mechanical Engineering, RAS, Bol'shoi prospekt, V. O. 61, St. Petersburg 199178, Russia

  • Institut für Theoretische Physik IV, Heinrich-Heine-Universität Düsseldorf, Universitätsstrasse 1, D-40225 Düsseldorf, Germany

  • Institut für Theoretische Physik C, RWTH Aachen University, Templergraben 55, D-52056 Aachen, Germany

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Phys. Rev. E 85, 021605 – Published 21 February, 2012

DOI: https://doi.org/10.1103/PhysRevE.85.021605

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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References (16)

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Phys. Rev. E 85, 021605– Published 21 February, 2012
  • Received 17 December 2011

©2012 American Physical Society

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