Capillary-Wave Description of Rapid Directional Solidification
Mesoscale and Nanoscale Physics
2015-06-03 v1 Materials Science
Other Condensed Matter
Statistical Mechanics
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.
Cite
@article{arxiv.1112.4091,
title = {Capillary-Wave Description of Rapid Directional Solidification},
author = {Alexander L. Korzhenevskii and Richard Bausch and Rudi Schmitz},
journal= {arXiv preprint arXiv:1112.4091},
year = {2015}
}