Capillary-Wave Description of Rapid Directional Solidification

Details Capillary-Wave Description of Rapid Directional Solidification Capillary-Wave Description of Rapid Directional Solidification

2011-12-17

arxiv.org/abs/1112.4091v1

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

Scientific paper

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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