Interfacial instabilities in directional solidification of dilute binary alloys: the Kuramoto-Sivashinsky equation
type: Item
instance of: scholarly article
title: Interfacial instabilities in directional solidification of dilute binary alloys: the Kuramoto-Sivashinsky equation
zbMATH Open document ID: 0625.58035
DOI: 10.1016/0167-2789(87)90240-5
published in: Physica D
publication date: 1987-01-01T00:00:00Z
full work available at URL: http://purl.umn.edu/3318
review text: Directional solidification processes in the presence of an impurity are studied in the limit in which the dimensionless parameter \(\overline {W}=GD/VC_ 0(g+f_ c)\) is small. Here \(G\) is the imposed temperature gradient, \(D\) is the diffusion coefficient of the impurity, \(V\) is the imposed transport velocity, \(g\) is equal to minus the slope of the liquidus line, \(C_ 0\) is the impurity concentration at the liquid side of a planar interface, and \(f_ c\) is a coefficient reflecting deviations from local thermal equilibrium. The dynamics of interfacial kinetics becomes important in this limit and the phenomenological model of \textit{S. R. Coriell} and \textit{R. F. Sekerka} [J. Cryst. Growth 61, 499--508 (1983)] is used to model these processes. In this limit, the Kuramoto-Sivashinsky equation is shown to be an asymptotically valid description of the interfacial dynamics. The Kuramoto-Sivashinsky equation is known to exhibit intermittancy superimposed on a relatively stable array of cusps or wrinkles \textit{[D. M. Michelson} and \textit{G. I. Sivashinsky}, Acta Astronaut. 4, 1207--1221 (1977; Zbl 0427.76048)] and thus may give a reasonable limiting description of the solidification interface just before coherency is lost. These cusps may also be important in the initiation of dendritic growth by serving as defect points.
Mathematics Subject Classification ID: 80A22
Mathematics Subject Classification ID: 76R50
Mathematics Subject Classification ID: 35K60
zbMATH DE Number: 4015772
zbMATH Keywords: solidification processes
zbMATH Keywords: Kuramoto-Sivashinsky equation
author: Amy Novick-Cohen
MaRDI profile type: Publication
OpenAlex ID: W1994770663
cites work: Nonlinear analysis of hydrodynamic instability in laminar flames—II. Numerical experiments
cites work: On the solidification front of a dilute binary alloy: Thermal diffusivity effects and breathing solutions
cites work: Instability and turbulence of wavefronts in reaction-diffusion systems.
description: scientific article; zbMATH DE number 4015772