Solvability conditions for dendritic growth in the boundary-layer model with capillary anisotropy
- 1 August 1986
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review A
- Vol. 34 (2), 1462-1471
- https://doi.org/10.1103/physreva.34.1462
Abstract
This paper is concerned primarily with the development of an analytic approach to the theory of steady-state velocity selection in the boundary-layer model of dendritic solidification. We consider the two-dimensional version of this model with a fourfold crystalline anisotropy α in the surface tension. By extending a WKB method introduced in an earlier paper, we are able to determine the α dependence of the selected growth rate in the limit of small α; and we are also able to study this rate for larger α’s in the limit in which the dimensionless undercooling approaches unity. Portions of the paper are devoted to a reinterpretation of the mathematical structure of the solvability condition in problems of this kind.Keywords
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