Solvability conditions for dendritic growth in the boundary-layer model with capillary anisotropy

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.