Theory of dendritic growth—I. Elements of a stability analysis

Abstract

We propose that the maximum-velocity principle previously used in theories of dendritic crystal growth be replaced by a stability criterion of the form υρ 2 = constant, where υ is the growth rate and ρ the tip radius of a dendrite. This form of the stability criterion is valid for small Péclet numbers (ρ much smaller than the diffusion length). A direct evaluation of the relevant constant of proportionality yields values of υ and ρ, as functions of undercooling, which are in substantial agreement with the measurements of Glicksman et al. [3] on dendritic growth of succinonitrile crystals. In this paper, we summarize our basic ideas and describe qualitatively our theoretical results. Mathematical details are presented in two subsequent papers.