Dynamic scaling in dendritic growth

Abstract

We use simple scaling analysis to examine the fundamental relations in dendritic growth between dynamic parameters such as dendrite tip radius and growth velocity, and the dimensionless net heat flux through the dendrite surface (Péclet number). The resulting relations are then expanded in powers of the Péclet number. It is demonstrated that for a small Péclet number, a two term expansion is sufficient to fit the entire range of data in supercooling of Glicksman's recent microgravity experiment [M.E. Glicksman, M.B. Koss and E.A. Winsa, Phys. Rev. Lett. 73 (1994) 573; M.E. Glicksman, M.B. Koss, L.T. Bushnell, J.C. LaCombe and E.A. Winsa, ISIJ Int. 35 (1995) 1216; MRS Fall Meeting, Symp. P, Boston, MA, 1995, in press]. We also show that conventional theories using a single parameter are not supported from basic scaling arguments, nor do they correspond to experimental observations.