Multiscale simulations of micro-structure selection in binary alloy solidification

We demonstrate that the competition of dendritic crystals in a solidifying sample gives rise to two qualitatively different micro-structure solutions depending on the density p of crystals in the melt. Here we show for the first time, that there is a non-steady transition from one to the other. The precise p-dependence of the transition point is determined by the Biot number. Our investigation is based on a scaling analysis for the tip velocity of the dendritic crystals, which we assume to be aligned in an array and to be coupled via the transport of heat. We develop our analytical solutions based upon the asymptotic Kruskal-Segur reduction to a differential equation in the complex plane. It is supported by numerical simulations of a multiscale model of alloy growth. On the one hand this solution can be used to improve the accuracy of applied solidification simulations. On the other hand it yields additional insight in the universality of diffusion limited crystal growth in the presence of competing micro-structures. (C) 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.