Transport mechanisms of falling crystals detached from the freezing front during solidification of a hypereutectic binary mixture

Abstract

Experiments studying transport phenomena during directional solidification of a hypereutectic binary solution in a top-cooled rectangular cavity are often characterized by the descendence of fragmented solid crystals through the unfrozen fluid. This observation, however, is yet to be fundamentally explained from a theoretical perspective. In this Letter, we propose a new model to describe stochastic dynamics of the falling crystals, which is not only applicable to this specific situation, but also appropriate for a generalized mathematical description of evolution of solid particles in the presence of stochastic fluctuations from the ambience accompanied by the growth or dissolution of crystals. Simulations of the proposed model also show an extremely good agreement between the theoretical predictions and earlier experimental findings.