Averaged solute transport during solidification of a binary mixture: Active dispersion in dendritic structures

Abstract

The macroscopic conservation equations governing solute transport during solidification of binary alloys are derived using an averaging procedure in the context of macroscale nonequilibrium. Special attention is focused on the derivation of the associated closure problems, leading to the determination of the effective dispersion tensor and macroscopic interphase coefficients that characterize active dispersion phenomena. These closure problems are solved numerically using schematic structures and digitized images of real columnar dendritic structures observed experimentally during solidification of succinonitrile-4 wt pct acetone. The influence of the geometry and dispersion on the effective solute-properties transport is analyzed, and comparison with passive dispersion is provided. The theoretical and numerical results indicate, first, that tortuosity effects are small, and this is related to the impact of the boundary condition at the interface between the two phases, and, second, that dispersion becomes very important only at very large Peclet numbers.