Effect of fraction solid on coarsening of secondary dendrite arms

Abstract

Coarsening of secondary dendrite arms in mushy zones has been investigated theoretically and experimentally for many decades and simple phenomenological models have been developed describing the cube root dependence of the spacing on the solidification time. These models neglect in their description of mass transport between dendrite arms, that the finite volume fraction modifies the transport fluxes considerably. This paper describes an extension of conventional theoretical models for the secondary arm spacing based on finite volume fraction effect models for Ostwald ripening of spherical or cylindrical ensembles. The model predicts a much larger coarsening rate while the kinetics (cube root dependence) is conserved.