The nonlinear dynamics of solidification of a binary melt with a quasi-equilibrium mushy region

Abstract

A mushy region (a two-phase zone) between the solid and liquid phases occurs often in the process of solidification of a binary melt. An analysis of the structure of the mushy region, which includes the liquid, solid particles, and dendrites extending from the bulk solid surface, is suggested. The processes of heat and mass transfer in the mushy region are considered on the basis of the small parameter method. The analysis leads to equations governing unsteady heat and mass transfer with internal heat, and mass sources within the mushy region, and it includes the condition for the absence of supercooling (the condition for the zone quasi-equilibrium), convection being neglected. The temperature, concentration of solute, and solid phase volume fraction are found. On the basis of this solution a new model of the process is formulated. Within the scope of this model the mushy region is replaced by a liquid–solid interface with discontinuous boundary conditions.