Directional solidification with a two-phase zone: thermodiffusion and temperature-dependent diffusivity

The effect of a temperature-dependent solute diffusion coefficient on the model of unidirectional solidification of a binary melt with a steady-state two-phase zone is studied. The Soret effect (thermodiffusion) is also included in the analysis. Analytical approaches and numerical calculations allow us to solve the nonlinear problem under consideration. The concentration and temperature fields in the liquid, solid and mixed state phases are found as functions of all thermophysical parameters. The rate of solidification and two-phase zone thickness are determined as well. The role of the nonlinear solute transport is detailed in the analysis. Our theory demonstrates that the mushy zone can be treated as a self-similar object.