THE NONLINEAR DYNAMICS OF SOLIDIFICATION OF A BINARY MELT WITH A NONEQUILIBRIUM MUSHY REGION

A new theoretical analysis of the solidification process of a binary melt with a mushy region, in which the temperature is below the equilibrium temperature, is presented. The mushy region consists of the liquid and the growing spherical particles. The equations of heat and mass of the solute and the kinetic equation for the particle size distribution function are used. The nucleation rate and the crystal growth rate are phenomenologically defined. An approximate expression for a portion of solid phase in the mushy region is given by the investigation of the kinetic equation. As a result, the dynamics of the nonequilibrium mushy region is determined by two nonlinear integro-differential equations with appropriate boundary conditions. An approximate analytical solution of this system of equations is obtained for the quasi-stationary regime of solidification. The temperature, concentration distribution, and the distribution function are defined for the mushy region. The method can be used for analysing the solute distribution pattern in solid materials obtained by solidification from a melt.