Analytical modeling of solute redistribution during the initial unsteady unidirectional solidification of binary dilute alloys

Abstract

Existing analytical models for calculating solute redistribution during the initial transient (unsteady) unidirectional solidification with an axially moving boundary of binary dilute alloys were reviewed. The analytical solution obtained by Smith, Tiller, Rutter (STR) [Can. J. Phys. 33 (1955) 723] for semi-infinite domains was derived independently in this work. In obtaining the solution, STR used Laplace transform technique. In this work, it was rigorously proved by using Laplace transform, nondimensional analysis, and by eliminating the advection term in Eq. (1), that the analytical solution found by STR is indeed “exact” and “unique” under the stated assumptions. A thorough comparison between the exact solution and some approximate solutions is provided for partition distribution coefficients smaller and larger than one. Transient and quasi-steady-state results obtained with the exact analytical solution for segregation profiles in the liquid and at the solid/liquid interface, liquid concentration gradient at the solid/liquid interface, and solutal boundary layer are discussed in details. The size of the initial transient region is calculated. The exact solution is then applied to investigate based on thermodynamic arguments the instability of the solid/liquid interface during the initial solidification regime of dilute alloys.