Analytical Solution for a Problem of Directional Solidification in a Ternary System

The seemingly trivial moving boundary problem of the crystallization of a solid phase from a cooled wall comes under the rubric of the so-called Stefan problems describing a wide range of physical processes. Their rich nonlinear behavior has attracted substantial scientific interest and their ubiquity in fields ranging from metallurgy to geophysics stimulates developing new mathematical approaches (including phase-field models) (see, among others [1–8]). Solidification of single-component and binary solutions within the framework of the classical frontal approach as well as of the mushy layer scenario has intensively been studied by many authors for the last few years. Some many natural and industrial processes frequently met in practice cannot be explained in terms of single-component or binary systems but can, at least partially, be understood in terms of ternary systems. The major features of the dynamics of ternary systems can be studied using laboratory system of two salts dissolved in water. The mathematical model under consideration and its analytical solution are based on laboratory experiments [9] where a ternary solution was cooled from below and all convection was suppressed because the buoyancy of the fluid released on crystallization always increased. The present study is concerned with new analytic results on the nonlinear dynamics of solidification of a three-component alloy with two mushy layers on the basis of experimental data on crystallization of the ternary alloy H2O–KNO3–NaNO3.