The Stefan problem of solidification of ternary systems in the presence of moving phase transition regions / Alexandrov D.V., Ivanov A.A. // Journal of Experimental and Theoretical Physics. - 2009. - V. 108, l. 5. - P. 821-829.

ISSN:
10637761
Type:
Article
Abstract:
The process of solidification of ternary systems in the presence of moving phase transition regions has been investigated theoretically in terms of the nonlinear equation of the liquidus surface. A mathematical model is developed and an approximate analytical solution to the Stefan problem is constructed for a linear temperature profile in two-phase zones. The temperature and impurity concentration distributions are determined, the solid-phase fractions in the phase transition regions are obtained, and the laws of motion of their boundaries are established. It is demonstrated that all boundaries move in accordance with the laws of direct proportionality to the square root of time, which is a general property of self-similar processes. It is substantiated that the concentration of an impurity of the substance undergoing a phase transition only in the cotectic zone increases in this zone and decreases in the main two-phase zone in which the other component of the substance undergoes a phase transition. In the process, the concentration reaches a maximum at the interface between the main two-phase zone and the cotectic two-phase zone. The revealed laws of motion of the outer boundaries of the entire phase transition region do not depend on the amount of the components under consideration and hold true for crystallization of a multicomponent system. © 2009 Pleiades Publishing, Ltd.
Author keywords:
Index keywords:
Approximate analytical solutions; Concentration of; Impurity concentration; Linear temperature; Liquidus surfaces; Multi-component systems; Self-similar process; Solid-phase; Square roots; Stefan prob
DOI:
10.1134/S1063776109050100
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Affiliations Gorkiy Ural State University, pr. Lenina 51, Yekaterinburg 620083, Russian Federation
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Correspondence Address Alexandrov, D. V.; Gorkiy Ural State University, pr. Lenina 51, Yekaterinburg 620083, Russian Federation; email: Dmitri.Alexandrov@usu.ru
Language of Original Document English
Abbreviated Source Title J. Exp. Theor. Phys.
Source Scopus