The Role of a Two-Phase Region in Directional Crystallization of Binary Liquids

Dmitri V. Alexandrov, Irina V. Alexandrova, Alexander A. Ivanov and Liubov V. Toropova ()
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Dmitri V. Alexandrov: Laboratory of Multi-Scale Mathematical Modeling, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin Ave., 51, Ekaterinburg 620000, Russia
Irina V. Alexandrova: Laboratory of Multi-Scale Mathematical Modeling, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin Ave., 51, Ekaterinburg 620000, Russia
Alexander A. Ivanov: Laboratory of Multi-Scale Mathematical Modeling, Department of Theoretical and Mathematical Physics, Ural Federal University, Lenin Ave., 51, Ekaterinburg 620000, Russia
Liubov V. Toropova: Laboratory of Mathematical Modeling of Physical and Chemical Processes in Multiphase Media, Ural Federal University, Ekaterinburg 620000, Russia

Mathematics, 2024, vol. 12, issue 14, 1-15

Abstract: Motivated by the widespread occurrence of directional crystallization in nature, laboratory experiments and industrial facilities, we consider how a two-phase (mushy) region filled simultaneously with liquid and solid material influences the process and changes the solute concentration in both the phases. A mushy layer arising as a result of constitutional supercooling in binary liquids drastically changes all process parameters in comparison with the frequently used approximation of a macroscopically planar phase interface. The heat and mass transfer problem with a moving mushy region is replaced by the equivalent model with a discontinuity interface that divides the liquid and solid phases and inherits the properties of a mushy layer. Analytical solutions that describe both crystallization modes with a planar phase interface and discontinuity interface (representing a mushy layer) are constructed for the steady-state and self-similar conditions. The switching time of the crystallization model with a planar phase interface to the model with a two-phase layer is determined. Our calculations, based on analytical solutions, show that the presence of a mushy layer can change the solute concentration in liquid and solid phases to a few tens of percent as compared to the planar interface model. This explains the importance of accounting for the two-phase region when describing the crystallization of supercooled binary liquids.

Keywords: phase transformation; heat and mass transfer; two-phase layer; moving boundary problem; binary system; constitutional supercooling (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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