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On the theory of directional crystallization with a two-phase region with vigorous convection

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Abstract

A time-dependent process of directional crystallization with a two-phase (mushy) region with allowance for vigorous convection in the liquid phase is analytically described. An exact solution of non-linear mushy layer equations is found in a parametric form. The temperature and solute concentration distributions, as well as the solid phase fraction profile, are determined in the two-phase and liquid regions. The moving boundary of phase transition, which is placed between the two-phase zone and liquid is defined as a function of time. The present analytical solutions are in good agreement with laboratory experiments on ice grown from aqueous solutions of isopropanol.

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Authors and Affiliations

  1. Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Ural Federal University, Lenin Avenue 51, Ekaterinburg, 620000, Russia

    Dmitri V. Alexandrov, Nikita K. Goltyakov, Alexander A. Ivanov & Irina V. Alexandrova

  2. Sirius University of Science and Technology, 1 Olympic Avenue, Sochi, 354340, Russia

    Dmitri V. Alexandrov, Nikita K. Goltyakov, Alexander A. Ivanov & Irina V. Alexandrova

Authors
  1. Dmitri V. Alexandrov
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  2. Nikita K. Goltyakov
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  3. Alexander A. Ivanov
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  4. Irina V. Alexandrova
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Correspondence to Irina V. Alexandrova.

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Alexandrov, D.V., Goltyakov, N.K., Ivanov, A.A. et al. On the theory of directional crystallization with a two-phase region with vigorous convection. Eur. Phys. J. Spec. Top. 229, 2951–2959 (2020). https://doi.org/10.1140/epjst/e2020-000048-8

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  • DOI: https://doi.org/10.1140/epjst/e2020-000048-8

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