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Directional crystallization with a mushy region. Part 1: linear analysis of dynamic stability

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Abstract

In this paper, a linear analysis of dynamic stability of the directional solidification process with a two-phase region is carried out. We show the possibility of oscillatory mode of instability development in relation to the steady-state crystallization process with a constant velocity. We determine the steady-state solutions and derive evolutionary equations for the perturbations, derive an equation for the neutral stability curve and obtain the parametric regions of stable/unstable crystallization. It is shown that the regions of monotonous/oscillatory instability and stability can exist. The boundaries separating these regions are defined. We demonstrate that a transition between oscillatory and monotonous instabilities occurs abruptly. In addition, we show that the crystallization process with a two-phase region stabilizes the dynamic perturbations with respect to the crystallization process with a flat front.

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Acknowledgements

This work was financially supported by the Russian Science Foundation (project no. 21-19-00279).

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Authors and Affiliations

  1. Department of Theoretical and Mathematical Physics, Laboratory of Multi-Scale Mathematical Modeling, Laboratory of Stochastic Transport of Nanoparticles in Living Systems, Ural Federal University, Lenin ave., 51, Ekaterinburg, 620000, Russian Federation

    Eugenya V. Makoveeva, Alexander A. Ivanov, Irina V. Alexandrova & Dmitri V. Alexandrov

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  1. Eugenya V. Makoveeva
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  2. Alexander A. Ivanov
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  3. Irina V. Alexandrova
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  4. Dmitri V. Alexandrov
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Correspondence to Dmitri V. Alexandrov.

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Structural Transformations and Non-Equilibrium Phenomena in Multicomponent Disordered Systems. Guest editors: Liubov Toropova, Irina Nizovtseva.

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Makoveeva, E.V., Ivanov, A.A., Alexandrova, I.V. et al. Directional crystallization with a mushy region. Part 1: linear analysis of dynamic stability. Eur. Phys. J. Spec. Top. 232, 1119–1127 (2023). https://doi.org/10.1140/epjs/s11734-023-00823-7

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