TY - JOUR

T1 - Directional crystallization with a mushy region. Part 1: linear analysis of dynamic stability

AU - Makoveeva, Eugenya V.

AU - Ivanov, Alexander A.

AU - Alexandrova, Irina V.

AU - Alexandrov, Dmitri v.

N1 - This work was financially supported by the Russian Science Foundation (project no. 21-19-00279).

PY - 2023

Y1 - 2023

N2 - 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. © 2023, The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature.

AB - 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. © 2023, The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature.

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U2 - 10.1140/epjs/s11734-023-00823-7

DO - 10.1140/epjs/s11734-023-00823-7

M3 - Article

VL - 232

SP - 1119

EP - 1127

JO - European Physical Journal: Special Topics

JF - European Physical Journal: Special Topics

SN - 1951-6355

IS - 8

ER -