Directional crystallization with a mushy region. Part 1: linear analysis of dynamic stability
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, 620000, Ekaterinburg, Russian Federation
Accepted: 21 March 2023
Published online: 3 April 2023
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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