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

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