Morphological/Dynamic Instability of Directional Crystallization in a Finite Domain with Intense Convection

Abstract

This study is devoted to the morphological/dynamic instability analysis of directional crystallization processes in finite domains with allowance for melt convection. At first, a linear instability theory for steady-state crystallization with a planar solid/liquid interface in the presence of convection was developed. We derived and analyzed a dispersion relation showing the existence of morphological instability over a wide range of wavenumbers. This instability results from perturbations arriving at the solid/liquid interface from the cooled wall through the solid phase. Also, we showed that a planar solid/liquid interface can be unstable when it comes to dynamic perturbations with a zero wavenumber (perturbations in its steady-state velocity). A branch of stable solutions for dynamic perturbations is available too. The crystallizing system can choose one of these branches (unstable or stable) depending of the action of convection. The result of morphological and dynamic instabilities is the appearance of a two-phase (mushy) layer ahead of the planar solid/liquid interface. Therefore, our next step was to analyze the dynamic instability of steady-state crystallization with a mushy layer, which was replaced by a discontinuity interface between the purely solid and liquid phases. This analysis showed the existence of dynamic instability over a wide range of crystallization velocities. This instability appears in the solid material at the cooled wall and propagates to the discontinuity interface, mimicking the properties of a mushy layer. As this takes place, at a certain crystallization velocity, a bifurcation of solutions occurs, leading to the existence of unstable and stable crystallization branches simultaneously. In this case, the system chooses one of them depending of the effect of the convection as before. In general, the crystallizing system may be morphologically/dynamically unstable when it comes to small perturbations arriving at the phase interface due to fluctuations in the heat and mass exchange equipment (e.g., fluctuations in the freezer temperature).