Towards the Stable Evolution of Dendrites in the Case of Intense Convection in the Melt

The solid-phase pattern in the form of a dendrite is one of the frequently met structures produced from undercooled liquids. In the last decades, an analytical approach describing the steady-state crystal growth in the presence of conductive heat and mass transport has been constructed. However, experimental works show that crystal patterns frequently grow in the presence of convection. In this paper, a theoretical description based on convective heat and solute concentration transport near the solid/liquid phase interface is developed. The stable regime of crystallization in the presence of vigorous convection near the steady-state crystal vertex is studied. The stability analysis, determining the stable growth mode, and the undercooling balance law have been applied to deduce the stable values for the growth rate and tip diameter. Our analytical predictions (with convective transport) well describe experimental data for a small melt undercooling. Moreover, we compare both convective and conductive mechanisms in the vicinity of the crystal vertex. Our theory shows that convective fluxes substantially change the steady-state growth of crystals. © 2021 Institute of Physics Publishing. All rights reserved.The present work comprises different parts of research studies, including (i) the model formulation, stability and solvability analyses, derivation of the selection criterion, and (ii) numerical simulations and comparison with experimental data. Different parts of this study were supported by different grants and programs. With this in mind, the authors are grateful to the following foundations, programs, and grants. The first theoretical part (i) was supported by the Russian Science Foundation (grant no. 21-19-00279). The second part (ii) was made possible due to the financial support from the Ministry of Science and Higher Education of the Russian Federation (FEUZ-2020-0057)