Numerical research of solidification dynamics with anisotropy and thermal fluctuations

¹ Department of Thermodynamics, Theory of Machines and Thermal Systems, Wrocław University of Science and Technology, Wybrzeże Wyspiańskiego 27 St. 50-370 Wrocław, Poland
² Institute of Fluid Science, Tohoku University, 2-1-1, Katahira, Aoba-ku, Sendai 980-8577, Japan

Abstract

The influence of thermal fluctuations and anisotropy on the solidification process of a pure component is analyzed. It helps to understand the unstable freezing process where complicated structures such as dendrites could be formed due to a supercooling event reached during the cooling of the biological material. The study consists of mathematical modeling, validation with an analytical solution, and shows the influence of thermal noises on phase front dynamics. The analysis has been modeled in the framework of the Phase Field Method with Cahn-Hilliard formulation of a free energy functional [1]. The phase front is described by the Eulerian approach of fluid fields and formulated as a Phase Field scalar variable (order parameter) with a predefined, diffused boundary thickness. The results describe an influence scale onto directional phase front propagation dynamics, and how significant are stochastic thermal noises in micro-scale freezing.