Effects of Temperature Difference and Heat Loss on Oscillation Characteristics of Thermo-Solutocapillary Convection in Toluene/N-Hexane Mixed Solution

Abstract

During the crystal growth process using the floating zone method, the uneven distribution of impurities on the surface of the melt can trigger a coupling mechanism between solutocapillary convection driven by the concentration gradient and thermocapillary convection driven by the temperature gradient, resulting in the Marangoni convection at the free surface. When the temperature and concentration gradients reach certain values, the crystal surface and interior exhibit time-dependent, periodic oscillations, leading to the formation of micrometer-scale impurity stripes within the crystal. This study focuses on the effects of temperature difference and heat loss in a liquid bridge under microgravity on the structure and interface oscillation characteristics of thermo-solutocapillary convection, aiming to explore the coupling phenomenon of this oscillation and provide valuable information for crystal growth processes. An improved level set method is employed to accurately track every displacement of the interface, while the surface tension is addressed using the CSF model. In addition, the area compensation method is used to maintain simulation quality balance. A comprehensive analysis is performed on the oscillation characteristics of thermo-solutocapillary convection at the free surface, ranging from the temperature, concentration, deformation, and velocity distributions at the upper and middle heights of the liquid bridge. The results indicate that under small temperature differences (ΔT = 1 − 3), the transverse velocity at the upper end exhibits a single-periodic oscillation, while the longitudinal velocity presents a double-periodic oscillation. At the intermediate height, both the transverse and longitudinal velocities display a single-periodic oscillation. Under a large temperature difference (ΔT = 6), the oscillation of velocities at the upper end and the middle position become multi-periodic. In addition, heat loss has certain regular effects on the oscillatory flow of thermo-solutocapillary convection within a certain range. The velocity, amplitude, and frequency of the upper end and the middle position at the free surface decrease gradually, and the oscillation intensity also weakens with the increase in heat loss (Bi = 0.2 − 0.6). These new discoveries can provide a valuable reference for optimizing the crystal growth process, thereby enhancing the quality and performance of crystal materials.