Marangoni convection in a hemispheric molten silicon droplet and its control by an applied magnetic field

Abstract

A numerical simulation study was conducted for the "sessile drop method" that is one of the essential tools for conducting measurements of physical properties in droplets. The effect of the Marangoni convection on the maximum flow velocity in a hemispheric molten silicon droplet was examined. The maximum Reynolds number was correlated with the Marangoni and Biot numbers, and the surrounding temperature by Re_{max}= [-209.4{T_a(&pi;/2)/T_{mp}} + 216.8] … (BiMa)(when BiMa < 40) and Re_{max} = [-472.5{T_a(&pi;/2)/T_{mp}} + 491.3] …(BiMa) ^{2/3} (when BiMa > 40). Simulation results show that the application of a vertical magnetic field can suppress the flow in the droplet near the plate, and consequently prevent the movement of the drop, and give rise to a diffusion-limited-condition near the plate where accurate measurements of the physical properties of a melt can be made.