Influence of Surface Waves on Liquid-to-Gas Mass Transfer in Molten Silicon

The paper focuses on the numerical analysis of the mass transfer of impurities from the wavy surface of molten silicon to the gas phase. The mathematical model is described herein, with the modelling of a wavy silicon melt surface being done with the moving mesh technique. The model employs assumptions about the mass transfer process on the surface, namely, that it can be modelled with effective diffusion across the interface. The assumption is verified against limited experimental data for a stationary melt surface, and reasonable agreement is obtained. Thereafter, numerical studies are undertaken for a wavy melt surface. The dependence of impurity removal rate on the wave amplitude, wavelength and frequency is analysed. It is shown that the waves on the surface of the liquid increase the mass transfer rate in a certain parameter range. Finally, results are analysed to find an explanation for this increase and to determine technological factors that impact it. Surface enlargement due to waves and altered flow patterns near the silicon melt are determined as potential reasons for the improved impurity removal rate. A dimensionless criterion for the minimal wave amplitude required to obtain improved impurity removal is found and discussed.