Gas effects on horizontal ribbon growth

Three-phase (solid, melt, and gas) and two-phase (solid and melt) models of horizontal ribbon growth were compared to identify the significance of different gas effects. The boundary conditions at the melt-gas and solid-gas interfaces for two-phase simulations were obtained from decoupled simulations of the gas phase. The results showed that the gas shear stress strongly changes the flow and temperature fields and the position of the triple-phase line. Also, the gas pressure distribution determined the vertical position of the triple-phase line. In the absence of growth angle effects, the results of the two-phase model with specified convective heat transfer coefficient, shear stress, and pressure as boundary conditions along the gas phase interface closely matched that of the three-phase model. Even with non-zero growth angle effects, the two-phase model with all the boundary conditions agreed well with three-phase simulation results, despite increased deviations at higher pull speeds. Finally, the results indicated that gas-induced velocities are significant compared to the Marangoni and buoyancy velocities, which could lead to flow instabilities and the variations in solid shape as observed in HRG experiments.