中文摘要：

本文建立了毛细模型，采用微流动两相流水平集法计算了熔融态硅液与壁面的润湿角，以人造金刚石作为壁面材料的计算结果与实验结果进行比较，验证了该模型和计算方法的正确性。在此基础上，分别选用碳化硅、石墨和人造金刚石作为壁面材料，探讨了不同壁面材料表面张力和壁面黏附力对润湿角的影响规律。结果发现，相同温度下的毛细力作用使得熔融硅液出现起伏上升现象；润湿角均有不同程度的减小然后增大，最终趋于稳定；初始阶段，由于气/熔融硅液表面张力与气/壁面表面张力之差变化较大，液面起伏波动较大；随后趋于稳定上升。同时发现石墨作为壁面材料时，以上变化更易趋于稳定。该研究为熔体中生长晶体硅获得更稳定的生长环境提供了理论依据。

英文摘要：

A capillary model is developed for calculating the wetting angle of molten silicon on different walls by using the microfluidic two-phase flow level set method and studying the characteristics of the rising process. A mathematical model formulation rigorously accounts for the mass and momentum conservation by using the improved Navier-Stokes equation and considering the Marangoni effect. Compared with the experimental data, the change of the wetting angle on the chemical vapor deposition （CVD） diamond wall indicates the grids independence and the validity of the numerical algorithm. We also discuss the influence of surface tension, and Marangoni stress induced by the gradient of surface tension coe？cient, and wall adhesion to the change of wetting angle for three different walls, which include SiC wall, graphite wall, and CVD diamond wall, at different temperatures （1683-1873 K）. Result shows that at the same temperature, the thermal-capillary effects that induce the molten silicon to undulation are raised. The wetting angle is reduced after first being increased and finally stabilized. At the initial stage, the fluctuation of the liquid-air interface is volatile due to the large changes of the liquid-air and the wall-air surface tensions, and subsequently, the fluctuation tends to be stable while the wetting angle is close to a fixed value. It is also found that with the graphite wall, these changes are more likely to be stable. This research provides a theoretical guide to obtain a stable growth environment for silicon belt fabricated from the molten silicon.