Conjugate mass transfer and immobilization of silicon vapor during the saturation of a porous medium based on carbon fiber

Abstract

We constructed a conjugate physical and mathematical model that describes a high-temperature mass transfer of silicon vapor from the melt mirror to a porous carbon material, the process of its filtration, and deposition inside the sample. In the outer region, the distribution of vapor is determined by a general nonlinear diffusion equation that takes into account the convective mass transfer in the working space of the retort. Inside the porous sample, the behavior of gaseous silicon is described by a system of equations in the framework of the MIM-approach. It is assumed that the silicon deposition mainly depends on the temperature distribution inside the sample. For simplicity, a one-dimensional problem is considered. The boundary conditions are chosen taking into account the significantly different permeabilities of the carrier medium and the porous carbon fiber. The temperature outside the material is assumed to be constant, while inside a non-uniform distribution is maintained. The constructed boundary value problem was solved numerically with the use of the finite difference method. The distributions of silicon vapor outside and inside the sample were obtained. It is shown that the non-linearity in the mass transfer equation leads to a distortion of the distribution from the melt mirror to the sample, which indicates a significant contribution of the convective mass transfer to the silicon vapor flow in this region.