Physical and mathematical model of gaseous silicon transfer during high-temperature siliconization of carbon composite materials

Abstract

We propose a new physical and mathematical model for description of silicon vapor high-temperature transfer under medium vacuum conditions from the melt mirror to the surface of an absorbing porous medium in an atmosphere of residual gas. The developed model is simplified to the greatest extent possible and is intended for further numerical implementation in the course of modeling a non-stationary three-dimensional process of high-temperature siliconization of arbitrary-shaped porous carbon products under the condition of a complex distribution of silicon sources. The physical and mathematical model of transport consists of only one non-linear partial differential equation for the silicon vapor concentration in an atmosphere of argon or any other residual gas. In the limiting case of the simplest geometry and one-dimensional formulation of the problem, we obtained a stationary analytical solution that explains the anomalously large silicon vapor flux into the porous material in full-scale experiments. The obtained analytical solution for the studied gas mixtures is expressed in terms of the known verified values of the material parameters. It shows that despite the low saturation density of silicon vapor, the vapor-liquid-phase process of high-temperature siliconization of carbon materials is physically possible in a reasonable time.