Three-Dimensional Numerical Simulation of Silicon Vapor Transport during the Infiltration of a Porous Carbon Matrix

A new equation for silicon vapor transport in a foreign gas has been derived to describe the high-temperature silicification of porous carbon fiber. The modified nonlinear diffusion equation is obtained from the complete system of hydrodynamic equations. Additional convective silicon transport is represented by a term quadratic in the concentration gradient. Its contribution is characterized by a new parameter with the same dimensionality as the diffusion coefficient, which depends on the properties of the carrier gas. The applicability of the resulting partial differential equation is demonstrated by three-dimensional numerical simulations of silicon vapor transport in a retort under conditions closely approximating a particular technological process. The results show that, after evaporation begins at the melt surface, silicon rapidly fills almost the entire volume of the retort, except for a thin boundary layer near the product surface, where complete absorption of silicon is assumed to occur. The theoretical derivation agrees well with experimental data, as the proposed concentration gradient at the carbon surface is sufficient to achieve silicification within the timescale observed in experiments. The developed approach is contrasted with a purely diffusive transport model, which fails to account for the observed intensive silicon mass transfer in the retort.