Physical model and numerical simulation of high-temperature silicification of carbon composite material

A mathematical model is developed to describe the process of high-temperature silicification of a carbon porous material. The cause of pores blockage is the condensation of gaseous silicon at the inner walls of tubules. Phenomenological temperature dependences for the coefficients of condensation and evaporation are proposed, which determine the intensity of the siliconizing process. It is assumed that the diffusion of the silicon vapour is the main mechanism of the material open pores filling. Numerical modelling is carried out by the finite difference method using an explicit scheme in the case of a constant value of the mobile concentration at the input and for different variants of boundary conditions on temperature. These temperature distributions on boundaries make it possible to describe siliconized regions and to delimit from them the sample parts that remain 'dry' during the silicification process. The dynamics of main physical quantities change, i.e. porosity of the composite material and concentration of the immobile component in the volume, are analysed. The results of numerical simulation for the time of full silicification and the weight gain of the product are in qualitative and quantitative agreement with all known experimental data. This article is part of the theme issue 'New trends in pattern formation and nonlinear dynamics of extended systems'.