Modelling chemical vapour infiltration of pyrolytic carbon as moving boundary problem

Chemical vapour infiltration (CVI) of pyrolytic carbon is described as a moving boundary problem to determine the evolution of the pyrolytic carbon layer in space and time. Derived from real geometries, a one-dimensional single pore model is developed yielding a nonlinear coupled system of partial differential equations for the concentrations of the gas phase species and the height of the carbon layer within cylindrical pores. The evolution of the moving boundary of the gas phase domain is governed by a non-differentiable minimisation condition. Additionally, a CVI reactor model to describe the infiltration of several cylindrical pores within a porous substrate is presented on the basis of the single pore model. Both models are new in that they combine the following features: (i) derivation of the equations rigorously taking into account the temporal change of the gas phase, (ii) the explicit construction of the position of the gas-solid interface, (iii) the influence of the local curvature of the carbon layer on its growth velocity, and (iv) modelling of chemical kinetics using a reduced reaction scheme with intermediate gas phase species and several surface reactions. The models are solved numerically using a staggered strongly decoupled scheme with implicit Euler time integration. The results allow the identification of process conditions and geometries for which a complete infiltration of the pores or the whole substrate is achieved. For low pressures, the predictions of the CVI reactor model are in agreement with the available experimental data.