Phase-field model for deposition of pyrolytic carbon

A diffuse interface model for the determination of the evolution of the deposited substrate surface during isobaric, isothermal chemical vapour infiltration (CVI) of pyrolytic carbon is proposed. A continuous scalar phase-field parameter is introduced to label explicitly the solid and the gas phases within the system. Following the conceptual line of Ginzburg-Landau theory, we formulate the initial boundary value problem of CVI. In variance with the traditional formulations, we account for the different intensities of homogeneous and heterogeneous chemical reactions during CVI by introducing a scalar-valued intensity parameter that depends only on the phase-field. The various homogeneous and heterogeneous reaction processes during CVI are described in terms of a reduced chemical reaction scheme. Finally, we discuss the application of the developed methodology for numerical simulation of a simplified two-dimensional model problem. Using a finite element method, we obtain numerical approximations for the concentration profiles along the direction of infiltration.