7.2.2 Reaction-Diffusion Balance for Surface Chemistry

Reactions at surfaces change gas-phase, surface-adsorbed (site) and bulk (solid) species. On reacting surfaces, the mass flux of each gas specie due to diffusion and convection to/from the surface is balanced with its rate of consumption/production on the surface ,

$$\rho_{\rm wall} D_i \frac{\partial Y_{i, \rm wall}}{\partial n} - \dot{m}_{\rm dep} Y_{i,\rm wall} = M_{w,i} \hat{R}_{i,{\rm gas}} \; \; \; \; \; i = 1, 2, 3, \dots, N_g$$ (7.2-9)

$$\frac{\partial \left[S_i\right]_{\rm wall}}{\partial t} = \hat{R}_{i,{\rm site}} \phantom{M_{w,i}} \; \; \; \; \; i = 1, 2, 3, \dots, N_s$$ (7.2-10)

The wall mass fraction $Y_{i,\rm wall}$ is related to concentration by

$\dot{m}_{\rm dep}$ is the net rate of mass deposition or etching as a result of surface reaction; i.e.,

$\left[S_i\right]_{\rm wall}$ is the site species concentration at the wall, and is defined as

where $\rho_{\rm site}$ is the site density and $Z_i$ is the site coverage of species $i$.

Equations  7.2-9 and 7.2-10 are solved for the dependent variables $Y_{i,\rm wall}$ and $Z_i$ using a point-by-point coupled Newton solver. The effective gas-phase reaction source terms are then available for solution of the gas-phase species transport Equation  7.1-1.