Heterogeneous reactions at a gas-surface interface affect the mass and energy balance at the interface, and thus have an important influence on the boundary conditions in a chemically reacting flow simulation. The convective and diffusive mass fluxes of gas-phase species at the surface are balanced by the production (or depletion) rates of gas-phase species by surface reactions. This relationship is

(4–40)

where is the unit inward-pointing normal vector to the surface, and the gas-phase diffusion velocities are related to the species and temperature gradients by

(4–41)

Here the are the gas-phase mole fractions, the are the gas-phase mass fractions, is the mean molecular weight, is the ordinary multicomponent diffusion coefficient matrix, and the are the thermal diffusion coefficients. (Both types of diffusion coefficients can be evaluated by calls to the Transport Package) In nonreacting fluid mechanics the fluid velocity normal to a solid wall is zero. However, if there are chemical reactions at the wall, then the velocity can be nonzero. This so-called Stefan flow velocity occurs when there is a net mass flux between the surface and the gas. The induced Stefan velocity is given by

(4–42)

The expression for the Stefan velocity is easily obtained from the interfacial mass balance (Equation 4–40 ) by summing over all species and noting that the mass fractions must sum to one, that is,

(4–43)

and that the sum of the diffusion fluxes must be zero, that is,

(4–44)

Exothermicity (or endothermicity) of surface reactions contributes to the energy balance at an interface. Diffusive and convective fluxes in the gas phase are balanced by thermal radiative and chemical heat release at the surface. This balance is stated as

(4–45)

The summation on the right-hand side runs over all surface and bulk species. It is interesting to note that by substituting Equation 4–40 into the flux term on the left-hand side, the energy balance can be written in a more compact form as

(4–46)

Now the reaction-rate summation on the left-hand side runs over all species, including the gas-phase species.

The Surface Kinetics package allows the user to specify mass densities for the bulk species. A possible use for the densities would be to convert surface reaction rate-of-production of a bulk species (in mole/cm² /sec) into a growth rate (in cm/sec). The needed relationship is

(4–47)