Although the mixture-averaged transport approximation is inadequate for some applications (for example, CVD at very low pressures, or when a carrier gas is not used), it has some properties that make it attractive for numerical computation. It is significantly less computationally intensive than the full multicomponent transport formulation (see Gas-phase Species Transport Properties for more information). Also, the mixture-averaged diffusion velocity of species (Equation 12–6 ) depends explicitly on the concentration gradient of species , but the multicomponent diffusion velocity of Equation 12–5 depends on the concentration gradients of all the remaining species. As a result, the Jacobian of the diffusion velocity has a strong diagonal term in the former case, but not in the latter case.

We find that solution of the set of differential/algebraic equations is aided by using a form for the multicomponent diffusion coefficient discussed by Coltrin, et al.,[86] found by equating Equation 12–5 and Equation 12–6 and solving for ,

(12–25)

The denominator in Equation 12–25 is found by noting that

(12–26)

Here, we implement multicomponent transport using the diffusion velocity of the form in Equation 12–6 , with calculated using Equation 12–25 .

Mass conservation requires that the diffusive mass fluxes sum to zero

(12–27)

However, a consequence of using the mixture-averaged transport formulation in Equation 12–6 to define a diffusion velocity and using the mixture-averaged diffusion coefficients is that mass is not always conserved, that is, the diffusive mass fluxes are not guaranteed to sum to zero. Therefore, at the mixture-averaged level of closure of the transport formulation some corrective measures must be taken. The user has two options. One is to apply an ad-hoc correction velocity,[34] defined as

(12–28)

When this correction velocity (independent of species, ) is added to all the species diffusion velocities as computed from Equation 12–6 , diffusional mass conservation is assured. This Correction Velocity option can be specified in the User Interface.

Another option to account for the deficiencies of the mixture-averaged closure of the transport problem and to assure mass conservation is to solve only gas-phase species conservation equations and to determine the remaining mass fraction by requiring . (The mixture-averaged transport closure is asymptotically correct in the trace-species limit.) In cases where one species is present in large excess (such as a carrier gas), this is a reasonable option. The carrier-gas composition is conveniently determined as

(12–29)

Where is the species for which we have chosen to apply the closure constraint. The program will determine as the index of the species with the highest concentration. If the user does not specify use of a correction velocity, it is assumed that the species is the carrier gas and thus a corresponding conservation equation (Equation 12–2 ) for that species is not solved. Instead, for that species, Equation 12–29 applies.