For the mixture-averaged formula, we assume the diffusion velocity to be composed of three parts:

(13–6)

is the ordinary diffusion velocity and is given in the Curtiss-Hirschfelder[35] approximation by

(13–7)

where is the mole fraction, and where the mixture-averaged diffusion coefficient is given explicitly in terms of the binary diffusion coefficients

(13–8)

A non-zero thermal diffusion velocity is included only for the low molecular weight species , , and . The trace, light-component limit is employed in determining , that is,

(13–9)

where is the thermal diffusion ratio.[47] The sign of makes the lower molecular weight species diffuse from low to high temperature regions.

The correction velocity (independent of species but a function of the distance ) is included to insure that the mass fractions sum to unity or equivalently

(13–10)

The formulation of the correction velocity is the one recommended by Coffee and Heimerl[34] , [100] in their extensive investigation of approximate transport models in hydrogen and methane flames and discussed further in The Mixture-averaged Properties (Equation 5–84 ).