where Dkm is the diffusion coefficient for species k in the mixture and DkT is the thermal mass diffusion coefficient for species k. In many cases of interest to a reactor engineer, the contribution of thermal diffusion is very small compared to the diffusive flux due to concentration gradients. For modeling pressure-driven separation processes, it may be necessary to include the diffusive flux due to pressure (for more details, see Brodkey and Hershey, 1988; Bird, 1998). If only the most dominant term, the diffusion due to concentration gradient, is considered, the species conservation equations become

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