Thermal diffusion employed with flow

We have observed that the direct separation of components in static systems is commonly carried out with both electrical and sedimentation fields. By contrast, we rarely hear of direct (Sc) separations using thermal diffusion. At present, thermal diffusion is nearly always employed with flow in such a manner that the flow multiplies the separability [46]. It is reasonable to inquire if an opportunity has been overlooked in the neglect of static separations by thermal diffusion. In obtaining an answer to this question, we develop an approach that can be used for judging the potential effectiveness of other uncommon gradients and fields in direct Sc separations as well. 

In the case of turbulent flow it is possible to employ the same eddy concepts as were used in connection with the consideration of thermal transport. In the case of steady, uniform flow between parallel plates the eddy diffusivity may be defined by... 

In the operator L, the first term represents convection and the second diffusion. Equation (44) therefore describes a balance of convective, diffusive, and reactive effects. Such balances are very common in combustion and often are employed as points of departure in theories that do not begin with derivations of conservation equations. If the steady-flow approximation is relaxed, then an additional term, d(p(x)/dt, appears in L this term represents accumulation of thermal energy or chemical species. For species conservation, equations (48) and (49) may be derived with this generalized definition of L, in the absence of the assumptions of low-speed flow and of a Lewis... 

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