Thermal Diffusion Overlooked Opportunity

Thermal diffusion is a process in which solute is driven through solvent by the action of a temperature gradient rather than by a concentration (or chemical potential) gradient [46]. It is a natural outgrowth of the laws of irreversible thermodynamics (Section 3.2) in which all driving forces are expected to be associated with some transport of matter. 

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. 

Since thermal diffusion is a nonisothermal process and thus cannot be considered as driven by chemical potential gradients, we must go directly to the solute flux equations to understand the capacity of thermal diffusion for separation. The basic law expressing the flux density caused by thermal diffusion [46-48] is 

TABLE 8.2 Range of Values of Thermal Diffusion Factor a 

Inasmuch as mean molecular velocity is given by U = Jlc, Eq. 3.14, the velocity induced by thermal diffusion is simply 

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