Separation efficiency, general theory

Davis (1993) extended the statistical overlap theory to generalized -dimensional separations with the consistent result that the separations get much better, but as dimensionality increases the efficiency of using that separation space decreases. For -dimensional separations, Davis says... 

The technical cost of a separation is paid in units of time and pressure-both of which are limited in practice. It follows, that there is a limit to the maximum time that can be tolerated before an analysis is completed. Conversely, there will also be a limit to the complexity of a mixture that can be separated in an acceptable time. Column theory must allow these limits to be identified. Although, as already stated, only packed columns are presently in general use, it may be possible that eventually chromatographic apparatus, particularly the detector and injection system, will be improved to the point where capillary columns become a viable alternative. Column theory must, therefore, also aid in capillary column design and be able to define the specifications of the ancillary apparatus that will permit the efficient use of such columns. 

An SLM extraction can be seen as a combination of extraction into an organic solvent followed by a back-extraction into a second aqueous phase. However, as these two extraction steps occur simultaneously, the mass transfer kinetics will be different, and generally more efficient, compared to the situation when the steps are performed in sequence in separation funnels. The general mass transfer theory for SLM extraction in flow systems has been described in detail [45], with some additional aspects described more recently [46]. 

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