enrichment factor, \(S\)

in liquid-liquid distribution
https://doi.org/10.1351/goldbook.E02127
The factor by which the ratio of two substances in the feed must be multiplied to give their ratio after treatment. \[\frac{Q_{\text{A}}}{Q_{\text{B}}} = S_{\text{A,B}}\ \frac{Q_{\text{A}}^{'}}{Q_{\text{B}}^{'}}\] where \(Q_{\text{A}}\) and \(Q_{\text{A}}^{'}\) are the final and initial amounts of species A and \(Q_{\text{B}}\) and \(Q_{\text{B}}^{'}\) are the final and initial amounts of species B. Hence \(S_{\text{A,B}}=\frac{E_{\text{A}}}{E_{\text{B}}}\) where \(E\) is the @F02503@. In terms of \(D\),\(n\),\(r\) (where \(n\) is the number of stages and \(r\) the phase ratio), \[S_{\text{A,B}} = \frac{1- (1\,+\,r\ D_{\text{A}})^{-n}}{1- (1\,+\,r\ D_{\text{B}})^{-n}}\]
Sources:
Orange Book, 2nd ed., p. 90 [Terms]
PAC, 1993, 65, 2373. (Nomenclature for liquid-liquid distribution (solvent extraction) (IUPAC Recommendations 1993)) on page 2382 [Terms] [Paper]