enrichment factor, S in liquid-liquid distribution

https://dx.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.
Q A Q B = S A,B Q A ' Q B '
where Q A and Q A ' are the final and initial amounts of species A and Q B and Q A ' are the final and initial amounts of species B. Hence S A,B = E A E B where E is the fraction extracted. In terms of D,n,r (where n is the number of stages and r the phase ratio),
S A,B = 1 − ( 1 + r D A ) − n 1 − ( 1 + r D B ) − n
Source:
PAC, 1993, 65, 2373 (Nomenclature for liquid-liquid distribution (solvent extraction) (IUPAC Recommendations 1993)) on page 2382