Easy Computation of the Various Topologies and Modes of Liquid–Liquid Partition Chromatography by the Theory of Random Walks

Abstract

The article revisits the discrete recurrence method to model the instruments of liquid–liquid partition chromatography as counter-current chromatography (CCC) and centrifugal partition chromatography (CPC). The purpose is to simplify the computation of the concentration profiles without supplementary approximations, rather by going back to the seminal model of binomial random walks, associated with the stochastic master equation that generates simple discrete recurrence relations. It fits the model of the prototype of liquid–liquid chromatography: the Craig’s apparatus. Three emblematic separation technique group cases are computed in batch injection, batch multiple dual mode (MDM), and continuous injection by the “True Moving Bed” (TMB) in CPC.