Modelling counter-current and dual counter-current chromatography using longitudinal mixing cell and eluting counter-current distribution models

Two well known approaches are considered to analyze the processes of counter-current and dual counter-current chromatography: the longitudinal mixing cell model and the Craig's counter-current distribution model. The cell model represents perfectly mixed, equally sized cells in series. The number of cells characterizes the rates of longitudinal mixing in the stationary and mobile phases. In the eluting counter-current distribution (CCD) model, the CCC process is considered as a continuous form of Craig's counter-current distribution. For a cascade of equilibrium stages theoretical elution profiles of the CCC process by using the CCD and cell model approaches have been compared. It is shown that in general, distribution functions of the CCD and cell models differ. It is established that the distribution of a solute between two solvent phases in the dual CCC process is determined by the extraction factor c, the total number of equilibrium stages n and the position of the sample inlet m by the equation Qx = (1 − cm)/(1 − cn + 1) with c = F2KD/F1 (KD, F1, F2 and Qx are the distribution constant, the phase flow-rates and the portion of solute eluted by the first phase, respectively).