Comparing two models of gradient elution in counter-current chromatography

Gradient change of mobile phase composition is commonly used in liquid chromatography to shorten analysis duration. Gradient elution is possible in counter-current chromatography if it is demonstrated that the mobile phase composition changes are not associated with liquid stationary phase composition changes. Also, the solute distribution ratios in initial (1) and final (2) eluting systems must be known. If the solute distribution ratios during the changing mobile phase composition are modeled, the full gradient separation can be modeled using classical equations of liquid chromatography. Another approach allowed modeling empirically the gradient step. It considered the decreasing volume of mobile phase 1 and the increasing volume of mobile phase 2 used at each gradient time to derive a very simple equation. The two equations were compared computing the retention volumes of five test solutes. A remarkable agreement was observed considering the very different mathematical expressions of the two models. The step-gradient method was also modeled and its results compared to those of the linear gradient method.