Mathematical model of computer-programmed intermittent dual countercurrent chromatography applied to hydrostatic and hydrodynamic equilibrium systems

Dual high-speed countercurrent chromatography (dual CCC) literally permits countercurrent flow of two immiscible solvent phases continuously through the coiled column for separation of solutes according to their partition coefficients. Application of this technique has been successfully demonstrated by separation of analytes by gas–liquid and liquid–liquid two-phase systems. However, the method cannot be directly applied to the system with a set of coiled columns connected in series, since the countercurrent process is interrupted at the junction between the columns. However, this problem can be solved by intermittent dual CCC by eluting each phase alternately through the opposite ends of the separation column. This mode of application has an advantage over the conventional dual CCC in that the method can be applied to all types of CCC systems including hydrostatic equilibrium systems such as toroidal coil CCC and centrifugal partition chromatography. Recently, the application of this method to high-speed CCC (hydrodynamic system) has been demonstrated for separation of natural products by Hewitson et al. using a set of conventional multilayer coil separation columns connected in series. Here, we have developed a mathematical model for this intermittent dual CCC system to predict retention time of the analytes, and using a simplified model system the validity of the model is justified by a series of basic studies on both hydrodynamic and hydrostatic CCC systems with a computer-programmed single sliding valve. The present method has been successfully applied to spiral tube assembly high-speed CCC (hydrodynamic system) and toroidal coil CCC (hydrostatic system) for separation of DNP-amino acid samples with two biphasic solvent systems composed of hexane–ethyl acetate–methanol–0.1 M hydrochloric acid (1:1:1:1 and 4:5:4:5, v/v).