Multiple dual mode counter-current chromatography with periodic sample injection: Steady-state and non-steady-state operation

•Analytical solutions for periodic sample injection.•Continuous steady-state operation.•Several options of non-steady-state method.•Periodic sample injection is both selective and productive. The multiple dual mode (MDM) counter-current chromatography (CCC) separation consists of a succession of two isocratic counter-current steps and is carried out in series alternating between normal phase and reversed phase operation. The performance of the MDM technique can be improved by the sample re-injection between each of the dual-mode steps. The objective of this work was to develop analytical expressions to describe the MDM CCC with periodic sample injection, which can be used to simulate these processes and select optimal operating conditions for the separation of a given feed mixture. Two possible methods of the MDM separation with periodic sample injection are considered: 1 – steady-state separation: the duration of the flow periods of the phases is kept constant for all the cycles and the steady-state regime is achieved after a certain number of cycles. 2 – non-steady-state separation with variable duration of phase elution steps. It is shown that proper selection of the duration of phase flow times allows to reach complete separation of solutes in continuous steady-state operation mode even in a low efficiency column. This mode of operation provides both high productivity and high resolution. The non-steady-state method with variable duration of phase elution steps offers several options to split a mixture into groups of compounds and/or concentrate target compounds.