Nonlinear liquid-liquid chromatography: Modeling a binary mixture separation.

In liquid-liquid chromatography (LLC), mixture components are separated due to their different distribution between the phases of a biphasic liquid system composed of three or four solvents. LLC separations are typically modeled assuming that only the solutes distribute between the two liquid phases and their distribution can be described with a concentration-independent distribution constant. With increasing solute concentration, the physicochemical properties of the biphasic system change, and the distribution of the solutes becomes a function of their concentration. However, the experimental determination of liquid-liquid equilibria in multicomponent systems is time-intensive, and its prediction using thermodynamic models is often not sufficiently accurate for process design purposes. Thus, in this work, we propose a simple approach to model and simulate LLC separations in the nonlinear (concentration-dependent) range of the solutes' distribution equilibria, namely cannabidiol (CBD) and cannabigerol (CBG). Using the inverse method, the distribution equilibrium equation parameters were estimated from pulse injection experiments of single solutes at concentrations ranging from 1 to 100 mg/mL and 1-50 mg/mL for CBD and CBG, respectively. The obtained parameters were then successfully used to predict the elution profiles of binary mixtures of different compositions at 40 mg/mL total cannabinoid concentration. The approach was demonstrated and validated for CBD and CBG as model compounds and n-hexane/methanol/water 10/7.5/2.5 (v/v/v) as the biphasic solvent system. It should be noted that the applicability of the proposed approach is system-dependent, and hence, it should be evaluated for each separation task individually.