Researchers from the Technical University of Munich (Freising, Germany) and Lund University (Lund, Sweden) developed a new modeling approach for liquid-liquid chromatography. Their procedures were published in the Journal of Chromatography A (1).
Liquid-liquid chromatography (LLC), the mobile and stationary phases, both of which are liquid, are prepared by mixing preselected portions of three or more solvents that form two liquid phases at equilibrium. Either of the phases of the biphasic liquid system can be used as the stationary phase. In ascending (ASC) mode, the upper phase is used as the mobile phase and the lower phase as the stationary phase. In descending (DSC) mode, the lower phase is used as the mobile phase. To keep a liquid stationary phase in place, columns with one axis of rotation, centrifugal partition chromatography (CPC) columns, or countercurrent chromatography (CCC) columns with two axes of rotation, are used.
LLC and liquid-liquid extraction (LLX) both operate with two liquid phases. LLX, which involves the exchange of certain compounds between two immiscible (or partially miscible) solvents, uses columns that can be described as a series of perfectly mixed stirred tank reactors (2). LLX commonly involves high solute concentrations, where phase compositions, volumes, and physical properties are also affected. With these factors in mind, the scientists theorized that modeling approaches from LLX could be adapted to LLC.
In this work, the scientists combined a chromatography model with a liquid-liquid equilibria thermodynamic model to simulate the propagation of a solute and solvents along an LLC column. A n-hexane/methanol/water/cannabidiol-system was used as a demonstration, where the first three components helped prepare the mobile and stationary phase, with cannabidiol (CBD) in the solute. The liquid-liquid equilibria (LLE) were modeled using the NonRandom Two-Liquid (NRTL) model, which is an activity coefficient model widely used in phase equilibria calculations (3). The model’s parameters were fit to the LLE data of the quaternary system measured in this work, using a root mean square error (RMSE), which is a commonly used measure for evaluating the quality of predictions, of 1% between the experimental and predicted LLE data. Further, an overflow term was included in mass balance equations to account for restrictions in the maximum retained stationary phase volume in the LLC column and simulate possible stationary phase transfer through and out of the column.
For the elution profile simulations, the number of cells in the model was determined from pulse injection experiments of CBD with low injection concentration, performed in both elution modes, ASC and DSC. The mass transfer coefficient was selected at a high enough level to simulate near-instantaneous phase equilibration in each cell. This model, according to the researchers, could be used to study the effects of different operating conditions, such as injection volume and concentration, on elution profiles and reproduce the peak shape according to the shape of the solution distribution isotherm. The method validation with experimentally obtained elution profiles showed a satisfactory agreement between simulation and experiment for ASC mode, while in DSC mode, an earlier elution was predicted compared to the experiment. This is mostly likely due to the NRTL model inaccurately describing changes in the lower phase composition.
The proposed modeling approach was found to be a powerful tool for describing nonlinear LLC. Simultaneously, it improved upon the understanding of the influence of the concentration of the injected sample on the elution profiles, their position, and their shape. These developments helped to select the operating mode and conditions that favor separation while minimizing stationary phase loss. The approach can be applied to systems with any number of solutes and solvents for which LLE data are available and for which LLC processes can be modeled can be modeled with sufficient accuracy, either with the NRTL or any other thermodynamic model.
(1) Gerigk, M.; Peng, D.; Espinoza, D.; et al. Nonlinear Liquid-Liquid Chromatography: A Comprehensive Modeling Approach. J. Chromatogr. A 2025, 1757, 466099. DOI:
(2) Sandtorv, A. 2.3: Liquid-Liquid Extraction. LibreTexts Chemistry 2025.
(3) Gebreyohannes, S.; Neely, B. J.; Gasem, K. A. M. Generalized Nonrandom Two-Liquid (NRTL) Interaction Model Parameters for Predicting Liquid–Liquid Equilibrium Behavior. Ind. Eng. Chem. Res. 2014, 53 (31), 12445–12454. DOI:
