A mathematical model of a lateral electrochromatography device for continuous chiral separation

Abstract

The separation of enantiomers in a continuous manner represents a nontrivial task. Identical physical properties of an enantiomeric pair render the standard separation methods unusable, and its separation traditionally relies on the use of a chiral environment. Here, we theoretically analyze lateral electrochromatography as a potential method for continuous steady-state enantiomer separation. The developed mathematical model of a lateral electrochromatography device (LEC) treats the stationary (selective) phase as a pseudo-homogeneous environment. The intensity of the solute transport in that phase is given by an effective diffusion coefficient which depends on the degree of solute-stationary phase interactions. Under the assumptions of phase equilibrium and neglected diffusion/dispersion transport, we derived simplified algebraic expressions determining the slopes (deflections) of solute concentration trajectories allowing the solute separation. These expressions may assist in optimizing the LEC geometry and setting the control parameters such as the applied voltage or pressure difference. Numerical simulations on spatially two- and three-dimensional domains are in good agreement with both simplified algebraic predictions and available experimental observations. We show that LEC can separate enantiomers continuously in a steady-state regime under optimized operating conditions. However, the separation efficiency strongly depends on the enantioselectivity of the stationary phase. The results of the simulations also offer basic designing rules for a LEC that is compatible with continuous synthesis and separation of pharmaceuticals and other special chemicals.