Mathematical modeling and simulation of two-dimensional general rate model of liquid chromatography for multi-component adsorption with uneven saturation capacities

This study presents a two-dimensional general rate model (2D-GRM) for simulating multi-component liquid chromatography involving solutes with unequal saturation capacities. Recognizing the limitations of conventional one-dimensional models that neglect radial variations, the proposed framework incorporates both axial and radial mass transport coupled with nonlinear adsorption kinetics. The model captures component-specific saturation behaviors, accounting for size-exclusion and chiral discrimination phenomena commonly encountered in affinity chromatography. A finite volume scheme is employed to discretize the resulting system of partial differential equations, ensuring mass conservation and numerical stability. Simulations reveal key chromatographic behaviors such as elution-order inversion, the influence of radial Peclet numbers, and the effects of kinetic parameters. The results demonstrate the importance of radial gradients and uneven saturation effects in accurately predicting solute elution profiles, with implications for improving the design and optimization of preparative liquid chromatographic processes.