Numerical Investigation of Chromatographic Models with a Tri-Langmuir Isotherm

Chromatography is an essential analytical tool in pharmaceuticals, chemical engineering, and environmental science for separating and analyzing complex mixtures. As systems grow more complex, accurate modeling becomes important. Equilibrium models like the Equilibrium Dispersive Model (EDM) neglect key dynamics such as mass transfer resistance and kinetic adsorption, limiting their applicability in fast, nonlinear systems.

This study conducts a numerical investigation of non-equilibrium liquid chromatography using the Lumped Kinetic Model (LKM) with linear and non-linear Tri-Langmuir isotherms. The LKM captures finite mass transfer kinetics between mobile and stationary phases, making it suitable for dynamic conditions. The governing transport equations exhibit conservative and scaling symmetry properties under dimensionless transformation, while the nonlinear adsorption mechanism reflects heterogeneous yet structured interactions among adsorption sites. Koren’s high-resolution finite volume method (HR-FVM) is extended to solve the governing equations, preserving the symmetric structure of concentration transport while effectively handling convection-dominated behavior and steep solution gradients.

Simulations explore the impact of mass transfer rate, interstitial velocity, and injection time on solute elution. Results show that the Tri-Langmuir isotherm best models heterogeneous adsorption sites, especially in multi-component systems, capturing nonlinear effects like peak asymmetry, saturation, and competitive binding. Effects of different parameters such as mass transfer coefficient, adsorption coefficients and injection time are considered for single- and multi-component systems.

The study underscores the value of kinetic models and nonlinear isotherms for accurate simulation. Furthermore, the preservation of conservative transport symmetry within the numerical framework improves the stability and physical consistency of the computed solutions, aiding chromatographic design and optimization while reducing reliance on experimental methods.