Discontinuous Galerkin finite element method for solving non-linear model of gradient elution chromatography

In this study, a discontinuous Galerkin (DG) finite element method is employed to solve the nonlinear equilibrium dispersive (ED) model, for the simulation of multi-component gradient elution chromatography using a liquid mobile phase in fixed-bed columns. The ED model comprises a set of coupled nonlinear convection-dominated partial differential equations integrated with nonlinear Langmuir type adsorption isotherms. Gradient elution, characterized by the gradual increase in eluent strength through variations in the chemical composition of the mobile phase, is analyzed. An investigation into the advantages of gradient elution chromatography in comparison to isocratic elution is conducted via a sequence of numerical test experiments that assess the influence of solvent strength, modulator concentration, gradient start and end times, and gradient slope on the elution profiles and temporal moments. It has been observed that gradient elution chromatography influences the behavior, shape, and propagation speed of elution profiles, which subsequently affect the cycle time and column efficiency. The results of this study provide significant insights that are critical for understanding, optimizing, and enhancing gradient elution chromatography.