Numerical Approximation of the General Rate Model for Gradient Elution Chromatography Utilizing Core–Shell Particles

This study presents a fundamental theoretical investigation of gradient elution chromatography employing core-shell particles and variable mobile phase composition. An extended form of the general rate model (GRM) is developed to examine the influence of column overloading on elution performance. The linear solvent strength (LSS) model is incorporated to describe variations in Henry's constant and the nonlinearity coefficient with solvent composition, while accounting for intraparticle diffusion, film mass transfer resistance, and axial dispersion. Core-shell particles enhance separation efficiency by reducing the accessible pore volume and diffusion path lengths, thereby allowing higher flow rates. To approximate the resulting nonlinear model equations, a semidiscrete high-resolution finite volume scheme is adapted and applied. The numerical framework enables a detailed analysis of the effects of key model parameters on the behavior and shape of the elution profiles, providing valuable insights into chromatographic dynamics. Validation of the proposed model and evaluation of the numerical scheme are conducted through benchmark test problems. Specific performance metrics are employed to identify the most influential parameters. The study utilizes binary mixtures as a model system to establish a fundamental understanding of elution behavior, refine numerical strategies, and provide insights that support the optimization of experimental conditions. The findings offer a foundational framework for enhancing separation performance with broader implications for more complex systems.