Analytical and numerical solutions of two-dimensional general rate models for liquid chromatographic columns packed with core-shell particles

This work is concerned with the analytical and numerical solutions of linear and nonlinear two-dimensional general rate models (2D-GRMs) describing the transport of single-solute and multi-component mixtures through chromatographic columns of cylindrical geometry packed with core-shell particles. The finite Hankel and Laplace transformations are successively applied to derive analytical solutions for a single-solute model considering linear adsorption isotherms and two different sets of boundary conditions. Moreover, analytical temporal moments are derived from the Laplace domain solutions. The process is further analyzed by numerically approximating the nonlinear 2D-GRM for core-shell particles considering multi-component mixtures and nonlinear Langmuir isotherm. A high resolution finite volume scheme is extended to solve the considered 2D-model equations. Several case studies of single-solute and multi-component mixtures are considered. The derived analytical results are validated against the numerical solutions of a high resolution finite volume scheme. Typical performance criteria are utilized to analyze the performance of the chromatographic process. The results obtained are considered to be useful to support further development of liquid chromatography.