Analytical solution of a two-dimensional model of liquid chromatography including moment analysis

This work presents an analysis of a two-dimensional model of a liquid chromatographic column. Constant flow rates and linear adsorption isotherms are assumed. Different sets of boundary conditions are considered, including injections through inner and outer regions of the column inlet cross section. The finite Hankel transform technique in combination with the Laplace transform method is applied to solve the model equations. The developed analytical solutions illustrate the influence and quantify the magnitude of the solute transport in the radial direction. Comparing Dirichlet and Danckwerts boundary conditions, the predicted elution profiles differ significantly for large axial dispersion coefficients. For further analysis of the solute transport behavior, the temporal moments up to the fourth order are derived from the Laplace-transformed solutions. The analytical solutions for the concentration profiles and the moments are in good agreement with the numerical solutions of a high resolution flux limiting finite volume scheme. Results of different case studies are presented and discussed covering a wide range of mass transfer characteristics. The derived analytical solutions provide useful tools to quantify jointly occurring longitudinal and radial dispersion effects. •An analysis of a two-dimensional model of a chromatographic column is presented.•The finite Hankel and Laplace transforms are jointly applied to solve the model.•Analytical solutions quantify the influence of solute transport in the radial direction.•Different sets of boundary conditions are considered.•For further analyses, temporal moments up to the fourth order are derived.