Analytical solutions and moment analysis of chromatographic models for rectangular pulse injections

• Two linear chromatographic models are analyzed for rectangular pulse injection.
• The first four moments for both models are analytically and numerically calculated.
• A close connection between the models is analyzed for linear adsorption isotherms.
• Discontinuous Galerkin (DG) method is applied to solve the models numerically.
• Results of DG-method are compared with the analytical solutions.

This work focuses on the analysis of two standard liquid chromatographic models, namely the lumped kinetic model and the equilibrium dispersive model. Analytical solutions, obtained by means of Laplace transformation, are derived for rectangular single solute concentration pulses of finite length and breakthrough curves injected under linear conditions. In order to analyze the solute transport behavior by means of the two models, the temporal moments up to fourth order are calculated from the Laplace-transformed solutions. The limiting cases of continuous injection and negligible mass transfer limitations are evaluated. For validation, the analytical solutions are compared with the numerical solutions of models using the discontinuous Galerkin finite element method. Results of different case studies are discussed for linear and nonlinear adsorption isotherms. The discontinuous Galerkin method is employed to obtain moments for both linear and nonlinear models numerically. Analytically and numerically determined concentration profiles and moments were found to be in good agreement.