Two-dimensional non-equilibrium model of liquid chromatography: Analytical solutions and moment analysis

This paper presents a set of semi-analytical solutions and analytical moments for two-dimensional lumped kinetic model (LKM) describing non-equilibrium solute transport through a chromatographic column of cylindrical geometry. General solutions are derived for the solute concentration by successive implementation of finite Hankel and Laplace transforms assuming different sets of boundary conditions and linear sorption kinetic process. For further analysis, statistical temporal moments are derived from the Laplace transformed solutions. The current solutions extend and generalize the recent solutions of two-dimensional equilibrium dispersive transport model (EDM). Typical examples of concentration profiles and moments resulting from different sets of initial and inlet conditions are presented and briefly discussed. The derived semi-analytical solutions for concentration profiles and analytical moments are validated against the numerical results of a high resolution finite volume scheme. Good agreements in the results verify the correctness of analytical solutions and accuracy of the proposed numerical algorithm.