Two-dimensional general rate model for non-isothermal liquid chromatography considering finite rates of adsorption–desorption kinetics

Abstract

In this work, a two-dimensional general rate model for nonisothermal liquid chromatography is formulated considering adsorption saturation capacity, enthalpy of adsorption, mass and energy dispersion coefficients, conductivity and diffusivity of heat, heat transfer between the stationary and mobile phases of the column and finite rates of adsorption–desorption kinetics. Semi-analytical solutions of the model are derived by linearizing the adsorption and desorption rates and considering the Danckwerts boundary conditions with inner and outer annular regions of sample injection. These two injection regions are helpful to trigger temperature and concentration gradients along the cylindrical coordinate of the column. In deriving the semi-analytical solutions, we have successively applied the Hankel and Laplace transforms one after the other together with the Eigen-decomposition technique. The validity of the semi-analytical solutions is checked by comparing with the numerical solutions obtained by applying a flux limiting high resolution finite volume scheme of Koren. Several numerical test problems are carried out to inspect the key parameters that influence the chromatographic process performance. The numerical values of parameters obtained in this work will play an important role in the future theoretical developments of column liquid chromatography.