Monte Carlo model of nonlinear chromatography: correspondence between the microscopic stochastic model and the macroscopic Thomas kinetic model

The Monte Carlo model of chromatography is a description of the chromatographic process from a molecular (microscopic) point of view and it is intrinsically based on the stochastic theory of chromatography originally proposed by Giddings and Eyring. The program was previously validated at infinite dilution (i.e., in linear conditions) by some of the authors of the present paper. In this work, it has been further validated under nonlinear conditions. The correspondence between the Monte Carlo model and the well-known Thomas kinetic model (macroscopic model), for which closed-form solutions are available, is demonstrated by comparing Monte Carlo simulations, performed at different loading factors, with the numerical solutions of the Thomas model calculated under the same conditions. In all the cases investigated, the agreement between Monte Carlo simulations and Thomas model results is very satisfactory. Additionally, the exact correspondence between the Thomas kinetic model and Giddings model, when near-infinite dilution conditions are approached, has been demonstrated by calculating the limit of the Thomas model when the loading factor goes to zero. The model was also validated under limit conditions, corresponding to cases of very slow adsorption-desorption kinetics or very short columns. Different hypotheses about the statistical distributions of the random variables "residence time spent by the molecule in mobile and stationary phase" are investigated with the aim to explain their effect on the peak shape and on the efficiency of the separation.