The range of validity of sorption kinetic models

Several hundred papers are published yearly reporting liquid-phase adsorption kinetics data. In general the data is analyzed using a variety of standard models such as the pseudo first- and second-order models and the Intraparticle-Diffusion model. The validity of these models is often assessed empirically via their ability to fit the data, independently of their physicochemical soundness. The aim of the present paper is to rationalize the analysis of liquid-phase adsorption kinetics data, and to investigate experimental factors that influence the adsorption kinetics, in addition to the characteristics of the adsorbent material itself. For that purpose we use a simple Langmuir adsorption-diffusion model, which enables us to identify three dimensionless numbers that characterize the working regime of any batch adsorption experiment: an adsorption Thiele modulus, a saturation modulus, and a loading modulus. The standard models are found to be particular cases of the general adsorption-diffusion model for specific values of the dimensionless numbers. This provides sound physicochemical criteria for the validity of the models. Based on our modeling, we also propose a general yet simple data analysis procedure to practically estimate the diffusion coefficient in adsorbent pellets starting from adsorption half-times.