Variable diffusivity homogeneous surface diffusion model and analysis of merits and fallacies of simplified adsorption kinetics equations

[Display omitted] •15 most popular adsorption kinetics equations are presented.•Diffusion-based and reaction kinetics-based models are discussed.•A new versatile variable diffusivity HSDM numerical model is presented.•Comparison between numerical, analytical and approximate models is performed. Adsorption and ion exchange phenomena are encountered in several separation processes, which in turn, are of vital importance across various industries. Although the literature on adsorption kinetics modeling is rich, the majority of the models employed are empirical, based on chemical reaction kinetics or oversimplified versions of diffusion models. In this paper, the fifteen most popular simplified adsorption kinetics equations are presented and discussed. A new versatile variable-diffusivity two-phase homogeneous diffusion model is presented and used to evaluate the analytical adsorption models. Aspects of ion exchange kinetics are also addressed.