Brouers-Sotolongo fractal kinetics versus fractional derivative kinetics: A new strategy to analyze the pollutants sorption kinetics in porous materials

Highlights: •The fractal kinetics of pollutants sorption in porous materials is discussed. •Brouers-Sotolongo ($BSf(n,\alpha )$) and fractional derivatives models are compared. •The $BSf(n,\alpha )$ model give slightly better fit to the experimental data. •A better agreement is obtained if one introduces a time dependent coefficient. •The sorption strength, the half-life, and the time rate are also discussed. - Abstract: This study presents a detailed comparison of the two most popular fractal theories used in the field of kinetics sorption of pollutants in porous materials: the Brouers-Sotolongo model family of kinetics based on the BurrXII statistical distribution and the fractional kinetics based on the Riemann-Liouville fractional derivative theory. Using the experimental kinetics data of several studies published recently, it can be concluded that, although these two models both yield very similar results, the Brouers-Sotolongo model is easier to use due to its simpler formal expression and because it enjoys all the properties of a well-known family of distribution functions. We use the opportunity of this study to comment on the information, in particular, the sorption strength, the half-life time, and the time dependent rate, which can be drawn from a complete analysis of measured kinetics using a fractal model. This is of importance to characterize and classify sorbent-sorbate couples for practical applications. Finally, a generalization form of the Brouers-Sotolongo equation is presented by introducing a time dependent fractal exponent. This improvement, which has a physical meaning, is necessary in some cases to obtain a good fit of the experimental data.