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This study presents a detailed comparison of the two most popular fractaltheories used in the field of kinetics sorption of pollutants in porousmaterials: the Brouers-Sotolongo model family of kinetics based on the BurrXIIstatistical distribution and the fractional kinetics based on theRiemann-Liouville fractional derivative theory. Using the experimental kineticsdata of several studies published recently, it can be concluded that, althoughthese two models both yield very similar results, the Brouers-Sotolongo modelis easier to use due to its simpler formal expression and because it enjoys allthe properties of a well-known family of distribution functions. We use theopportunity of this study to comment on the information, in particular, thesorption strength, the half-life time, and the time dependent rate, which canbe drawn from a complete analysis of measured kinetics using a fractal model.This is of importance to characterize and classify sorbent-sorbate couples forpractical applications. Finally, a generalization form of the Brouers-Sotolongoequation is presented by introducing a time dependent fractal exponent. Thisimprovement, which has a physical meaning, is necessary in some cases to obtaina good fit of the experimental data.

Fractal kinetics versus fractional derivative kinetics