Description of sorption kinetics of azo dye onto birch chips by means of fractional derivatives

Abstract

The adsorption kinetics is investigated in order to measure time necessary to reach equilibrium between the molecules of separated substance attracted to the sorbent surface and those left in the solution. Models of adsorption kinetics such as Lagergren’s, Ho and McKay’s, and Elovich’s are quoted in technical articles. The application of pseudo-first-order Lagergren’s kinetic model is recommended when physical adsorption is the dominant mechanism. On the other hand, when the process is mainly influenced by chemisorption, the pseudo-second-order model of Ho and McKay’s as well as Elovich’s equation are suggested. At the same time, no general method combining both mechanisms of adsorption is proposed. In the case of chemically complex sorbents and the mixed mechanism of sorption, this kind of approach is insufficient; however, such systems may be modelled using fractional derivatives . Recently, a considerable number of papers and monographs have been published on applying fractional derivatives. Most of them treat of solving linear equations and special functions such as the Mittag–Leffler function. This paper presents the results and mathematical description of azo dye adsorption kinetics on a natural plant-based sorbent.