Modeling of sorption kinetics: the pseudo-second order equation and the sorbate intraparticle diffusivity

Abstract

The applicability of the pseudo-second order equation (PSOE) has been explained on the ground of the model assuming that the overall sorption rate is limited by the rate of sorbate diffusion in the pores of sorbent (intraparticle diffusion model). Mathematical expressions have been proposed in order to describe the dependence of the pseudo-second order constant on such parameters as the initial sorbate concentration, the progress of the sorption process and the solid/solution ratio. Further, it has been shown that equilibrium sorption capacities estimated by using PSOE may be much lower than the actual ones: it depends mainly on how the sorption system is close to equilibrium. The values of parameters applied in calculations were taken from the literature and correspond to the biosorption systems designed to remove the heavy metals from the aqueous solution.

Kinetic models assessment for swelling of coal induced by methane and carbon dioxide sorption

“…The mathematical form of the PSOE was first proposed by Blanchard et al (1984) to describe the kinetics of heavy metal removal by natural zeolites. It is the most commonly used equation to describe sorption kinetic data (Płaziński et al 2013;Marczewski et al 2013). The general form of the differential equation describing the rate of fractional uptake given by Marecka and Mianowski (1993) is:…”

Reducing the Content of Metal Ions from Mine Water by Using Converter Sludge

“…Desorption is the release of one substance from another, either from the surface or through the surface. Desorption can occur when an equilibrium situation is altered [23]. The kinetic equation of the pseudo-second order is described by Equation (4):…”

Kinetics of methane and carbon dioxide sorption and sorption–induced expansion of coal – kinetic equations assessment

“…It is the most commonly used equation to describe sorption kinetic data [32]. The general time-integrated form of the equation is:…”

“…First approach proposed by Busch et al [18] consider the combination of two first-order rate functions and represent the traditional approach to interpret experimental data in terms of fast and slow sorption process. The other empirical kinetic equations are: the pseudo-second-order kinetic equation (PSOE) proposed by Blanchard et al [31], in original time-integrated form [32]; Elovich equation developed to describe kinetics of chemisorption [33][34] and stretched exponential equation (SE) also known as the KEKAM equation [35][36].…”