Modeling of sorption kinetics: the pseudo-second order equation and the sorbate intraparticle diffusivity
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Modeling of sorption kinetics: the pseudo-second order equation and the sorbate intraparticle diffusivity Wojciech Plazinski • Jakub Dziuba Wladyslaw Rudzinski
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Received: 22 October 2010 / Accepted: 22 February 2013 / Published online: 6 March 2013 The Author(s) 2013. This article is published with open access at Springerlink.com
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.
cl, ql
q(t), qe b D KH R0, l cin, ce
k2 f q(C) e Ai-Ei and ai-ei
Local concentrations of sorbate within a particle, in the solution and in the adsorbed phase, respectively Total adsorbed amounts at time t and at equilibrium, respectively Defined in Eq. (5) Defined in Eqs. (8) and (9) The Henry constant Constants related to the dimension of sorbent particles The initial and the equilibrium sorbate concentrations in the bulk solution, respectively The pseudo-second order constant Parameter defined in Eq. (12) ‘‘Adjustable’’ value of qe in PSOE Best-fit parameters in Eqs. (13) and (14)
Keywords Sorption kinetics Sorption modeling Intraparticle diffusivity Pseudo-second order Biosorption 1 Introduction List of symbols r, x Coordinates in Eqs. (1) and (2) t Time Db Intraparticle diffusion coefficient b Constant related to the physical properties of sorbent W. Plazinski (&) W. Rudzinski Institute of Catalysis and Surface Chemistry, Polish Academy of Sciences, ul. Niezapominajek 8, 30-239, Kracow, Poland e-mail: [email protected] J. Dziuba W. Rudzinski Department of Theoretical Chemistry, Faculty of Chemistry, UMCS, pl. M. Curie-Sklodowskiej 3, 20-031 Lublin, Poland
The mathematical form of the pseudo-second order equation (PSOE) was first proposed by Blanchard et al. (1984) to describe the kinetics of heavy metal removal by natural zeolites. At present it is the most commonly used mathematical expression applied to description and correlation of the kinetic data monitored in the solid/solution sorption systems (Ho and McKay 1999; Ho 2006a; Febrianto et al. 2009; Gupta and Suhas 2009). The application of PSOE includes the systems containing various kinds of sorbates (heavy metals in both cationic and anionic forms, organic dyes, phenols, etc.) and sorbents (inorganic minerals, activated carbons, raw biomass
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