Kinetics of liquid phase batch adsorption experiments
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Kinetics of liquid phase batch adsorption experiments Stefano Brandani1 Received: 23 May 2020 / Revised: 19 August 2020 / Accepted: 25 August 2020 © The Author(s) 2020
Abstract Batch adsorption experiments are carried out by adding a known amount of adsorbent to a liquid solution at a known initial concentration and following the evolution in time of the concentration of the adsorbate. This is a very common method to obtain equilibrium and kinetic information in liquid systems, but in most cases kinetic results are analysed on the basis of empirical models. Two phenomenological models based on macropore diffusion in beads and shrinking core kinetics are used to generate data that are then interpreted with the widely used unconstrained linear regression methods. The results show that for both cases R 2 values close to unity are obtained leading to the incorrect interpretation of the mechanism of mass transport. It is recommended that batch adsorption experiments should be analysed using phenomenological models to obtain physical parameters that are applicable to other systems and to reduce the experiments required to characterise fully the kinetics of adsorption. Keywords Batch adsorption · Immersion experiment · Pseudo first order kinetics · Pseudo second order kinetics · Elovich kinetics · Langmuir kinetics · Diffusion in particles List of symbols aS Surface to volume ratio of solid (m−1) A Constant defined in Eq. 9c AD Slope of short time regression line for the diffusion model (mol m−3 s− 0.5) b Langmuir affinity (m3 mol−1) B Elovich constant (mol−1 m3) c0 Initial concentration in the fluid phase (mol m−3) c∞ Final concentration in the fluid phase (mol m−3) c Fluid phase concentration (mol m−3) C Intercept of short time regression line for the diffusion model (mol m−3) cP Concentration in the macropores (mol m−3) c̄ P Average concentration in the macropores (mol m−3) Dm Molecular diffusivity (m2 s−1) App DP Apparent diffusivity from linear and constant concentration model (m2 s−1) Electronic supplementary material The online version of this article (https://doi.org/10.1007/s10450-020-00258-9) contains supplementary material, which is available to authorized users. * Stefano Brandani [email protected] 1
School of Engineering, University of Edinburgh, Edinburgh, UK
DP Effective diffusivity defined in Eq. 12 (m2 s−1) DEL Pore diffusivity linear model defined in Eq. 30b P (m2 s−1) DS Solid diffusivity in shrinking core model (m2 s−1) k1 Pseudo first order kinetic constant (s−1) k2 Pseudo second order kinetic constant (mol−1 m3 s−1) K Slope of dimensionless secant of the equilibrium Q isotherm, c ∞ Eff
∞
K2 Alternative pseudo second order kinetic constant ̄ ∞ k2 (s−1) Q kA Langmuir adsorption rate constant (mol−1 m3 s−1) kD Langmuir desorption rate constant (s−1) kE Elovich rate constant (mol m−3 s−1) kF Film mass transfer coefficient (m s−1) kLDF Linear driving force coefficient (m s−1) kQDF Quadratic driving force coefficient (mol−1 m3
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