The zero length column technique to measure adsorption equilibrium and kinetics: lessons learnt from 30 years of experie
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The zero length column technique to measure adsorption equilibrium and kinetics: lessons learnt from 30 years of experience Stefano Brandani1 · Enzo Mangano1 Received: 1 July 2020 / Revised: 31 August 2020 / Accepted: 24 September 2020 © The Author(s) 2020
Abstract The zero length column technique has been developed over the past 30 years as a versatile experimental method to measure adsorption equilibrium and kinetics. In this review we discuss in detail the theory that forms the basis for the technique in order to understand how to design and operate efficiently a system. Experimental checks that should be performed to ensure the correct interpretation of the dynamic response are presented and examples are used to identify how to avoid major errors in determining diffusion time constants. The review concludes with an overview of all experimental studies available in the literature to date and a set of recommendations that should help improve the standard in the reported equilibrium and kinetic properties. Keywords Adsorption kinetics · Adsorption equilibrium · Zero length column Abbreviations CSD Crystal size distribution DSL Dual site Langmuir FR-ZLC Frequency response ZLC LDF Linear driving force LZLC Liquid ZLC MZLC Multicomponent ZLC PL Partial loading experiment PZLC Pulse ZLC SZLC ZLC—Stability test TZLC Tracer-ZLC ZLC Zero Length Column – gas ZLC-E ZLC equilibrium study List of symbols a Surface to volume ratio of solid (m–1) ae Pre-exponential coefficient of long-time exponential decay
Electronic supplementary material The online version of this article (https://doi.org/10.1007/s10450-020-00273-w) contains supplementary material, which is available to authorized users. * Stefano Brandani [email protected] 1
School of Engineering, University of Edinburgh, Edinburgh EH9 3FB, UK
akn Pre-exponential factor in the analytical solution of fluid phase concentration for the combined surface barrier and diffusion model an Pre-exponential factor in the analytical solution of fluid phase concentration be Coefficient of long-time exponential decay (s–1) bn Pre-exponential factor the in analytical solution of the average adsorbed phase concentration c Concentration in the fluid phase (mol m–3) c̄ Average concentration in the fluid phase (mol m–3) c0 Initial concentration in the fluid phase (mol m–3) cP Fluid concentration in the pellet, mol m–3 cS Fluid phase concentration at the second switch of the partial loading experiment (mol m–3) ∗ c Fluid phase concentration at corresponding to q∗ (mol m–3) D Diffusion coefficient (m2 s–1) DP Pore (macro-) diffusion coefficient (m2 s–1) DEP Effective pellet diffusivity defined in Eq. 16 (m2 s–1) F Volumetric flowrate (m3 s–1) FCarr Volumetric flowrate of carrier gas, m3 s–1 ΔH Heat of adsorption (J mol–1) k Surface mass transfer resistance, (m s–1) K Dimensionless Henry law constant Kc Dimensionless Henry law constant in microporous material
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Adsorption
kT Thermal conductivity of the
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