A New Film Diffusion Controlling Kinetic Model for Adsorption at the Solid/Solution Interface

Document Type : Research Article


Department of Chemical Engineering, Faculty of Engineering, University of Mazandaran, Babolsar, I.R. IRAN


A convenient adsorption kinetic equation has been offered for the modeling of adsorption kinetics in batch systems when diffusion taking parts to the rate-controlling step of adsorption. This model is suggested based on the Smoluchowski-Waite equation for diffusion-controlled second-order reactions. The proposed new model has better performance (lower absolute values of the relative errors (AARE) %) with respect to the pseudo-second-order. Results of this equation are in agreement with experiment data especially at the initial times of adsorption that diffusion contributes to the rate-controlling step of adsorption.


Main Subjects

[1] Samarghandi M.R., Zarrabi M., Removal of Acid Red 14 by Pumice Stone as a Low Cost Adsorbent: Kinetic and Equilibrium Study, Iran. J. Chem. Chem. Eng. (IJCCE), 31:19-27(2012).
[2] Javadnia  N., Farrokhnia A.,  The Thermodynamic And Kinetics Study of Removal of Cd(II) by Nanoparticles of Cobalt Oxide in Aqueous Solution, Iran. J. Chem. Chem. Eng. (IJCCE), 38:127-139(2019).
[4] Moral-Rodriguez A.I., Leyva-Ramos R., Ocampo-Perez R., Mendoza-Barron J., Serratos-Alvarez I.N., Salazar-Rabago J.J., Removal of Ronidazole and Sulfamethoxazole from Water Solutions by Adsorption on Granular Activated Carbon: Equilibrium and Intraparticle Diffusion Mechanisms, Adsorption.,  22: 89–103(2016).
[6]Low M. J. D, Kinetics Of Chemisorption of Gases on Solids, Chem. Rev., 60: 267−312 (1960).
[10] Azizian S, Kinetic Models of Sorption: A Theoretical Analysis, J. Colloid Interface Sci., 276:47−52 (2004).
[11] Haerifar M., Azizian S., An Exponential Kinetic Model For Adsorption at Solid/Solution Interface, Chem. Eng. J. 215−216: 65−71(2013).
[12] Eris S., Azizian S., Analysis of Adsorption Kinetics at Solid/Solution Interface Using A Hyperbolic Tangent Model, J.Mol. Liq., 231: 523–527(2017).
[14] Yang X., Al-Duri B., Kinetic Modeling of Liquid-Phase Adsorption of Reactive Dyes on Activated Carbon, J. Colloid Interface Sci., 287: 25−34 (2005).
[15] Azizian S, Naviri-Fallah R, A New Empirical Rate Equation for Adsorption Kinetics at Solid/Solution Interface, Appl. Surf. Sci., 256:5153−5156 (2010).
[17] Azizian, S.; Naviri-Fallah, R., A New Empirical Rate Equation for Adsorption Kinetics at Solid/Solution Interface, Appl. Surf. Sci., 256: 5153−5156(2010).
[19] Marczewski A, Application of Mixed Order Rate Equations to Adsorption of Methylene Blue on Mesoporous Carbons, Appl. Surf. Sci., 256: 5145–5152 (2010).
[20] Yoa C., Chen T., An Improved Regression Method For Kinetics of Adsorption From Aqueous Solutions, J. Water Process Eng., 31: 100840 (2019).
[21] Lagergren S, About the Theory of So-Called Adsorption of Soluble Substances, Kungliga Svenska Vetenskapsakademiens, Handlingar, 24: 1−39 (1898).
[22] Boyd G.E., Adamson A.W., Myers L.S., The Exchange Adsorption of Ions from Aqueous Solutions by Organic Zeolites.II. Kinetics. J. Am. Chem. Soc. 69: 2836–2848(1947).
[23] Smoluchowski M.V., Versuch Einer Mathematischen Theorie Der Koagulationskinetik Kolloider Losungen. Phys. Chem., 92: 129−168 (1917).
[25] Runping H, PAN H, Zhaohui C., Zhenhui Z, Mingsheng T., Kinetics and Isotherms of Neutral Red Adsorption on Peanut Husk, J. Envir. Sci., 20:1035–1041(2008).
[27] Ghodbane I, Nouri L, Hamdaoui O, Chiha M, Kinetic And Equilibrium Study for the Sorption of Cadmium (II) Ions from Aqueous Phase by Eucalyptus Bark, J. Hazard. Mater., 152: 148-158 (2008).
[28] G¨Unay A, Arslankaya E., Tosun I, Lead Removal from Aqueous Solution by Natural and Pretreated Clinoptilolite: Adsorption Equilibrium and Kinetics, J. Hazard. Mater., 146: 362–371(2007).
[32] Ma R., Zhu J., Wu B., Li X., Adsorptive Removal of Organic Chloride from Model Jet Fuel by Na-LSX Zeolite: Kinetic, Equilibrium and Thermodynamic Studies, Chem. Eng. Research. Design., 114: 321-330 (2016).
[33] Rafati L, Ehrampoush M.H., Rafati A.A, Mahvi M.H., Modeling of Adsorption Kinetic and Equilibrium Isotherms of Naproxen onto Functionalized Nano-Clay Composite Adsorbent, J. Mol. Liquid, 224: 832-841 (2016).