Deeper insights into fractal concepts applied to liquid-phase adsorption dynamics

Fluid‐Solid Adsorption in Batch and Continuous Processing: A Review and Insights into Modeling

“…This aspect has been first investigated in the extensive work of Kopelman and successively developed by Avrami , . More recently, Haerifar and Azizian proposed a possible interpretation of fractal concepts applied to adsorption kinetics, while Montagnaro , applied several fractal‐like modified kinetic equations for the data interpretation of a liquid‐solid system constituted by Cd in water onto coal combustion fly ashes. The fractal‐modified models can be classified in pseudo‐first‐ and pseudo‐second‐order kinetics, the exponential model, and Vermeulen's equation.…”

Copper Biosorption on Argan Nut Shell: Kinetic and Thermodynamic Studies

“…Kopelman introduced the following equation to express the rate coefficient that exhibited temporal "memories" [8] h f k k' t   (4) where k f is the instantaneous rate coefficient, k' is the time-independent rate coefficient and h is the fractal exponent. This parameter determines the fractal behavior [10].…”

Further verification of adsorption dynamic intraparticle model (ADIM) for fluid–solid adsorption kinetics in batch reactors

“…In particular, Eqs. (7), (8) have been adopted in the present paper for both molecular (WilkeChang) and ionic (Nernst-Haskell) compounds:…”

“…This technique is based on the transfer of one or more components from a fluid mixture to a solid surface, with which they establish chemical or physical interactions, thus causing an interfacial concentration variation with respect to the adjacent phases. Since the XVIII century, a systematic study of this phenomenon has been developed bringing to the derivation of equations for interpreting adsorption kinetics data collected in batch reactors and a huge number of models have been proposed for investigating both the equilibrium [4][5][6] and the kinetics of fluid-solid adsorption [7][8][9][10]. By considering the kinetic models, they can be roughly divided in two http://dx.doi.org/10.1016/j.cej.2015.08.066 1385-8947/Ó 2015 Elsevier B.V. All rights reserved.…”