article · The Journal of Physical Chemistry A
Standard mathematical models used to evaluate adsorption kinetics, such as pseudo-first-order and pseudo-second-order rate laws, often struggle to accurately capture experimental data, particularly during the early stages of a process. To address these limitations, a generalised fractional kinetic model has been developed using a fractional reaction-diffusion equation with a time-dependent reaction rate. This mathematical framework incorporates memory effects, long-range interactions, system heterogeneity, and nonequilibrium dynamics, thereby providing a more precise depiction of adsorption rates, capacities, and equilibrium points. The approach was tested on experimental data involving the removal of anionic acid yellow-17 and cationic brilliant green dyes across single and binary mixtures. By accounting for waiting times during adsorption and linking macroscopic conditions like pH to overall dynamics, the model successfully improves the interpretation of complex chemical adsorption behaviour.
Accurate modeling of chemical adsorption is essential for designing effective water treatment and separation systems. By capturing complex physical behaviours that standard formulas overlook, this method gives scientists and engineers more reliable predictions of how quickly and thoroughly pollutants can be removed from liquid waste streams.
This research is early-stage theoretical modelling validated against laboratory adsorption data. It could enable environmental engineers and industrial water treatment designers to better predict, simulate, and size filtration systems for organic dye removal. Before commercial uptake or integration into industrial software tools, the methodology would need broader validation across wider classes of industrial effluents and continuous-flow settings.
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Recently, there has been debate about using a pseudo-second-order model in adsorption kinetics and its ability to fit experimental data, especially at the initial stages. This paper introduces a generalized fractional kinetic model obtained via a fractional reaction-diffusion equation with a time-dependent reaction rate. This model is presented as a dependable approach to understanding chemical adsorption kinetics. It offers insights into the adsorbate history and extends classical kinetic models, such as pseudo-first-order and pseudo-second-order models. The generalized fractional kinetic model accounts for memory effects with long-range interactions, heterogeneity, and nonequilibrium dynamics, leading to more accurate predictions of adsorption rates, capacities, and equilibrium values. As an applied context, we use the fractional kinetic model to analyze experimental data on the adsorption of anionic acid yellow-17 and cationic brilliant green dyes in single and binary systems. The fractional kinetic model is employed to fit the data by incorporating waiting times into the adsorption process and correlating macroscopic properties, such as the pH, with adsorption dynamics.
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DOI: 10.1021/acs.jpca.3c07615
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