Abstract
Modelling of liquid–solid batch adsorption based on mass transfer and conservation equations results in differential equations that may have or not an analytical solution. Even when analytical solutions are available, several simplified models can be considered for evaluating kinetic data of batch adsorption experiments. However, these simplified models are commonly used regardless of the premises considered in its development, and the analysis of the kinetic experiments based on these simplified models may be severely compromised. For this reason, this work presents a detailed development of the phenomenological models, and the hypotheses considered in its development are clearly stated. Typical simplified models derived from the phenomenological ones are obtained, and the conditions considered in the simplification are critically assessed. It was observed that the simplified models fail mainly for considering the concentration of the bulk phase constant over time or considering a linear adsorption isotherm. It must be emphasised that even when phenomenological models must be solved through numerical procedures, its use must be preferred, since the agreement with model premises and experimental conditions are closer, ensuring the quality of the kinetic data analysis.
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The datasets used and analysed during the current study are available from the corresponding author on reasonable request.
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Acknowledgements
The authors thank CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico, Brazil) and CAPES (Coordenação de Aperfeiçoamento de Pessoal de Nível Superior, Brazil, Grant: 0001) (CAPES) for supporting this work and providing scholarships.
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VQ writing original draft; DSA writing and literature revision of LDF model; GHOM development and programming of finite bath models; ES revision of the manuscript; EBC revision of the manuscript; MS conceptualization and writing original draft.
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Queiroz, V., de Almeida, D.S., de Oliveira Miglioranza, G.H. et al. Analysis of commonly used batch adsorption kinetic models derived from mass transfer-based modelling. Environ Sci Pollut Res 29, 79875–79889 (2022). https://doi.org/10.1007/s11356-021-18479-y
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DOI: https://doi.org/10.1007/s11356-021-18479-y