An analytical investigation into solute transport and sorption via intra-particle diffusion in the dual-porosity limit

We develop a mathematical model for adsorption based on averaging the flow around, and diffusion inside, adsorbent particles in a column. The model involves three coupled partial differential equations for the contaminant concentration both in the carrier fluid and within the particle as well as the adsorption rate. The adsorption rate is modelled using the Sips equation, which is suitable for describing both physical and chemical adsorption mechanisms. Non-dimensionalisation is used to determine the controlling parameter groups as well as to determine negligible terms and so reduce the system complexity. The inclusion of intra-particle diffusion introduces new dimensionless parameters to those found in standard works, including a form of internal Damköhler number and a new characteristic time scale. We provide a numerical method for the full model and show how in certain situations a travelling wave approach can be utilized to find analytical solutions. The model is validated against published experimental data for the removal of Mercury(II) and CO2. The results show excellent agreement with measurements of column outlet contaminant concentration and provide insights into the underlying chemical reactions
This publication is part of the research projects PID2020-115023RB-I00 (funding M. Aguareles, T.G. Myers, M. CalvoSchwarzwalder) financed by MCIN/AEI/ 10.13039/501100011033/. L.C. Auton and T.G. Myers acknowledge the CERCA Programme of the Generalitat de Catalunya for institutional support, their work was also supported by the Spanish State Research Agency, through the Severo Ochoa and Maria de Maeztu Program for Centres and Units of Excellence in R&D (CEX2020-001084-M). A. Valverde acknowledges support from the Margarita Salas UPC postdoctoral grants funded by the Spanish Ministry of Universities with European Union funds - NextGenerationEU. M. Aguareles acknowledges the support of the “consolidated research group” (Ref 2021 SGR01352) of the Catalan Ministry of Research and Universities. Open Access funding provided thanks to the CRUE-CSIC agreement with Elsevier
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