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Analytical solutions for reactive shear dispersion with boundary adsorption and desorption

Published online by Cambridge University Press:  30 August 2022

Weiquan Jiang Open the ORCID record for Weiquan Jiang [Opens in a new window] ,
Li Zeng Open the ORCID record for Li Zeng [Opens in a new window] ,
Xudong Fu Open the ORCID record for Xudong Fu [Opens in a new window]  and
Zi Wu Open the ORCID record for Zi Wu [Opens in a new window]
Weiquan Jiang
Affiliation:
Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, PR China State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, PR China
Li Zeng
Affiliation:
State Key Laboratory of Simulation and Regulation of Water Cycle in River Basin, China Institute of Water Resources and Hydropower Research, Beijing 100038, PR China
Xudong Fu*
Affiliation:
Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, PR China State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, PR China
Zi Wu*
Affiliation:
Department of Hydraulic Engineering, Tsinghua University, Beijing 100084, PR China State Key Laboratory of Hydroscience and Engineering, Tsinghua University, Beijing 100084, PR China
*
†Email addresses for correspondence: xdfu@tsinghua.edu.cn, wuzi@tsinghua.edu.cn
†Email addresses for correspondence: xdfu@tsinghua.edu.cn, wuzi@tsinghua.edu.cn
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Abstract

Surface reactions such as the adsorption and desorption at boundaries are very common for solute dispersion in many applications of chemistry, biology, hydraulics, etc. To study how reversible adsorption affects the transient dispersion, Zhang, Hesse & Wang (J. Fluid Mech., vol. 828, 2017, pp. 733–752) have investigated the temporal evolution of moments using the Laplace transform method. Owing to difficulties introduced by the adsorption–desorption boundary condition, great challenges arise from the inverse Laplace transform: dealing with the singularities by the residue theorem can tremendously increase complexities. This work provides a much simpler analytical method to derive solutions in a more compact form that is valid for the entire range of the reactive transport process. Such a progress demonstrates that the classic framework of separation of variables can be extended and applied to this more general adsorption–desorption condition, based on which higher-order statistics including skewness and kurtosis can be explicitly explored in practice. Also extended is Gill's generalised dispersion model for solute concentration distributions, which can now address the entire transient dispersion characteristics, instead of just applied for the long-time asymptotic reactive process as done previously. Regarding the most classic Taylor dispersion problem, we investigate the influence of the reversible adsorption–desorption on the solute cloud in a tube flow. Not only the transient dispersion characteristics of transverse-average concentration distribution but also those of the bulk, surface and total-average distributions are discussed. We further investigate the influence of initial conditions on the non-uniformity of the transient dispersion over the cross-section.

JFM classification

Mass Transport: Dispersion Reacting Flows: Laminar reacting flows

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JFM Papers
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Journal of Fluid Mechanics , Volume 947 , 25 September 2022 , A37
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© The Author(s), 2022. Published by Cambridge University Press

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References

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