Analytical solution for concentration distribution in an open channel flow with phase exchange kinetics

Barik, Swarup; Dalal, D. C.

doi:10.1007/s10409-021-09037-y

Cited by 9 publications

(1 citation statement)

References 54 publications

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“…Most studies focused on the long-time asymptotic process of solute dispersion and there are several popular theoretical methods to this end. The homogenisation method with perturbation technique (Purnama 1988 a ; Ng & Yip 2001; Ng 2006; Allaire, Mikelić & Piatnitski 2010; Paul & Mazumder 2011; Barik & Dalal 2022), and the centre manifold method (Mercer & Roberts 1994), for example, are powerful and easy-to-apply to the treatment of transport processes with nonlinear reactions (Balakotaiah & Chang 1995, 2003; Barik & Dalal 2017). Alternatively, some other methods including the method of concentration moments by Aris (1956) and the generalised dispersion model by Gill (1967), are in nature capable of addressing the initial transient dispersion of solute immediately after its release.…”

Section: Introductionmentioning

confidence: 99%

Analytical solutions for reactive shear dispersion with boundary adsorption and desorption

Jiang

Zeng

et al. 2022

J. Fluid Mech.

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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.

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