Analytical solutions for reactive shear dispersion with boundary adsorption and desorption

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.

Theoretical analysis for bedload particle deposition and hop statistics

“…where the deposition rate Γ * can be related to P stop . Equation (2.5) is a Robin (third-type) boundary condition for partially reflecting boundaries, often used in reactive transport problems (Singer et al 2008;Andrews 2009;Jiang et al 2022;Wang et al 2022b).…”

Multi-scale analysis of concentration distribution in unsteady Couette–Poiseuille flows through a porous channel

“…see Poddar et al [40]), surface reaction such as adsorption and desorption (e.g. see Jiang et al [45]). The analysis based on a more fundamental initial condition such as solute release at a point source (e.g.…”

“…see Jiang et al. [45]). The analysis based on a more fundamental initial condition such as solute release at a point source (e.g.…”

“…[40]; Jiang et al. [45]). Because of the relevance of wetland flows with the porous media flows, it has also received attention in the field of wastewater treatment, ecological restoration, flood management, biodiversity protection and ecological remodelling [26–29].…”

“…Solute transport in liquid-filled porous medium flows offers some insights to understand the scientific and technological significance due its potential applications in engineering and biological situations, such as the movement of minerals (such as fertilizers) in soils, the transport of contaminants in soils, the movement of nutrients in bones, the intrusion of salt in fresh water in soils near ocean coasts, secondary recovery methods in oil reservoirs (where the injected fluid dissolves the reservoir's soil), the use of tracers in petroleum engineering, solute transport in the CNS, blood transport in impeded blood vessels and many more (see the studies by Goldsztein [34]; Bear [41]; Wu et al [28]; Dentz et al [42]; Sharp et al [37]; Jiang & Chen [43]; Roy et al [38]; Yang et al [44]; Poddar et al [40]; Jiang et al [45]). Because of the relevance of wetland flows with the porous media flows, it has also received attention in the field of wastewater treatment, ecological restoration, flood management, biodiversity protection and ecological remodelling [26][27][28][29].…”