Transient dispersion in a channel with crossflow and wall adsorption

Self Cite

Understanding the statistics of bedload particle motions is of great importance. To model the hop events which are defined as trajectories of particles moving successively from the start to the end of their motions, recently, Wu et al. (Water Resour. Res., vol. 56, 2020, p. e2019WR025116) have successfully performed individual-based simulations according to the Fokker–Planck equation for particle velocities. However, analytical solutions are still not available due to (i) difficulties in treating the velocity-dependent diffusivity, and (ii) a knowledge gap in incorporating the termination of particle motions for the equation. To tackle the above-mentioned challenges, we first specify a Robin boundary condition representing the deposition of particles. Second, for analytical solutions of hop statistics, a variable transformation is devised to deal with the velocity-dependent diffusivity. The original bedload transport problem is thus found to be governed by the classic equation for the solute transport in tube flows with a constant diffusivity after the transformation. Finally, through solving the spatial and temporal moments of the governing equation, we investigate the influence of the deposition rate on three key characteristics of particle hops. Importantly, we have related the deposition rate to the mean travel times and hop distances, enabling a direct determination of this physical parameter based on measured particle motion statistics. The analytical solutions are validated by experimental observations with different bedload particle diameters and transport conditions. Based on the limited experimental datasets, the deposition frequency is shown to decrease as the shear stress increases when the flow rate is not small.

Section: Formulationsmentioning

confidence: 99%

“…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).…”

Section: Initial and Boundary Conditionsmentioning

confidence: 99%

Theoretical analysis for bedload particle deposition and hop statistics

Jiang

Zeng

et al. 2023

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“…It was also shown that even if the flow oscillates with time, the trend remains the same, and α became a function of the frequency of the oscillation (Broeck 1982;Jansons 2006;Levesque et al 2012). Crossing between streamlines of substances is caused not only by thermal diffusion but also by advection such as cross-flow (Lin & Shaqfeh 2019;Wang et al 2022). Lin & Shaqfeh (2019) introduced a constant cross-flow into a plane Poiseuille flow and investigated the effect of the cross-flow strength on Taylor dispersion.…”

Section: Introductionmentioning

confidence: 99%

Flow-induced diffusion in a packed lattice of squirmers

Kogure,

Omori,

Ishikawa

2023

Mass transport in suspensions of swimming microorganisms is one of the most important factors for the colonisation and growth of microorganisms. Hydrodynamic interactions among swimming microorganisms play an important role in mass transport, especially in highly concentrated suspensions. To elucidate the influence of highly concentrated cells on mass transport, we numerically simulated mass transport in lattices of squirmers that were fixed in space and oriented in the same direction. The effects of different volume fractions, Péclet numbers ( $Pe$ ) and lattice configurations on mass transport were quantified by tracking Lagrangian material points that move with background flow with Brownian diffusivity. Although the flow field became periodic in space and each streamline basically extended in one direction, the motion of tracer particles became diffusive over long durations due to Brownian motion and cross-flows. Flow-induced diffusion was anisotropic and significantly enhanced over Brownian diffusion in the longitudinal direction. We also investigated mass transport in random configurations of squirmers to reproduce more general conditions. Similar enhanced diffusion was also observed in the random configurations, indicating that the flow-induced diffusion appears regardless of the configurations. The present flow-induced diffusion did not follow $Pe$ dependency of the conventional Taylor dispersion due to the cross-flows. The time and velocity scales were proposed, which enabled us to predict the flow-induced diffusivity from the data of the flow field and Brownian diffusivity without solving the mass conservation equation. The findings reported here improve our understanding of the transport phenomena in packed suspensions of swimming microorganisms.

“…2020; Wang et al. 2022). Therefore, this reversible kinetic sorption is generally more appropriate for applications in practice, whereas the corresponding transport processes are more complicated.…”

Section: Introductionmentioning

confidence: 99%

“…The term reversible describes that the adsorbed solute mass from the bulk to the boundary surface can be released back to the flow through the desorption process (Goodrich 1954;Boddington & Clifford 1983;Purnama 1988a), which is a generalisation of the irreversible pure-adsorption (wall absorption) process (Gupta & Gupta 1972;Pancharatnam & Homsy 1972;Mauri 1991;Sadeghi et al 2020;Wang et al 2022). Therefore, this reversible kinetic sorption is generally more appropriate for applications in practice, whereas the corresponding transport processes are more complicated.…”

Section: Introductionmentioning

confidence: 99%

Analytical solutions for reactive shear dispersion with boundary adsorption and desorption

Jiang

Zeng

et al. 2022

Self Cite

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.