Aris-Taylor dispersion in tubes with dead ends

Dagdug, Leonardo; Berezhkovskii, Alexander M.; Skvortsov, Alexei T.

doi:10.1063/1.4885854

Cited by 3 publications

(5 citation statements)

References 45 publications

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“…The main novelty of this study is that we consider a geometry with sharply changing boundary roughness, resulting in large RZ. Previous studies of dispersion in channels of varying apertures have been limited to smooth boundaries (Bolster et al 2009;Bouquain et al 2012) or ignore both large openings and the flow inside the stagnant areas (Laachi et al 2007; Dagdug et al 2014;Zitserman et al 2014). In this paper, we show that this boundary roughness leads to a qualitatively different behaviour compared to the aforementioned studies.…”

Section: Introductionmentioning

confidence: 63%

“…The dynamics may therefore be captured by modelling the RZ as stationary areas, where the exact shape of the RZ is not of importance, only their accessibility and characteristic residence time. Analytical expressions might be achievable through effective models, specifically along the lines of Levesque et al (2012) and Dagdug et al (2014). The model by Dagdug et al (2014) may be a good starting point; however, in its current form it is insufficient to model our system, because the square boundary roughness violates their assumptions of narrow cavity (dead-end) openings not affecting the main channel flow and the assumption of no flow inside the cavities.…”

Section: Discussionmentioning

confidence: 99%

“…Analytical expressions might be achievable through effective models, specifically along the lines of Levesque et al (2012) and Dagdug et al (2014). The model by Dagdug et al (2014) may be a good starting point; however, in its current form it is insufficient to model our system, because the square boundary roughness violates their assumptions of narrow cavity (dead-end) openings not affecting the main channel flow and the assumption of no flow inside the cavities. Our simulations indicate that it remains a challenge to model the complex dependence of the residence times on Re, Pe and b.…”

Section: Discussionmentioning

confidence: 99%

“…Therefore, dispersion has been the focus of much experimental, numerical and theoretical research. The understanding of dispersion in axially invariant channels has since Taylor (1953) and Aris & Taylor (1956) been extended to allow for alternating fluid boundary conditions (Adrover & Cerbelli 2017;Adrover, Cerbelli & Giona 2018) and boundaries absorbing the solute (Levesque et al 2012;Dagdug, Berezhkovskii & Skvortsov 2014). However, most channels and pores in natural and industrial systems are not perfectly flat.…”

Section: Introductionmentioning

confidence: 99%

“…However, it was limited to the transient regime. Dagdug et al (2014) studied how dispersion is affected by narrow dead ends where particles may be trapped for a finite time. Larger openings may lead to non-negligible flow inside the dead ends and non-trivial flow profiles.…”

Section: Introductionmentioning

confidence: 99%

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Solute dispersion in channels with periodic square boundary roughness

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Transport of solutes through channels with rough boundaries is abundant in natural and engineered settings. However, it is not known currently what the consequences of an abruptly alternating boundary are for the solute dispersion, in particular when advected by inertial fluid flow. To investigate this, we compute numerically the time-asymptotic longitudinal dispersion coefficient of a passive solute advected by fluid flow through a two-dimensional channel with square boundary roughness. We determine how the effective diffusion coefficient depends on the boundary amplitude, Péclet number and Reynolds number. For creeping flow, the effective diffusion coefficient is found to be enhanced significantly through the recirculation zones. Increasing fluid inertia reduces the effective diffusion coefficient by up to a factor of two for high Péclet numbers. We interpret this behaviour by analysing residence times computed from Lagrangian particle simulations.

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Section: Introductionmentioning

confidence: 63%

Section: Discussionmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Solute dispersion in channels with periodic square boundary roughness

2022

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Dispersion of solute released from a sphere flowing in a microchannel

Gekle

2017

J. Fluid Mech.

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A solute is released from the surface of a sphere flowing freely in a cylindrical channel mimicking a modern drug delivery agent in a blood vessel. The solute then disperses by the combined action of advection and diffusion. We consider reflecting boundary conditions on the sphere and absorbing boundary conditions on the channel surface mimicking a biochemical reaction between the drug and endothelial cells on the vessel surface. The drug is released either instantaneously or continuously in time.The two key observables are the mean residence time in the flow before the drug is absorbed and the width over which it is spread on the vessel surface upon reaction. We numerically solve the Fokker-Planck equation for the time-dependent substance concentration combined with an analytical solution of the flow field. As expected, we find that the presence of the sphere leads to a substantial reduction in mean residence time and reaction width. Surprisingly, however, even in the limit of very large Péclet numbers (high velocities) the sphere-free case is not generally recovered. This observation can be attributed mainly to the small, but non-negligible radial flow component induced by the moving sphere. We further identify a strong influence of the release position which sharply separates two qualitatively different regimes. If the release position is between θ 0 = 0 (front) and a critical θ c the substance is quickly advected away from the sphere and its overall behaviour is similar to free diffusion in an empty channel. For release between θ c and θ 0 = π (tail), on the other hand, the substance is pushed towards the sphere leading to behaviour reminiscent of confined diffusion between two infinitely long cylinders. The critical position θ c is generally smaller than π/2 which would correspond to an equatorial release position.

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Biased diffusion in three-dimensional comb-like structures

Berezhkovskii

Dagdug

Bezrukov

2015

The Journal of Chemical Physics

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In this paper, we study biased diffusion of point Brownian particles in a three-dimensional comb-like structure formed by a main cylindrical tube with identical periodic cylindrical dead ends. It is assumed that the dead ends are thin cylinders whose radius is much smaller than both the radius of the main tube and the distance between neighboring dead ends. It is also assumed that in the main tube, the particle, in addition to its regular diffusion, moves with a uniform constant drift velocity. For such a system, we develop a formalism that allows us to derive analytical expressions for the Laplace transforms of the first two moments of the particle displacement along the main tube axis. Inverting these Laplace transforms numerically, one can find the time dependences of the two moments for arbitrary values of both the drift velocity and the dead-end length, including the limiting case of infinitely long dead ends, where the unbiased diffusion becomes anomalous at sufficiently long times. The expressions for the Laplace transforms are used to find the effective drift velocity and diffusivity of the particle as functions of its drift velocity in the main tube and the tube geometric parameters. As might be expected from common-sense arguments, the effective drift velocity monotonically decreases from the initial drift velocity to zero as the dead-end length increases from zero to infinity. The effective diffusivity is a more complex, non-monotonic function of the dead-end length. As this length increases from zero to infinity, the effective diffusivity first decreases, reaches a minimum, and then increases approaching a plateau value which is proportional to the square of the particle drift velocity in the main tube.

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Aris-Taylor dispersion in tubes with dead ends

Cited by 3 publications

References 45 publications

Solute dispersion in channels with periodic square boundary roughness

Solute dispersion in channels with periodic square boundary roughness

Dispersion of solute released from a sphere flowing in a microchannel

Biased diffusion in three-dimensional comb-like structures

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