The lateral migration of spherical particles sedimenting in a stagnant bounded fluid

Vasseur, P.; Cox, R. G.

doi:10.1017/s0022112077001840

Cited by 174 publications

(164 citation statements)

References 17 publications

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“…For example, in the case of L periodic = 45.511, L x = 6.044, and ⌽ = 0.05 we found that x increases from 0.95 to 1.43 when Re p changes from 0.1 to 1. This behavior is reasonable since in a region of finite Re p particle sedimenting between two infinite vertical walls is shown by Vasseur and Cox [34] to migrate away from the closer wall due to a repulsive particle-wall interaction. On the other hand, as discussed in the analysis of moderate Re p by Koch [24], the particle migrates away from the wake of another particle.…”

Section: A Particle Density Distributionmentioning

confidence: 66%

Sedimentation dynamics of spherical particles in confined geometries

2004

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We study the steady-state dynamics of sedimenting non-Brownian particles in confined geometries with full hydrodynamic interactions at small but finite Reynolds numbers. We employ extensive computer simulations using a method where a continuum liquid phase is coupled through Stokesian friction to a discrete particle phase. In particular, we consider a sedimentation box which is otherwise periodic except that it is confined by two parallel walls parallel to gravity with a spacing L x . By systematically varying L x we explore the change in dynamics from a quasi-two-dimensional (2D) case to a three-dimensional case. We find that in such confined geometries there is a depletion of particle number density at the walls for small volume fractions, while for large volume fractions there is an excess number of particles at the walls. For the average sedimentation velocity, we find that the Richardson-Zaki law is well obeyed but the decrease of the velocity for dilute systems is slower for smaller values of L x . We study the anisotropy of the velocity fluctuations and find that in the direction of gravity there is excellent agreement with the predicted scaling with respect to L x . We also find that the behavior of the corresponding diffusion coefficients as a function of L x is qualitatively different in the direction parallel to gravity and perpendicular to it. In the quasi-2D limit where particles block each other, the velocity fluctuations behave differently from the other confined systems.

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Section: A Particle Density Distributionmentioning

confidence: 66%

Sedimentation dynamics of spherical particles in confined geometries

2004

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“…On the lower end of the Re spectrum, we have to mention the perturbation analysis of Vasseur & Cox (1977). Their theory, like all other theories of its kind, is unable to follow the actual motion of the particle.…”

Section: Comparison With Other Resultsmentioning

confidence: 99%

Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid Part 1. Sedimentation

1994

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This paper reports the result of direct simulations of fluid-particle motions in two dimensions. We solve the initial value problem for the sedimentation of circular and elliptical particles in a vertical channel. The fluid motion is computed from the Navier-Stokes equations for moderate Reynolds numbers in the hundreds. The particles are moved according to the equations of motion of a rigid body under the action of gravity and hydrodynamic forces arising from the motion of the fluid. The solutions are as exact as our finite-element calculations will allow. As the Reynolds number is increased to 600, a circular particle can be said to experience five different regimes of motion: steady motion with and without overshoot and weak, strong and irregular oscillations. An elliptic particle always turn its long axis perpendicular to the fall, and drifts to the centreline of the channel during sedimentation. Steady drift, damped oscillation and periodic oscillation of the particle are observed for different ranges of the Reynolds number. For two particles which interact while settling, a steady staggered structure, a periodic wake-action regime and an active drafting-kissing-tumbling scenario are realized at increasing Reynolds numbers. The nonlinear effects of particle-fluid, particle-wall and interparticle interactions are analysed, and the mechanisms controlling the simulated flows are shown to be lubrication, turning couples on long bodies, steady and unsteady wakes and wake interactions. The results are compared to experimental and theoretical results previously published. This paper reports the result of direct simulations of fluid-particle motions in two dimensions. We solve the initial value problem for the sedimentation of circular and elliptical particles in a vertical channel. The fluid motion is computed from the Navier-Stokes equations for moderate Reynolds numbers in the hundreds. The particles are moved according to the equations of motion of a rigid body under the action of gravity and hydrodynamic forces arising from the motion of the fluid. The solutions are as exact as our finite-element calculations will allow. As the Reynolds number is increased to 600, a circular particle can be said to experience five different regimes of motion: steady motion with and without overshoot and weak, strong and irregular oscillations. An elliptic particle always turn its long axis perpendicular to the fall, and drifts to the centreline of the channel during sedimentation. Steady drift, damped oscillation and periodic oscillation of the particle are observed for different ranges of the Reynolds number. For two particles which interact while settling, a steady staggered structure, a periodic wake-action regime and an active drafting-kissing-tumbling scenario are realized at increasing Reynolds numbers. The nonlinear effects of particle-fluid, particle-wall and interparticle interactions are analysed, and the mechanisms controlling the simulated flows are shown to be lubrication, turning couples on long bodies, s...

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“…In addition, two zero Dean velocity lines exist between the For a microparticle in fluid flow, because of the parabolic velocity profile of the Poiseuille flow, its upper side has a larger relative velocity (in magnitude) than its lower side. This reduces the pressure on the upper side of the particle and, consequently, F S is generated, by which the particle is pushed away from the centerline, towards the channel walls, until this force is balanced by F W [66,67]. In other words, a particle tends to follow the path along which its sides undergo a minimum difference in relative velocity.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

Microparticle Inertial Focusing in an Asymmetric Curved Microchannel

Özbey

Karimzadehkhouei

Alijani

et al. 2018

Fluids

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Inertial Microfluidics offer a high throughput, label-free, easy to design, and cost-effective solutions, and are a promising technique based on hydrodynamic forces (passive techniques) instead of external ones, which can be employed in the lab-on-a-chip and micro-total-analysis-systems for the focusing, manipulation, and separation of microparticles in chemical and biomedical applications. The current study focuses on the focusing behavior of the microparticles in an asymmetric curvilinear microchannel with curvature angle of 280 • . For this purpose, the focusing behavior of the microparticles with three different diameters, representing cells with different sizes in the microchannel, was experimentally studied at flow rates from 400 to 2700 µL/min. In this regard, the width and position of the focusing band are carefully recorded for all of the particles in all of the flow rates. Moreover, the distance between the binary combinations of the microparticles is reported for each flow rate, along with the Reynolds number corresponding to the largest distances. Furthermore, the results of this study are compared with those of the microchannel with the same curvature angle but having a symmetric geometry. The microchannel proposed in this study can be used or further modified for cell separation applications.

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The lateral migration of spherical particles sedimenting in a stagnant bounded fluid

Cited by 174 publications

References 17 publications

Sedimentation dynamics of spherical particles in confined geometries

Sedimentation dynamics of spherical particles in confined geometries

Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid Part 1. Sedimentation

Microparticle Inertial Focusing in an Asymmetric Curved Microchannel

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