The lateral migration of a spherical particle in two-dimensional shear flows

Vasseur, P.; Cox, R. G.

doi:10.1017/s0022112076002498

Cited by 310 publications

(232 citation statements)

References 19 publications

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“…gravitational acceleration perpendicular to the direction of flow) drops and bubbles has been relatively unexplored compared to the neutrally buoyant and longitudinally buoyant cases, although it is broadly relevant to the positioning of bubbles and drops in microfluidic flows. Most prior investigations of inertial lift on buoyant particles involved buoyant forces aligned with the direction of flow [38,60], rather than perpendicular to this direction (as in our experiments). Hogg investigated theoretically the inertial forces acting on settling particles in horizontal flow [61], and found that inertial forces are in general weak compared to buoyant forces.…”

Section: Discussionmentioning

confidence: 87%

Sheathless hydrodynamic positioning of buoyant drops and bubbles inside microchannels

et al. 2011

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Particles, bubbles, and drops carried by a fluid in a confined environment such as a pipe can be subjected to hydrodynamic lift forces, i.e. forces that are perpendicular to the direction of the flow. We investigated the positioning effect of lift forces acting on buoyant drops and bubbles suspended in a carrier fluid and flowing in a horizontal microchannel. We report experiments on drops of water in fluorocarbon liquid, and on bubbles of nitrogen in hydrocarbon liquid and silicone oil, inside microchannels with widths on the order of 0.1-1 mm. Despite their buoyancy, drops and bubbles could travel without contacting with the walls of channels; the most important parameters for reaching this flow regime in our experiments were the viscosity and the velocity of the carrier fluid, and the size of drops and bubbles. The dependencies of the transverse position of drops and bubbles on these parameters were investigated. At steady state the trajectories of drops and bubbles approached the center of the channel for drops and bubbles almost as large as the channel, carried by rapidly-flowing viscous liquids; among our experiments, these flow conditions were characterized by larger capillary numbers and smaller Reynolds numbers. Analytical models of lift forces developed for the flow of drops much smaller than the width of the channel failed to predict their transverse position, while computational fluid dynamic simulations of the experiments agreed better with the experimental measurements. The degrees of success of these predictions indicate the importance of confinement on generating strong hydrodynamic lift forces. We conclude that inside microfluidic channels, it is possible to support and position buoyant drops and bubbles simply by flowing a single-stream (i.e. "sheathless") carrier liquid that has appropriate velocity and hydrodynamic properties.

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Section: Discussionmentioning

confidence: 87%

Sheathless hydrodynamic positioning of buoyant drops and bubbles inside microchannels

et al. 2011

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“…This effect, which has been verified by follow-up experimental [3][4][5] and theoretical 6,7 works, induces the migration of neutrally buoyant spherical particles in pipe flows to an annulus at approximately 0.6 of the a) Authors to whom correspondence should be addressed. Electronic addresses: guoqing.hu@imech.ac.cn and sunjs@nanoctr.cn.…”

Section: Introductionmentioning

confidence: 83%

Inertial migration of deformable droplets in a microchannel

Chen

Xue

Zhang³

et al. 2014

Physics of Fluids

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The microfluidic inertial effect is an effective way of focusing and sorting droplets suspended in a carrier fluid in microchannels. To understand the flow dynamics of microscale droplet migration, we conduct numerical simulations on the droplet motion and deformation in a straight microchannel. The results are compared with preliminary experiments and theoretical analysis. In contrast to most existing literature, the present simulations are three-dimensional and full length in the streamwise direction and consider the confinement effects for a rectangular cross section. To thoroughly examine the effect of the velocity distribution, the release positions of single droplets are varied in a quarter of the channel cross section based on the geometrical symmetries. The migration dynamics and equilibrium positions of the droplets are obtained for different fluid velocities and droplet sizes. Droplets with diameters larger than half of the channel height migrate to the centerline in the height direction and two equilibrium positions are observed between the centerline and the wall in the width direction. In addition to the well-known Segré-Silberberg equilibrium positions, new equilibrium positions closer to the centerline are observed. This finding is validated by preliminary experiments that are designed to introduce droplets at different initial lateral positions. Small droplets also migrate to two equilibrium positions in the quarter of the channel cross section, but the coordinates in the width direction are between the centerline and the wall. The equilibrium positions move toward the centerlines with increasing Reynolds number due to increasing deformations of the droplets. The distributions of the lift forces, angular velocities, and the deformation parameters of droplets along the two confinement direction are investigated in detail. Comparisons are made with theoretical predictions to determine the fundamentals of droplet migration in microchannels. In addition, existence of the inner equilibrium position is linked to the quartic velocity distribution in the width direction through a simple model for the slip angular velocities of droplets.

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“…19,21,44,45 In rectangular microchannels, many research groups have reported two equilibrium positions centered at the two long walls when the aspect ratio AR (AR = W/H, where W is the channel width) highly deviates from the unity. 22,25,28,42,43,[46][47][48] This reduction of equilibrium position compared with square microchannels makes rectangular microchannels widely employed in particle focusing and separation. However, six or even eight positions have also been observed in rectangular microchannels with similar AR.…”

Section: Introductionmentioning

confidence: 99%

“…[37][38][39][40]46,[49][50][51] The inertial lift on the particle in a Poiseuille flow can be scaled as follows:…”

Section: Introductionmentioning

confidence: 99%

Inertial focusing of spherical particles in rectangular microchannels over a wide range of Reynolds numbers

et al. 2015

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Inertial microfluidics has emerged as an important tool for manipulating particles and cells. For a better design of inertial microfluidic devices, we conduct 3D direct numerical simulations (DNS) and experiments to determine the complicated dependence of focusing behaviour on the particle size, channel aspect ratio, and channel Reynolds number. We find that the well-known focusing of the particles at the two centers of the long channel walls occurs at a relatively low Reynolds number, whereas additional stable equilibrium positions emerge close to the short walls with increasing Reynolds number. Based on the numerically calculated trajectories of particles, we propose a two-stage particle migration which is consistent with experimental observations. We further present a general criterion to secure good focusing of particles for high flow rates. This work thus provides physical insight into the multiplex focusing of particles in rectangular microchannels with different geometries and Reynolds numbers, and paves the way for efficiently designing inertial microfluidic devices.

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The lateral migration of a spherical particle in two-dimensional shear flows

Cited by 310 publications

References 19 publications

Sheathless hydrodynamic positioning of buoyant drops and bubbles inside microchannels

Sheathless hydrodynamic positioning of buoyant drops and bubbles inside microchannels

Inertial migration of deformable droplets in a microchannel

Inertial focusing of spherical particles in rectangular microchannels over a wide range of Reynolds numbers

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