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Pressure-driven transport of particles through a converging-diverging microchannel
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Figures

Image of FIG. 1.

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FIG. 1.

(a) Schematic view of a 2D model of a circular particle in a converging-diverging microchannel. The narrowest part is defined as the throat of the converging-diverging microchannel. The origin of the coordinate system is fixed at the center of the throat. (b) Photograph of a fabricated converging-diverging microchannel on a polydimethylsiloxane device. The inset is a magnified view of the converging-diverging microchannel under a microscope.

Image of FIG. 2.

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FIG. 2.

Undeformed (a) and deformed (b) mesh adjacent to the particle surface.

Image of FIG. 3.

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FIG. 3.

Wall correction factor of a spherical particle moving along the axis of a cylindrical infinite channel. The dashed line indicates the limit of Haberman and Sayre’s analytical solution (Ref. 11).

Image of FIG. 4.

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FIG. 4.

Sequential images of a particle of in diameter moving along the centerline of the converging-diverging microchannel under a pressure difference of . The arrow denotes the direction of the particle transport. The time interval between adjacent images is 0.2 s. (a) The particle trajectory predicted by the NS-ALE model. The particle is marked with a circle. The color levels denote the magnitude of the fluid velocity with the maximum fluid velocity at the throat. (b) Experimental images captured by an inverted microscope with a charge-coupled device camera.

Image of FIG. 5.

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FIG. 5.

Translational velocity profiles (a) and velocity ratios (b) of a particle of in diameter moving along the centerline of the converging-diverging microchannel under different pressure differences. The axis denotes the centerline of the microchannel, and the zero coordinator represents the throat of the converging-diverging microchannel. Lines denote the numerical results and symbols represent the existing experimental data.

Image of FIG. 6.

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FIG. 6.

Translational velocity ratios of particles with different sizes moving along the centerline of the converging-diverging microchannel under a pressure difference of . The throat width is . The coordinators of points A, B, C, and D are , , , and 0, respectively.

Image of FIG. 7.

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FIG. 7.

The relationship between the ratio of the particle size to the throat width and the translational velocity ratio at the throat under a pressure difference of . The throat width is . The circles and solid line denote the numerical results and the fourth degree polynomial fitting curve, respectively. The translational velocity ratio at the throat with a zero particle size refers to the ratio of the fluid velocity at the throat to that in the upstream straight channel.

Image of FIG. 8.

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FIG. 8.

Effect of the cross-sectional area ratio between the throat and the straight channel on the translational velocity ratio at the throat with two different particle sizes. The pressure difference applied between the inlet and the outlet is . The width of the straight microchannel is . The solid line indicates the ratio of the fluid velocity at the throat to that in the upstream straight channel without particle transport through it.

Image of FIG. 9.

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FIG. 9.

Trajectories of a particle of in diameter moving through the converging-diverging microchannel with different initial transverse locations under a pressure difference of . The black dashed bold line denotes the boundary of the converging-diverging microchannel.

Image of FIG. 10.

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FIG. 10.

Rotational velocity profiles of a particle of in diameter moving through the converging-diverging microchannel with two different initial transverse locations under a pressure difference of .

Image of FIG. 11.

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FIG. 11.

Sequential images of the separation of two particles of in diameter moving through the converging-diverging microchannel under a pressure difference of . The initial leading and lagging particles are, respectively, marked with a hollow circle (○) and a solid circle (●). The color levels denote the magnitude of the fluid velocity with the maximum fluid velocity at the throat. The two arrows denote the direction of particle transport. (a) Two fore-and-aft located particles moving through the microchannel. The time interval between adjacent images is 0.2 s. (b) Two up-and-down located particles moving through the microchannel. The time interval between adjacent images is 0.25 s.

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/content/aip/journal/bmf/3/2/10.1063/1.3122594
2009-04-22
2014-04-24

Abstract

Pressure-driven transport of particles through a symmetric converging-diverging microchannel is studied by solving a coupled nonlinear system, which is composed of the Navier–Stokes and continuity equations using the arbitrary Lagrangian–Eulerian finite-element technique. The predicted particle translation is in good agreement with existing experimental observations. The effects of pressure gradient, particle size, channel geometry, and a particle’s initial location on the particle transport are investigated. The pressure gradient has no effect on the ratio of the translational velocity of particles through a converging-diverging channel to that in the upstream straight channel. Particles are generally accelerated in the converging region and then decelerated in the diverging region, with the maximum translational velocity at the throat. For particles with diameters close to the width of the channel throat, the usual acceleration process is divided into three stages: Acceleration, deceleration, and reacceleration instead of a monotonic acceleration. Moreover, the maximum translational velocity occurs at the end of the first acceleration stage rather than at the throat. Along the centerline of the microchannel, particles do not rotate, and the closer a particle is located near the channel wall, the higher is its rotational velocity. Analysis of the transport of two particles demonstrates the feasibility of using a converging-diverging microchannel for passive (biological and synthetic) particle separation and ordering.

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Scitation: Pressure-driven transport of particles through a converging-diverging microchannel
http://aip.metastore.ingenta.com/content/aip/journal/bmf/3/2/10.1063/1.3122594
10.1063/1.3122594
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