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Abstract
Pressuredriven transport of particles through a symmetric convergingdiverging microchannel is studied by solving a coupled nonlinear system, which is composed of the Navier–Stokes and continuity equations using the arbitrary Lagrangian–Eulerian finiteelement 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 convergingdiverging 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 convergingdiverging microchannel for passive (biological and synthetic) particle separation and ordering.
This work was supported, in part, by the Office of Research’s Multidisciplinary Grant (S.Q.) and the Korea Research Foundation Grant No. KRF2008313D00117 funded by the Korean Government (S.W.J.).
I. INTRODUCTION
II. MATHEMATICAL MODEL
III. COMPUTATIONAL METHOD AND CODE VALIDATION
IV. RESULTS AND DISCUSSION
A. Transient transport of a particle
B. Effect of pressure gradient
C. Effect of particle size
D. Effect of the crosssectional area
E. Effect of transverse location of the particle
F. Separation of two particles
V. CONCLUSIONS
Key Topics
 Microscale flows
 9.0
 Experiment design
 6.0
 Particle velocity
 6.0
 Fluid flows
 5.0
 Lagrangian mechanics
 5.0
Figures
(a) Schematic view of a 2D model of a circular particle in a convergingdiverging microchannel. The narrowest part is defined as the throat of the convergingdiverging microchannel. The origin of the coordinate system is fixed at the center of the throat. (b) Photograph of a fabricated convergingdiverging microchannel on a polydimethylsiloxane device. The inset is a magnified view of the convergingdiverging microchannel under a microscope.
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(a) Schematic view of a 2D model of a circular particle in a convergingdiverging microchannel. The narrowest part is defined as the throat of the convergingdiverging microchannel. The origin of the coordinate system is fixed at the center of the throat. (b) Photograph of a fabricated convergingdiverging microchannel on a polydimethylsiloxane device. The inset is a magnified view of the convergingdiverging microchannel under a microscope.
Undeformed (a) and deformed (b) mesh adjacent to the particle surface.
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Undeformed (a) and deformed (b) mesh adjacent to the particle surface.
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).
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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).
Sequential images of a particle of in diameter moving along the centerline of the convergingdiverging 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 NSALE 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 chargecoupled device camera.
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Sequential images of a particle of in diameter moving along the centerline of the convergingdiverging 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 NSALE 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 chargecoupled device camera.
Translational velocity profiles (a) and velocity ratios (b) of a particle of in diameter moving along the centerline of the convergingdiverging microchannel under different pressure differences. The axis denotes the centerline of the microchannel, and the zero coordinator represents the throat of the convergingdiverging microchannel. Lines denote the numerical results and symbols represent the existing experimental data.
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Translational velocity profiles (a) and velocity ratios (b) of a particle of in diameter moving along the centerline of the convergingdiverging microchannel under different pressure differences. The axis denotes the centerline of the microchannel, and the zero coordinator represents the throat of the convergingdiverging microchannel. Lines denote the numerical results and symbols represent the existing experimental data.
Translational velocity ratios of particles with different sizes moving along the centerline of the convergingdiverging microchannel under a pressure difference of . The throat width is . The coordinators of points A, B, C, and D are , , , and 0, respectively.
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Translational velocity ratios of particles with different sizes moving along the centerline of the convergingdiverging microchannel under a pressure difference of . The throat width is . The coordinators of points A, B, C, and D are , , , and 0, respectively.
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.
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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.
Effect of the crosssectional 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.
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Effect of the crosssectional 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.
Trajectories of a particle of in diameter moving through the convergingdiverging microchannel with different initial transverse locations under a pressure difference of . The black dashed bold line denotes the boundary of the convergingdiverging microchannel.
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Trajectories of a particle of in diameter moving through the convergingdiverging microchannel with different initial transverse locations under a pressure difference of . The black dashed bold line denotes the boundary of the convergingdiverging microchannel.
Rotational velocity profiles of a particle of in diameter moving through the convergingdiverging microchannel with two different initial transverse locations under a pressure difference of .
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Rotational velocity profiles of a particle of in diameter moving through the convergingdiverging microchannel with two different initial transverse locations under a pressure difference of .
Sequential images of the separation of two particles of in diameter moving through the convergingdiverging 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 foreandaft located particles moving through the microchannel. The time interval between adjacent images is 0.2 s. (b) Two upanddown located particles moving through the microchannel. The time interval between adjacent images is 0.25 s.
Click to view
Sequential images of the separation of two particles of in diameter moving through the convergingdiverging 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 foreandaft located particles moving through the microchannel. The time interval between adjacent images is 0.2 s. (b) Two upanddown located particles moving through the microchannel. The time interval between adjacent images is 0.25 s.
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Abstract
Pressuredriven transport of particles through a symmetric convergingdiverging microchannel is studied by solving a coupled nonlinear system, which is composed of the Navier–Stokes and continuity equations using the arbitrary Lagrangian–Eulerian finiteelement 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 convergingdiverging 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 convergingdiverging microchannel for passive (biological and synthetic) particle separation and ordering.
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