scholarly journals Transport of Non-Spherical Particles in Square Microchannel Flows: A Review

Micromachines ◽  
2021 ◽  
Vol 12 (3) ◽  
pp. 277
Author(s):  
Tohme Tohme ◽  
Pascale Magaud ◽  
Lucien Baldas
Keyword(s):  
Cross Section ◽  
Microfluidic Devices ◽  
Rotational Behavior ◽  
Spherical Particles ◽  
Inertial Effects ◽  
Lateral Migration ◽  
Streamwise Direction ◽  
Particle Rotation ◽  
Inertial Migration ◽  
Square Microchannel

Understanding the behavior of a single particle flowing in a microchannel is a necessary step in designing and optimizing efficient microfluidic devices for the separation, concentration, counting, detecting, sorting, or mixing of particles in suspension. Although the inertial migration of spherical particles has been deeply investigated in the last two decades, most of the targeted applications involve shaped particles whose behavior in microflows is still far from being completely understood. While traveling in a channel, a particle both rotates and translates: it translates in the streamwise direction driven by the fluid flow but also in the cross-section perpendicular to the streamwise direction due to inertial effects. In addition, particles’ rotation and translation motions are coupled. Most of the existing works investigating the transport of particles in microchannels decouple their rotational and lateral migration behaviors: particle rotation is mainly studied in simple shear flows, whereas lateral migration is neglected, and studies on lateral migration mostly focus on spherical particles whose rotational behavior is simple. The aim of this review is to provide a summary of the different works existing in the literature on the inertial migration and the rotational behavior of non-spherical particles with a focus and discussion on the remaining scientific challenges in this field.

Equilibrium radial positions of neutrally buoyant spherical particles over the circular cross-section in Poiseuille flow

2017 ◽  
Vol 813 ◽  
pp. 750-767 ◽  
Author(s):  
Yusuke Morita ◽  
Tomoaki Itano ◽  
Masako Sugihara-Seki
Keyword(s):  
Experimental Study ◽  
Cross Section ◽  
Poiseuille Flow ◽  
Equilibrium Position ◽  
Probability Function ◽  
Circular Cross Section ◽  
Spherical Particles ◽  
Inertial Migration ◽  
Entry Length ◽  
Neutrally Buoyant

An experimental study of the inertial migration of neutrally buoyant spherical particles suspended in the Poiseuille flow through circular tubes has been conducted at Reynolds numbers $(Re)$ from 100 to 1100 for particle-to-tube diameter ratios of ${\sim}$0.1. The distributions of particles in the tube cross-section were measured at various distances from the tube inlet and the radial probability function of particles was calculated. At relatively high $Re$, the radial probability function was found to have two peaks, corresponding to the so-called Segre–Silberberg annulus and the inner annulus, the latter of which was first reported experimentally by Matas et al. (J. Fluid Mech. vol. 515, 2004, pp. 171–195) to represent accumulation of particles at smaller radial positions than the Segre–Silberberg annulus. They assumed that the inner annulus would be an equilibrium position of particles, where the resultant lateral force on the particles disappears, similar to the Segre–Silberberg annulus. The present experimental study showed that the fraction of particles observed on the Segre–Silberberg annulus increased and the fraction on the inner annulus decreased further downstream, accompanying an outward shift of the inner annulus towards the Segre–Silberberg annulus and a decrease in its width. These results suggested that if the tubes were long enough, the inner annulus would disappear such that all particles would be focused on the Segre–Silberberg annulus for $Re<1000$. At the cross-section nearest to the tube inlet, particles were absent in the peripheral region close to the tube wall including the expected Segre–Silberberg annulus position for $Re>700$. In addition, the entry length after which radial migration has fully developed was found to increase with increasing $Re$, in contrast to the conventional estimate. These results may be related to the developing flow in the tube entrance region where the radial force profile would be different from that of the fully developed Poiseuille flow and there may not be an equilibrium position corresponding to the Segre–Silberberg annulus.

Inertial migration of neutrally buoyant spheres in a pressure-driven flow through square channels

2014 ◽  
Vol 749 ◽  
pp. 320-330 ◽  
Author(s):  
Kazuma Miura ◽  
Tomoaki Itano ◽  
Masako Sugihara-Seki
Keyword(s):  
Cross Sections ◽  
Side Wall ◽  
Reynolds Numbers ◽  
Spherical Particles ◽  
Lateral Migration ◽  
Inertial Migration ◽  
Square Channel ◽  
Circular Pipes ◽  
Pressure Driven Flow ◽  
Neutrally Buoyant

AbstractThe inertial migration of neutrally buoyant spherical particles in square channel flows was investigated experimentally in the range of Reynolds numbers ($\mathit{Re}$) from 100 to 1200. The observation of particle positions at several cross-sections downstream from the channel entrance revealed unique patterns of particle distribution which reflects the presence of eight equilibrium positions in the cross-section, located at the centres of the channel faces and at the corners, except for low $\mathit{Re}$. At $\mathit{Re}$ smaller than approximately 250, equilibrium positions at the corners are absent. The corner equilibrium positions were found to arise initially in the band formed along the channel face, followed by a progressive shift almost parallel to the side wall up to the diagonal line with increasing $\mathit{Re}$. Further increase in $\mathit{Re}$ moves the corner equilibrium positions slightly toward the channel corner, whereas the equilibrium positions at the channel face centres are shifted toward the channel centre. As the observation sites become downstream, the particles were found to be more focused near the equilibrium positions keeping their positions almost unchanged. These lateral migration behaviours and focusing properties of particles in square channels are different to that observed in microchannels at lower $\mathit{Re}$ and to what would be expected from extrapolating from the results for circular pipes at comparable $\mathit{Re}$.

Lateral Migration of Neutrally-Buoyant Particles in a Square Microchannel at Low Reynolds Numbers

2009 ◽  
Author(s):  
Byung Rae Cho ◽  
Young Won Kim ◽  
Jung Yul Yoo
Keyword(s):  
Reynolds Numbers ◽  
Spherical Particles ◽  
Channel Cross Section ◽  
Microfluidic Channels ◽  
Lateral Migration ◽  
Low Reynolds Numbers ◽  
Low Reynolds ◽  
Square Microchannel ◽  
External Forces ◽  
Neutrally Buoyant

Lateral migration of particles has drawn a lot of attention in suspension community for the last 50 years. Since there is no need for extra external forces, lateral migration of particles plays an important role in constructing microfluidic devices in diverse engineering applications. In this paper, an experimental study on lateral migration of neutrally-buoyant spherical particles transported through a square microchannel is carried out using a fluorescent microscope at low Reynolds numbers. Fluorescent microspheres with diameters of d = 6 μm, 10 μm, and 16 μm are adopted as the test particles, which yield channel-to-particle size ratios of 13.3, 8 and 5, respectively. Spatial distributions of the particles in dilute suspension are visualized at different Reynolds numbers. It is shown that particles are uniformly distributed over the channel cross-section at relatively low Reynolds numbers. As the Reynolds number increases, however, particles migrate inward from the wall and away from the central axis of the channel, so that consequently they accumulate at an equilibrium position, exhibiting the so-called “tubular pinch effect”, first observed by Segre´ and Silberberg as early as in 1962. Experimental results obtained in this work offer design rules for microfluidic channels that play important roles of particle separation or particle focusing.

Inertial migration of a spherical particle in laminar square channel flows from low to high Reynolds numbers

2015 ◽  
Vol 779 ◽  
pp. 776-793 ◽  
Author(s):  
Naoto Nakagawa ◽  
Takuya Yabu ◽  
Ryoko Otomo ◽  
Atsushi Kase ◽  
Masato Makino ◽  
...  
Keyword(s):  
Spherical Particle ◽  
Cross Section ◽  
Channel Wall ◽  
Heteroclinic Orbit ◽  
Reynolds Numbers ◽  
Channel Cross Section ◽  
Lateral Migration ◽  
Inertial Migration ◽  
Lateral Forces ◽  
The Cross

The lateral migration properties of a rigid spherical particle suspended in a pressure-driven flow through channels with square cross-sections were investigated numerically, in the range of Reynolds numbers ($Re$) from 20 to 1000. The flow field around the particle was computed by the immersed boundary method to calculate the lateral forces exerted on the particle and its trajectories, starting from various initial positions. The numerical simulation showed that eight equilibrium positions of the particle are present at the centres of the channel faces and near the corners of the channel cross-section. The equilibrium positions at the centres of the channel faces are always stable, whereas the equilibrium positions at the corners are unstable until $Re$ exceeds a certain critical value, $Re_{c}$. At $Re\approx Re_{c}$, additional equilibrium positions appear on a heteroclinic orbit that joins the channel face and corner equilibrium positions, and the lateral forces along the heteroclinic orbit are very small. As $Re$ increases, the channel face equilibrium positions are shifted towards the channel wall at first, and then shifted away from the channel wall. The channel corner equilibrium positions exhibit a monotonic shift towards the channel corner with increasing $Re$. Migration behaviours of the particle in the cross-section are also predicted for various values of $Re$. These numerical results account for the experimental observations of particle distributions in the cross-section of micro and millimetre scale channels, including the characteristic alignment and focusing of the particles, the absence of the corner equilibrium positions at low $Re$ and the progressive shift of the equilibrium positions with $Re$.

Nonlinear mechanics of fluidization of beds of spherical particles

1987 ◽  
Vol 177 ◽  
pp. 467-483 ◽  
Author(s):  
A. F. Fortes ◽  
D. D. Joseph ◽  
T. S. Lundgren
Keyword(s):  
Cross Section ◽  
Rectangular Cross Section ◽  
Two Dimensions ◽  
The Other ◽  
Three Dimensions ◽  
Spherical Particles ◽  
Inertial Effects ◽  
Nonlinear Mechanics ◽  
Clear Water ◽  
Cooperative Motion

Experiments on fluidization with water of spherical particles falling against gravity in columns of rectangular cross-section are described. All of them are dominated by inertial effects associated with wakes. Two local mechanisms are involved: drafting and kissing and tumbling into stable cross-stream arrays. Drafting, kissing and tumbling are rearrangement mechanisms in which one sphere is captured in the wake of the other. The kissing spheres are aligned with the stream. The streamwise alignment is massively unstable and the kissing spheres tumble into more stable cross-stream pairs of doublets which can aggregate into larger relatively stable horizontal arrays. Cross-stream arrays in beds of spheres constrained to move in two dimensions are remarkable. These arrays may even coalesce into aggregations of close-packed spheres separated by regions of clear water. A somewhat weaker form of cooperative motion of cross-stream arrays of rising spheres is found in beds of square cross-section where the spheres may move freely in three dimensions. Horizontal arrays rise where drafting spheres fall because of greater drag. Aggregation of spheres seems to be associated with relatively stable cooperative motions of horizontal arrays of spheres rising in their own wakes.

Inertial migration of rigid spheres in two-dimensional unidirectional flows

1974 ◽  
Vol 65 (2) ◽  
pp. 365-400 ◽  
Author(s):  
B. P. Ho ◽  
L. G. Leal
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Poiseuille Flow ◽  
Initial Position ◽  
Rigid Sphere ◽  
Simple Shear Flow ◽  
Two Dimensional ◽  
Lateral Migration ◽  
Rigid Spheres ◽  
Inertial Migration

The familiar Segré-Silberberg effect of inertia-induced lateral migration of a neutrally buoyant rigid sphere in a Newtonian fluid is studied theoretically for simple shear flow and for two-dimensional Poiseuille flow. It is shown that the spheres reach a stable lateral equilibrium position independent of the initial position of release. For simple shear flow, this position is midway between the walls, whereas for Poiseuille flow, it is 0·6 of the channel half-width from the centre-line. Particle trajectories are calculated in both cases and compared with available experimental data. Implications for the measurement of the rheological properties of a dilute suspension of spheres are discussed.

Suspensions with a tunable effective viscosity: a numerical study

2012 ◽  
Vol 693 ◽  
pp. 345-366 ◽  
Author(s):  
L. Jibuti ◽  
S. Rafaï ◽  
P. Peyla
Keyword(s):  
Effective Viscosity ◽  
Volume Fraction ◽  
Numerical Study ◽  
Spherical Particles ◽  
Dimensionless Number ◽  
Particle Rotation ◽  
Concentrated Suspensions ◽  
Sheared Suspensions ◽  
Neutrally Buoyant ◽  
Universal Behaviour

AbstractIn this paper, we conduct a numerical investigation of sheared suspensions of non-colloidal spherical particles on which a torque is applied. Particles are mono-dispersed and neutrally buoyant. Since the torque modifies particle rotation, we show that it can indeed strongly change the effective viscosity of semi-dilute or even more concentrated suspensions. We perform our calculations up to a volume fraction of 28 %. And we compare our results to data obtained at 40 % by Yeo and Maxey (Phys. Rev. E, vol. 81, 2010, p. 62501) with a totally different numerical method. Depending on the torque orientation, one can increase (decrease) the rotation of the particles. This results in a strong enhancement (reduction) of the effective shear viscosity of the suspension. We construct a dimensionless number $\Theta $ which represents the average relative angular velocity of the particles divided by the vorticity of the fluid generated by the shear flow. We show that the contribution of the particles to the effective viscosity can be suppressed for a given and unique value of $\Theta $ independently of the volume fraction. In addition, we obtain a universal behaviour (i.e. independent of the volume fraction) when we plot the relative effective viscosity divided by the relative effective viscosity without torque as a function of $\Theta $. Finally, we show that a modified Faxén law can be equivalently established for large concentrations.

scholarly journals Derivation of Equations for a Size Distribution of Spherical Particles in Non-Transparent Materials

2021 ◽  
Vol 5 (4) ◽  
pp. 53-60
Author(s):  
Daniel Gurgul ◽  
Andriy Burbelko ◽  
Tomasz Wiktor
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Size Distribution ◽  
Density Function ◽  
Cross Section ◽  
Three Dimensional ◽  
Spherical Particles ◽  
Two Dimensional ◽  
Mathematical Formulas ◽  
Transparent Materials

This paper presents a new proposition on how to derive mathematical formulas that describe an unknown Probability Density Function (PDF3) of the spherical radii (r3) of particles randomly placed in non-transparent materials. We have presented two attempts here, both of which are based on data collected from a random planar cross-section passed through space containing three-dimensional nodules. The first attempt uses a Probability Density Function (PDF2) the form of which is experimentally obtained on the basis of a set containing two-dimensional radii (r2). These radii are produced by an intersection of the space by a random plane. In turn, the second solution also uses an experimentally obtained Probability Density Function (PDF1). But the form of PDF1 has been created on the basis of a set containing chord lengths collected from a cross-section.The most important finding presented in this paper is the conclusion that if the PDF1 has proportional scopes, the PDF3 must have a constant value in these scopes. This fact allows stating that there are no nodules in the sample space that have particular radii belonging to the proportional ranges the PDF1.

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