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 $Re$.

Long waves in a straight channel with non-uniform cross-section

2015 ◽  
Vol 770 ◽  
pp. 156-188 ◽  
Author(s):  
Patricio Winckler ◽  
Philip L.-F. Liu
Keyword(s):  
Boundary Layer ◽  
Wave Propagation ◽  
Cross Section ◽  
Three Dimensional ◽  
Channel Cross Section ◽  
Cross Sectional ◽  
New Model ◽  
One Dimensional ◽  
Uniform Channel ◽  
The Cross

A cross-sectionally averaged one-dimensional long-wave model is developed. Three-dimensional equations of motion for inviscid and incompressible fluid are first integrated over a channel cross-section. To express the resulting one-dimensional equations in terms of the cross-sectional-averaged longitudinal velocity and spanwise-averaged free-surface elevation, the characteristic depth and width of the channel cross-section are assumed to be smaller than the typical wavelength, resulting in Boussinesq-type equations. Viscous effects are also considered. The new model is, therefore, adequate for describing weakly nonlinear and weakly dispersive wave propagation along a non-uniform channel with arbitrary cross-section. More specifically, the new model has the following new properties: (i) the arbitrary channel cross-section can be asymmetric with respect to the direction of wave propagation, (ii) the channel cross-section can change appreciably within a wavelength, (iii) the effects of viscosity inside the bottom boundary layer can be considered, and (iv) the three-dimensional flow features can be recovered from the perturbation solutions. Analytical and numerical examples for uniform channels, channels where the cross-sectional geometry changes slowly and channels where the depth and width variation is appreciable within the wavelength scale are discussed to illustrate the validity and capability of the present model. With the consideration of viscous boundary layer effects, the present theory agrees reasonably well with experimental results presented by Chang et al. (J. Fluid Mech., vol. 95, 1979, pp. 401–414) for converging/diverging channels and those of Liu et al. (Coast. Engng, vol. 53, 2006, pp. 181–190) for a uniform channel with a sloping beach. The numerical results for a solitary wave propagating in a channel where the width variation is appreciable within a wavelength are discussed.

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 $\mathit{Re}$.

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.

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.

scholarly journals Effect of inertial lift on a spherical particle suspended in flow through a curved duct

2019 ◽  
Vol 875 ◽  
pp. 1-43 ◽  
Author(s):  
Brendan Harding ◽  
Yvonne M. Stokes ◽  
Andrea L. Bertozzi
Keyword(s):  
Reynolds Number ◽  
Spherical Particle ◽  
Cross Section ◽  
Bend Radius ◽  
Cross Sectional ◽  
Particle Reynolds Number ◽  
Curved Duct ◽  
Sectional Plane ◽  
Flow Through ◽  
The Cross

We develop a model of the forces on a spherical particle suspended in flow through a curved duct under the assumption that the particle Reynolds number is small. This extends an asymptotic model of inertial lift force previously developed to study inertial migration in straight ducts. Of particular interest is the existence and location of stable equilibria within the cross-sectional plane towards which particles migrate. The Navier–Stokes equations determine the hydrodynamic forces acting on a particle. A leading-order model of the forces within the cross-sectional plane is obtained through the use of a rotating coordinate system and a perturbation expansion in the particle Reynolds number of the disturbance flow. We predict the behaviour of neutrally buoyant particles at low flow rates and examine the variation in focusing position with respect to particle size and bend radius, independent of the flow rate. In this regime, the lateral focusing position of particles approximately collapses with respect to a dimensionless parameter dependent on three length scales: specifically, the particle radius, duct height and duct bend radius. Additionally, a trapezoidal-shaped cross-section is considered in order to demonstrate how changes in the cross-section design influence the dynamics of particles.

Three-dimensional features in low-Reynolds-number confined corner flows

2010 ◽  
Vol 668 ◽  
pp. 33-57 ◽  
Author(s):  
LAURA GUGLIELMINI ◽  
R. RUSCONI ◽  
S. LECUYER ◽  
H. A. STONE
Keyword(s):  
Reynolds Number ◽  
Secondary Flow ◽  
Cross Section ◽  
Low Reynolds Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Channel Cross Section ◽  
Radius Of Curvature ◽  
Matched Asymptotic Expansion ◽  
Low Reynolds

In recent microfluidic experiments with solutions of bacteria we observed the formation of biofilms in the form of thread-like structures, called ‘streamers’, which float in the middle plane of the channel and are connected to the side walls at the inner corners. Motivated by this observation, we discuss here the pressure-driven low-Reynolds-number flow around a corner bounded by the walls of a channel with rectangular cross-section. We numerically solve the flow field in a channel of constant cross-section, which exhibits 90° sharp corners, or turns with constant curvature, or portions with slowly changing curvature along the flow direction, for finite, but small, values of the Reynolds numbers and including the limit of vanishingly small Reynolds numbers. In addition, we develop a matched asymptotic expansion solution for the flow around two boundaries intersecting at an angle α and spanning the small gap h between two horizontal plates. We illustrate the basic features of the flow in these channel geometries by describing the three-dimensional velocity field and the distribution of streamwise vorticity and helicity, and comparing the numerical solutions with predictions based on the asymptotic approach. We demonstrate that near a corner or a change in the curvature of the side wall the flow is three-dimensional and pairs of counter-rotating vortical structures are present, as identified by Balsa (J. Fluid Mech., vol. 372, 1998, p. 25). Finally, we discuss how this secondary flow depends on the significant geometric parameters, the aspect ratio of the channel cross-section, the radius of curvature of the turn and, more generally, the variation of the curvature of the channel side boundary. We believe that these three-dimensional secondary flow structures are relevant to transport problems where accumulation of material at the boundary is possible.

scholarly journals The influence of secondary flow in a two-phase gas-solid system in straight channels with a non-circular cross-section

2016 ◽  
Vol 20 (suppl. 5) ◽  
pp. 1419-1434
Author(s):  
Sasa Milanovic ◽  
Milos Jovanovic ◽  
Boban Nikolic ◽  
Vladislav Blagojevic
Keyword(s):  
Turbulent Flow ◽  
Secondary Flow ◽  
Cross Section ◽  
Circular Cross Section ◽  
Channel Cross Section ◽  
Two Phase ◽  
Cross Sectional ◽  
Specific Flow ◽  
Sectional Plane ◽  
The Cross

The paper considers two-phase gas-solid turbulent flow of pneumatic transport in straight horizontal channels with a non-circular cross-section. During turbulent flow, a specific flow phenomenon, known as secondary flow, occurs in these channels in the cross-sectional plane. The existence of strong temperature gradients in the cross-sectional plane of the channel or the cases of curved channels result in the appearance of the secondary flow of the first kind. However, in straight channels with a non-circular cross-section, in the developed turbulent flow mode, a secondary flow, known as Prandtl?s secondary flow of the second kind, is induced. The paper presents a numerical simulation of a developed two-phase turbulent flow by using the PHOENICS 3.3.1 software package. Reynolds stress model was used to model the turbulence. The paper provides the data on the changes in turbulent stresses in the channel cross-section as well as the velocities of solid particles transported along the channel.

scholarly journals A Dark Matter WIMP That Can Be Detected and Definitively Identified with Currently Planned Experiments

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 270
Author(s):  
Caden LaFontaine ◽  
Bailey Tallman ◽  
Spencer Ellis ◽  
Trevor Croteau ◽  
Brandon Torres ◽  
...  
Keyword(s):  
Dark Matter ◽  
Cross Section ◽  
Cross Sections ◽  
Direct Detection ◽  
Vector Boson ◽  
Massive Particle ◽  
Current Evidence ◽  
Channel Cross Section ◽  
Dark Matter Annihilation ◽  
The Cross

A recently proposed dark matter WIMP (weakly interacting massive particle) has only second-order couplings to gauge bosons and itself. As a result, it has small annihilation, scattering, and creation cross-sections, and is consequently consistent with all current experiments and the observed abundance of dark matter. These cross-sections are, however, still sufficiently large to enable detection in experiments that are planned for the near future, and definitive identification in experiments proposed on a longer time scale. The (multi-channel) cross-section for annihilation is consistent with thermal production and freeze-out in the early universe, and with current evidence for dark matter annihilation in analyses of the observations of gamma rays by Fermi-LAT and antiprotons by AMS-02, as well as the constraints from Planck and Fermi-LAT. The cross-section for direct detection via collision with xenon nuclei is estimated to be slightly below 10−47 cm2, which should be attainable by LZ and Xenon nT and well within the reach of Darwin. The cross-section for collider detection via vector boson fusion is estimated to be ∼1 fb, and may be ultimately attainable by the high-luminosity LHC; definitive collider identification will probably require the more powerful facilities now being proposed.

scholarly journals Mapping inertial migration in the cross section of a microfluidic channel with high-speed imaging

2020 ◽  
Vol 6 (1) ◽  
Author(s):  
Jian Zhou ◽  
Zhangli Peng ◽  
Ian Papautsky
Keyword(s):  
Cross Section ◽  
High Speed ◽  
Microfluidic Channel ◽  
Channel Cross Section ◽  
High Speed Imaging ◽  
Cross Sectional ◽  
Inertial Migration ◽  
Imaging Results ◽  
New Findings ◽  
Migration Pathways

AbstractThe wide adoption of inertial microfluidics in biomedical research and clinical settings, such as rare cell isolation, has prompted the inquiry of its underlying mechanism. Although tremendous improvement has been made, the mechanism of inertial migration remains to be further elucidated. Contradicting observations are not fully reconciled by the existing theory, and details of the inertial migration within channel cross sections are missing in the literature. In this work, for the first time, we mapped the inertial migration pathways within channel cross section using high-speed imaging at the single-particle level. This is in contrast to the conventional method of particle streak velocimetry (PSV), which provides collective information. We also applied smoothed particle hydrodynamics (SPH) to simulate the transient motion of particles in 3D and obtained cross-sectional migration trajectories that are in agreement with the high-speed imaging results. We found two opposing pathways that explain the contradicting observations in rectangular microchannels, and the force analysis of these pathways revealed two metastable positions near the short walls that can transition into stable positions depending on the flow condition and particle size. These new findings significantly improve our understanding of the inertial migration physics, and enhance our ability to precisely control particle and cell behaviors within microchannels for a broad range of applications.

A New Approach to the Demonstration of Oxidase-Localization Using Tannic Acid Or Catechin

1973 ◽  
Vol 31 ◽  
pp. 698-699
Author(s):  
V. Mizuhira ◽  
Y. Futaesaku
Keyword(s):  
Cross Section ◽  
Tannic Acid ◽  
Elastic Fiber ◽  
The Other ◽  
New Approach ◽  
Tissue Block ◽  
Active Reaction ◽  
The Cross

Previously we reported that tannic acid is a very effective fixative for proteins including polypeptides. Especially, in the cross section of microtubules, thirteen submits in A-tubule and eleven in B-tubule could be observed very clearly. An elastic fiber could be demonstrated very clearly, as an electron opaque, homogeneous fiber. However, tannic acid did not penetrate into the deep portion of the tissue-block. So we tried Catechin. This shows almost the same chemical natures as that of proteins, as tannic acid. Moreover, we thought that catechin should have two active-reaction sites, one is phenol,and the other is catechole. Catechole site should react with osmium, to make Os- black. Phenol-site should react with peroxidase existing perhydroxide.

Sign in / Sign up

Export Citation Format

Share Document