Scaling laws for segregation forces in dense sheared granular flows

In order to better understand the mechanism governing segregation in dense granular flows, the force experienced by a large particle embedded in a granular flow made of small particles is studied using discrete numerical simulations. Accurate force measurements have been obtained in a large range of flow parameters by trapping the large particle in a harmonic potential well to mimic an optical tweezer. Results show that positive or negative segregation lift forces (perpendicular to the shear) exist depending on the stress inhomogeneity. An empirical expression of the segregation force is proposed as a sum of a term proportional to the gradient of pressure and a term proportional to the gradient of shear stress, which both depend on the local friction and particle size ratio.

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Two-Aperture Microfluidic Probes as Flow Dipoles: Theory and Applications

Scientific Reports ◽

10.1038/srep11943 ◽

2015 ◽

Vol 5 (1) ◽

Cited By ~ 19

Author(s):

Mohammadali Safavieh ◽

Mohammad A. Qasaimeh ◽

Ali Vakil ◽

David Juncker ◽

Thomas Gervais

Keyword(s):

Open Space ◽

Scaling Laws ◽

Microfluidic System ◽

Flow Rate Ratio ◽

Published Data ◽

Tissue Slices ◽

Flow Parameters ◽

Mobile Channel ◽

Injection Flow ◽

Organotypic Tissue

Abstract A microfluidic probe (MFP) is a mobile channel-less microfluidic system under which a fluid is injected from an aperture into an open space, hydrodynamically confined by a surrounding fluid and entirely re-aspirated into a second aperture. Various MFPs have been developed and have been used for applications ranging from surface patterning of photoresists to local perfusion of organotypic tissue slices. However, the hydrodynamic and mass transfer properties of the flow under the MFP have not been analyzed and the flow parameters are adjusted empirically. Here, we present an analytical model describing the key transport properties in MFP operation, including the dimensions of the hydrodynamic flow confinement (HFC) area, diffusion broadening and shear stress as a function of: (i) probe geometry (ii) aspiration-to-injection flow rate ratio (iii) gap between MFP and substrate and (iv) reagent diffusivity. Analytical results and scaling laws were validated against numerical simulations and experimental results from published data. These results will be useful to guide future MFP design and operation, notably to control the MFP “brush stroke” while preserving shear-sensitive cells and tissues.

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Scaling laws for migrating cloud of low-Reynolds-number particles with Coulomb repulsion

Journal of Fluid Mechanics ◽

10.1017/jfm.2017.772 ◽

2017 ◽

Vol 835 ◽

pp. 880-897 ◽

Cited By ~ 2

Author(s):

Sheng Chen ◽

Wenwei Liu ◽

Shuiqing Li

Keyword(s):

Reynolds Number ◽

Scaling Laws ◽

Particle Number ◽

Coulomb Repulsion ◽

Particle Number Density ◽

Particle Size Ratio ◽

Wide Range ◽

Self Similar ◽

Charge Parameter ◽

Strong Repulsion

We investigate the evolution of spherical clouds of charged particles that migrate under the action of a uniform external electrostatic field. Hydrodynamic interactions are modelled by Oseen equations and the Coulomb repulsion is calculated through pairwise summation. It is shown that strong long-range Coulomb repulsion can prevent the breakup of the clouds covering a wide range of particle Reynolds number $Re_{p}$ and cloud-to-particle size ratio $R_{0}/r_{p}$. A dimensionless charge parameter $\unicode[STIX]{x1D705}_{q}$ is constructed to quantify the effect of the repulsion, and a critical value $\unicode[STIX]{x1D705}_{q,t}$ is deduced, which successfully captures the transition of a cloud from hydrodynamically controlled regime to repulsion-controlled regime. Our results also reveal that, with sufficiently strong repulsion, the cloud undergoes a universal self-similar expansion. Scaling laws of cloud radius $R_{cl}$ and particle number density $n$ are obtained by solving a continuum convection equation.

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Scaling Laws for the Slip Velocity in Dense Granular Flows

Physical Review Letters ◽

10.1103/physrevlett.108.238002 ◽

2012 ◽

Vol 108 (23) ◽

Cited By ~ 21

Author(s):

Riccardo Artoni ◽

Andrea C. Santomaso ◽

Massimiliano Go’ ◽

Paolo Canu

Keyword(s):

Slip Velocity ◽

Scaling Laws ◽

Granular Flows ◽

Dense Granular Flows

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Scaling of myocardial mass to flow and morphometry of coronary arteries

Journal of Applied Physiology ◽

10.1152/japplphysiol.01261.2007 ◽

2008 ◽

Vol 104 (5) ◽

pp. 1281-1286 ◽

Cited By ~ 90

Author(s):

Jenny Susana Choy ◽

Ghassan S. Kassab

Keyword(s):

Coronary Arteries ◽

Scaling Laws ◽

Myocardial Mass ◽

Arterial Tree ◽

Flow Parameters ◽

Diffuse Coronary Artery Disease ◽

Cumulative Length ◽

Artery Disease ◽

Function Relationship ◽

Relationship Of

There is no doubt that scaling relations exist between myocardial mass and morphometry of coronary vasculature. The purpose of this study is to quantify several morphological (diameter, length, and volume) and functional (flow) parameters of the coronary arterial tree in relation to myocardial mass. Eight normal porcine hearts of 117–244 g (mean of 177.5 ± 32.7) were used in this study. Various coronary subtrees of the left anterior descending, right coronary, and left circumflex arteries were perfused at pressure of 100 mmHg with different colors of a polymer (Microfil) to obtain rubber casts of arterial trees corresponding to different regions of myocardial mass. Volume, diameter, and cumulative length of coronary arteries were reconstructed from casts to analyze their relationship to the perfused myocardial mass. Volumetric flow was measured in relationship with perfused myocardial mass. Our results show that arterial volume is linearly related to regional myocardial mass, whereas the sum of coronary arterial branch lengths, vessel diameters, and volumetric flow show an ∼3/4, 3/8, and 3/4 power-law relationship, respectively, in relation to myocardial mass. These scaling laws suggest fundamental design principles underlying the structure-function relationship of the coronary arterial tree that may facilitate diagnosis and management of diffuse coronary artery disease.

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A modified calculation of particle buoyant forces in vibro-fluidized beds

EPJ Web of Conferences ◽

10.1051/epjconf/202124903047 ◽

2021 ◽

Vol 249 ◽

pp. 03047

Author(s):

Zhixiong Zhang ◽

Xihua Chu ◽

Yanran Wang

Keyword(s):

Large Particle ◽

Brazil Nut ◽

Flow Conditions ◽

Buoyant Force ◽

Segregation Behavior ◽

Particle Size Ratio ◽

Segregation Process ◽

Brazil Nut Effect ◽

Effect Of Particle Size ◽

The Difference

Segregation of granular materials under vibration or flow conditions such as the Brazil nut effect has been well known, however, there is yet no consensus mechanisms to explain this phenomenon. This study attempts to investigate particle buoyant forces in the segregation process. To explain the difference of the segregation behavior for the large particle with different size, a modified calculation method of particle buoyant force is suggested for considering the effect of particle size ratio. A simple verification illustrates its validity.

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Core mechanisms of drag enhancement on bodies settling in a stratified fluid

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.524 ◽

2019 ◽

Vol 875 ◽

pp. 622-656 ◽

Cited By ~ 9

Author(s):

Jie Zhang ◽

Matthieu J. Mercier ◽

Jacques Magnaudet

Keyword(s):

Scaling Laws ◽

Relative Magnitude ◽

Stratified Fluid ◽

The Body ◽

Lower Atmosphere ◽

Governing Equations ◽

Flow Parameters ◽

Induced Drag ◽

Widespread Belief ◽

Living Organisms

Stratification due to salt or heat gradients greatly affects the distribution of inert particles and living organisms in the ocean and the lower atmosphere. Laboratory studies considering the settling of a sphere in a linearly stratified fluid confirmed that stratification may dramatically enhance the drag on the body, but failed to identify the generic physical mechanism responsible for this increase. We present a rigorous splitting scheme of the various contributions to the drag on a settling body, which allows them to be properly disentangled whatever the relative magnitude of inertial, viscous, diffusive and buoyancy effects. We apply this splitting procedure to data obtained via direct numerical simulation of the flow past a settling sphere over a range of parameters covering a variety of situations of laboratory and geophysical interest. Contrary to widespread belief, we show that, in the parameter range covered by the simulations, the drag enhancement is generally not primarily due to the extra buoyancy force resulting from the dragging of light fluid by the body, but rather to the specific structure of the vorticity field set in by buoyancy effects. Simulations also reveal how the different buoyancy-induced contributions to the drag vary with the flow parameters. To unravel the origin of these variations, we analyse the different possible leading-order balances in the governing equations. Thanks to this procedure, we identify several distinct regimes which differ by the relative magnitude of length scales associated with stratification, viscosity and diffusivity. We derive the scaling laws of the buoyancy-induced drag contributions in each of these regimes. Considering tangible examples, we show how these scaling laws combined with numerical results may be used to obtain reliable predictions beyond the range of parameters covered by the simulations.

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