Inertial migration of a neutrally buoyant circular particle in a planar Poiseuille flow with thermal fluids

2021 ◽  
Vol 33 (6) ◽  
pp. 063315
Author(s):  
Wenwei Liu ◽  
Chuan-Yu Wu
Keyword(s):  
Poiseuille Flow ◽  
Inertial Migration ◽  
Thermal Fluids ◽  
Circular Particle ◽  
Neutrally Buoyant

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.

Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 2. Couette and Poiseuille flows

1994 ◽  
Vol 277 ◽  
pp. 271-301 ◽  
Author(s):  
J. Feng ◽  
H. H. Hu ◽  
D. D. Joseph
Keyword(s):  
Poiseuille Flow ◽  
Driving Forces ◽  
Particle Surface ◽  
Particle Rotation ◽  
Element Simulation ◽  
Circular Particle ◽  
Dimensional Finite Element ◽  
Shear Slip ◽  
Neutrally Buoyant ◽  
Solid Bodies

This paper reports the results of a two-dimensional finite element simulation of the motion of a circular particle in a Couette and a Poiseuille flow. The size of the particle and the Reynolds number are large enough to include fully nonlinear inertial effects and wall effects. Both neutrally buoyant and non-neutrally buoyant particles are studied, and the results are compared with pertinent experimental data and perturbation theories. A neutrally buoyant particle is shown to migrate to the centreline in a Couette flow, and exhibits the Segré-Silberberg effect in a Poiseuille flow. Non-neutrally buoyant particles have more complicated patterns of migration, depending upon the density difference between the fluid and the particle. The driving forces of the migration have been identified as a wall repulsion due to lubrication, an inertial lift related to shear slip, a lift due to particle rotation and, in the case of Poiseuille flow, a lift caused by the velocity profile curvature. These forces are analysed by examining the distributions of pressure and shear stress on the particle. The stagnation pressure on the particle surface are particularly important in determining the direction of migration.

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.

Direct Simulation of the Motion of Neutrally Buoyant Circular Cylinders in Plane Poiseuille Flow

2002 ◽  
Vol 181 (1) ◽  
pp. 260-279 ◽  
Author(s):  
Tsorng-Whay Pan ◽  
Roland Glowinski
Keyword(s):  
Poiseuille Flow ◽  
Circular Cylinders ◽  
Direct Simulation ◽  
Plane Poiseuille Flow ◽  
Neutrally Buoyant

Inertial migration of a 3D elastic capsule in a plane Poiseuille flow

2015 ◽  
Vol 54 ◽  
pp. 87-96 ◽  
Author(s):  
Boyoung Kim ◽  
Cheong Bong Chang ◽  
Sung Goon Park ◽  
Hyung Jin Sung
Keyword(s):  
Poiseuille Flow ◽  
Plane Poiseuille Flow ◽  
Inertial Migration

The motion of a single and multiple neutrally buoyant elliptical cylinders in plane Poiseuille flow

2012 ◽  
Vol 24 (10) ◽  
pp. 103302 ◽  
Author(s):  
Shih-Di Chen ◽  
Tsorng-Whay Pan ◽  
Chien-Cheng Chang
Keyword(s):  
Poiseuille Flow ◽  
Plane Poiseuille Flow ◽  
Neutrally Buoyant ◽  
Elliptical Cylinders

Pressure drop due to the motion of a sphere near the wall bounding a Poiseuille flow

1973 ◽  
Vol 60 (1) ◽  
pp. 81-96 ◽  
Author(s):  
Peter M. Bungay ◽  
Howard Brenner
Keyword(s):  
Pressure Drop ◽  
Poiseuille Flow ◽  
Circular Tube ◽  
Tube Wall ◽  
Previous Method ◽  
Pronounced Increase ◽  
Additional Pressure ◽  
Sphere Radius ◽  
Neutrally Buoyant ◽  
Quiescent Fluid

An expression is derived for the (low Reynolds number) additional pressure drop created by a relatively small sphere moving near the wall of a circular tube through which there is a Poiseuille flow. Two specific applications are examined: (i) the sedimentation of a homogeneous non-neutrally buoyant sphere in a quiescent fluid; and (ii) the motion of a neutrally buoyant sphere. In the latter case a pronounced increase in the additional pressure drop is predicted when the separation between the sphere and the tube wall is reduced to zero.This analysis, which includes the behaviour for a sphere in contact with the tube wall, supplements previous ‘method of reflexions’ treatments valid only when the distance from the sphere centre to the wall is large compared with the sphere radius.

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