Kinematics of a Free Particle Moving Between Two Parallel Walls

2010 ◽  
Author(s):  
Ste´phane Champmartin ◽  
Abdlehak Ambari ◽  
Abderrahim Ben Richou
Keyword(s):  
Poiseuille Flow ◽  
Settling Velocity ◽  
Free Particle ◽  
Symmetry Plane ◽  
Angular Velocities ◽  
Resistance Matrix ◽  
Neutrally Buoyant ◽  
Physical Phenomena ◽  
Adjacent Wall ◽  
Very High

The understanding of some physical phenomena involved in the transport of free particles such as fibers during injection processes is an important issue. To answer some of the questions arising in such problems, we study here numerically the quasi-steady kinematics of a free cylindrical solid particle moving in a Newtonian fluid confined between two parallel plane walls taking the hydrodynamic interactions into account. This is achieved by the use of the resistance matrix technique relating the kinematics of the particle to the forces and the torques exerted on the particle and to the dissipation induced by the motion of this particle. Our approach is confirmed by asymptotical developments and by a comparison with other authors in some cases. The solutions of three practical problems are given. In the first one, the sedimentation of the particle is studied. It is found that the maximum settling velocity of the free particle is obtained at a position off the symmetry plane. The cylinder is observed to rotate counter intuitively against the direction of rolling along the adjacent wall. Moreover the angular velocity has an influence on the settling velocity when the concentration is very high. The second problem concerns the transport of a neutrally buoyant cylindrical particle in a Poiseuille flow. This study reveals that there are relative translational and angular velocities between the free particle and the undisturbed fluid particle contrary to the commonly admitted hypothesis used in several models and numerical codes. Finally the third problem is a combination of the two previous situations: the transport of a non-neutrally buoyant particle in a Poiseuille flow. Depending on the ratio of the buoyancy forces to the viscous ones, different solutions are possible and exposed. Other problems can also be solved with this approach which is less time-consuming than complex methods such as DNS.

Feedback control to delay or advance linear loss of stability in planar Poiseuille flow

1994 ◽  
Vol 447 (1930) ◽  
pp. 299-312 ◽  
Keyword(s):  
Feedback Control ◽  
Poiseuille Flow ◽  
Control Strategies ◽  
Linear Stability Theory ◽  
Flow Instabilities ◽  
Loss Of Stability ◽  
Stress Sensors ◽  
Shear Stress Sensors ◽  
Linear Loss ◽  
Adjacent Wall

By using linear stability theory, we demonstrate theoretically that the critical Reynolds number for the loss of stability of planar Poiseuille flow can be significantly increased or decreased through the use of feedback control strategies which enhance or suppress disturbance dissipating mechanisms in the flow. The controller studied here consists of closely packed, wall mounted, shear stress sensors and thermoelectric actuators. The sensors detect flow instabilities and direct the actuators to alter the fluid’s viscosity by modulating the adjacent wall temperature in such a way as to suppress or enhance flow instabilities. Results are presented for water and air flows.

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

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.

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.

A buoyancy mechanism found in cranchid squid

1969 ◽  
Vol 174 (1036) ◽  
pp. 271-279 ◽  
Keyword(s):  
Ammonium Chloride ◽  
Sea Water ◽  
Coelomic Fluid ◽  
Low Density ◽  
Additional Species ◽  
High Concentrations ◽  
Neutrally Buoyant ◽  
Very High

Three species of cranchid squid have been studied at sea and found to be nearly neutrally buoyant in sea water. They each possess a very large coelom filled with a fluid whose density is low in comparison with sea water and this gives a lift sufficient to balance the denser tissues of the animal. This coelomic fluid is nearly iso-osmotic with sea water and its relatively low density arises because it is principally a solution of ammonium chloride in water. The fluid is acid and the significance of this is discussed. Two additional species of cranchid squid whose buoyancies were not measured were also shown to have very high concentrations of ammonium chloride in their coeloms and it seems likely that this buoyancy mechanism is used by all the Cranchidae.

Dispersion of a ball settling through a quiescent neutrally buoyant suspension

1998 ◽  
Vol 361 ◽  
pp. 309-331 ◽  
Author(s):  
JAMES R. ABBOTT ◽  
ALAN L. GRAHAM ◽  
LISA A. MONDY ◽  
HOWARD BRENNER
Keyword(s):  
Settling Velocity ◽  
Volume Fraction ◽  
Functional Dependence ◽  
Vertical Component ◽  
Transversely Isotropic ◽  
Suspended Particles ◽  
Three Dimensions ◽  
Ball Diameter ◽  
The Mean ◽  
Neutrally Buoyant

Individual falling balls were allowed to settle through otherwise quiescent well-mixed suspensions of non-colloidal neutrally buoyant spheres dispersed in a Newtonian liquid. Balls were tracked in three dimensions to determine the variances in their positions about a mean uniform vertical settling path. The primary experimental parameters investigated were the size of the falling ball and the volume fraction and size of the suspended particles. Unlike the horizontal variances, the vertical variances were found to be affected by short-time deterministic behaviour relating to the instantaneous local configurational arrangement of the suspended particles. For sufficiently long intervals between successive observations, the trajectories of the balls were observed to disperse about their mean settling paths in a random manner. This points to the existence of a Gaussian hydrodynamic dispersivity that characterizes the linear temporal growth of the variance in the position of a falling ball. The functional dependence of these horizontal and vertical dispersivities upon the parameters investigated was established.The dispersivity dyadic was observed to be transversely isotropic with respect to the direction of gravity, with the vertical component at least 25 times larger than the horizontal component. The vertical dispersivity Dˆv (made dimensionless with the diameter of the suspended spheres and the mean settling velocity) was observed to decrease with increasing falling ball diameter, but to decrease less rapidly with concentration than theoretically predicted for very dilute suspensions; moreover, for falling balls equal in size to the suspended spheres, Dˆv increased linearly with increasing volume fraction ϕ of suspended solids.In addition to the above experiments performed on suspensions of spheres, previously published settling-velocity data on the fall of balls through neutrally buoyant suspensions of rods possessing an aspect ratio of 20 were re-analysed, and vertical dispersivities calculated therefrom. (These data, taken by several of the present investigators in conjunction with other researchers, had only been grossly analysed in prior publications to extract the mean settling velocity of the ball, no attempt having been made at the time to extract dispersivity data too.) The resulting vertical dispersivities, when rendered dimensionless with the rod length and mean settling velocity, showed no statistically significant dependence upon the falling-ball diameter; moreover, all other things being equal, these dispersivities were observed to increase with increasing rod concentration.

Gravitational and zero-drag motion of a spheroid adjacent to an inclined plane at low Reynolds number

1994 ◽  
Vol 268 ◽  
pp. 267-292 ◽  
Author(s):  
Richard Hsu ◽  
Peter Ganatos
Keyword(s):  
Reynolds Number ◽  
Angular Velocity ◽  
Shear Flow ◽  
Equilibrium Position ◽  
Prolate Spheroid ◽  
Inclined Plane ◽  
Gravitational Settling ◽  
Angular Velocities ◽  
Planar Wall ◽  
Neutrally Buoyant

The first highly accurate solutions for the resistance tensor of an oblate or prolate spheroid moving near a planar wall obtained by Hsu & Ganatos (1989) are used to compute the translational and angular velocities and trajectories of a neutrally buoyant spheroid in shear flow and the gravitational settling motion of a non-neutrally buoyant spheroid adjacent to an inclined plane. The neutrally buoyant spheroid in shear flow undergoes a periodical motion toward and away from the wall as it continually tumbles forward. For some orientation angles it is found that the wall actually enhances the angular velocity of the particle. For certain inclinations a spheroid settling under gravity near an inclined plane reaches an equilibrium position, after which it translates parallel to the wall without rotation.

The instability of oscillatory plane Poiseuille flow

1982 ◽  
Vol 116 ◽  
pp. 91-114 ◽  
Author(s):  
Christian H. Von Kerczek
Keyword(s):  
Steady Flow ◽  
Poiseuille Flow ◽  
Growth Rates ◽  
Oscillatory Flow ◽  
Amplitude Ratio ◽  
Perturbation Technique ◽  
Wave Number ◽  
Plane Poiseuille Flow ◽  
Velocity Amplitude ◽  
Very High

The instability of oscillatory plane Poiseuille flow, in which the pressure gradient is time-periodically modulated, is investigated by a perturbation technique. The Floquet exponents (i.e. the complex growth rates of the disturbances to the oscillatory flow) are computed by series expansions, in powers of the oscillatory to steady flow velocity amplitude ratio, about the values of the growth rates of the disturbances of the steady flow. It is shown that the oscillatory flow is more stable than the steady flow for values of Reynolds number and disturbance wave number in the vicinity of the steady flow critical point and for values of frequencies of imposed oscillation greater than about one tenth of the frequency of the steady flow neutral disturbance. At very high and low values of imposed oscillation frequency, the unsteady flow is slightly less stable than the steady flow. These results hold for the values of the velocity amplitude ratio at least up to 0·25.

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