Simple shear flow round a rigid sphere: inertial effects and suspension rheology

1970 ◽  
Vol 44 (1) ◽  
pp. 1-17 ◽  
Author(s):  
Chen-Jung Lin ◽  
James H. Peery ◽  
W. R. Schowalter
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Particle Surface ◽  
Rigid Sphere ◽  
Simple Shear Flow ◽  
Suspension Rheology ◽  
Inertial Effects ◽  
Fluid Inertia ◽  
Pressure Fields ◽  
Sphere Radius

An analysis is presented of the flow field near a neutrally-buoyant rigid spherical particle immersed in an in compressible Newtonian fluid which, at large distances from the particle, is undergoing simple shear flow. Subject to conditions of continuity of stress at the particle surface and to conditions of zero net torque and zero net force on the sphere, the effect of fluid inertia on the velocity and pressure fields in the vicinity of the particle has been computed to $O(R^{\frac{3}{2}})$, where R = a2G/ν is a shear Reynolds number, a being the sphere radius, G the velocity gradient in the free stream (taken to be a positive number), and ν the kinematic viscosity.Some streamlines have been computed and plotted. These illustrate how the fore–aft symmetry of the creeping-motion solution is destroyed when one includes inertial effects.Knowledge of the velocity and pressure fields enables one to compute the effect of inertial forces in suspension rheology. The results include a correction to the Einstein viscosity law to $O(R^{\frac{3}{2}})$ for a dilute (non-interacting) suspension of spheres. In addition it is found that inertial effects give rise to a non-isotropic normal stress.

Three-dimensional calculations of the simple shear flow around a single particle between two moving walls

1995 ◽  
Vol 283 ◽  
pp. 273-285 ◽  
Author(s):  
H. Nirschl ◽  
H. A. Dwyer ◽  
V. Denk
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Simple Shear ◽  
Particle Surface ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Rigid Sphere ◽  
Simple Shear Flow ◽  
Number Range ◽  
Grid Scheme

Three-dimensional solutions have been obtained for the steady simple shear flow over a spherical particle in the intermediate Reynolds number range 0.1 [les ] Re [les ] 100. The shear flow was generated by two walls which move at the same speed but in opposite directions, and the particle was located in the middle of the gap between the walls. The particle-wall interaction is treated by introducing a fully three-dimensional Chimera or overset grid scheme. The Chimera grid scheme allows each component of a flow to be accurately and efficiently treated. For low Reynolds numbers and without any wall influence we have verified the solution of Taylor (1932) for the shear around a rigid sphere. With increasing Reynolds numbers the angular velocity for zero moment for the sphere decreases with increasing Reynolds number. The influence of the wall has been quantified with the global particle surface characteristics such as net torque and Nusselt number. A detailed analysis of the influence of the wall distance and Reynolds number on the surface distributions of pressure, shear stress and heat transfer has also been carried out.

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.

On the rotation of a circular porous particle in 2D simple shear flow with fluid inertia

2016 ◽  
Vol 808 ◽  
Author(s):  
Chenggong Li ◽  
Mao Ye ◽  
Zhongmin Liu
Keyword(s):  
Angular Velocity ◽  
Shear Flow ◽  
Simple Shear ◽  
Momentum Equation ◽  
Confinement Effect ◽  
Porous Particle ◽  
Simple Shear Flow ◽  
Rotational Behaviour ◽  
Two Dimensional ◽  
Fluid Inertia

We investigate numerically the rotational behaviour of a circular porous particle suspended in a two-dimensional (2D) simple shear flow with fluid inertia at particle shear Reynolds number up to 108. We use the volume-averaged macroscopic momentum equation to formulate the flow field inside and outside the moving porous particle, which is solved by a modified single relaxation time lattice Boltzmann method. The effects of fluid inertia, confinement of the bounding walls, and permeability of the particle are studied. Our two-dimensional simulation results confirm that the permeability has little effect on the rotation of a porous particle in unbounded shear flow without fluid inertia (Masoud, Stone & Shelley, J. Fluid Mech., vol. 733, 2013, R6), but also suggest that the role of permeability cannot be neglected when the confinement effect is significant, or the fluid inertia is not negligible. The fluid inertia and the confined walls have similar effects on the rotation of a porous particle as that on a solid impermeable particle. The angular velocity decays with an increase in fluid inertia, and the confinement effect suppresses the angular velocity to a shear rate ratio below 0.5. A simple scaling argument based on the balance of torque exerted by fluid flows adjacent to the two bounding walls and that due to the flow recirculation can explain our results.

Inertial effects on fibre motion in simple shear flow

2005 ◽  
Vol 535 ◽  
pp. 383-414 ◽  
Author(s):  
G. SUBRAMANIAN ◽  
DONALD L. KOCH
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Simple Shear Flow ◽  
Inertial Effects

The influence of surface roughness on the particle-pair distribution function of dilute suspensions of non-colloidal spheres in simple shear flow

1997 ◽  
Vol 339 ◽  
pp. 1-24 ◽  
Author(s):  
INDRESH RAMPALL ◽  
JEFFREY R. SMART ◽  
DAVID T. LEIGHTON
Keyword(s):  
Surface Roughness ◽  
Distribution Function ◽  
Shear Flow ◽  
Simple Shear ◽  
Pair Distribution Function ◽  
Closed Orbit ◽  
Particle Surface ◽  
Particle Interaction ◽  
Recognition Algorithm ◽  
Simple Shear Flow

The pair distribution function of 3.18 mm diameter particles was measured in the plane of shear of a simple shear flow at concentrations of 5%, 10% and 15% by volume. A new direct flow-visualization procedure and a new pattern recognition algorithm were used in the investigation. The measurements show a depletion of bound pairs of particles in the direction of flow. A simple model which includes the effect of particle surface roughness on the particle interactions and the pair distribution function is presented. An important effect of surface roughness is that the particles in a suspension can experience irreversible interactions in the presence of an externally imposed simple shear flow. The model shows that such irreversibilities eliminate all bound pairs of particles in the plane of shear by displacing particles out of the closed orbit trajectory region. Surface roughness is found to induce significant asymmetry in the fore and aft region of a two-particle interaction. The measurements and predictions are in qualitative agreement with these conclusions.

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