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.

Simulations of Droplet Collisions in Shear Flow

2012 ◽  
Author(s):  
Orest Shardt ◽  
J. J. Derksen ◽  
Sushanta K. Mitra
Keyword(s):  
Reynolds Number ◽  
Shear Flow ◽  
Capillary Number ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Simple Shear Flow ◽  
Number Range ◽  
Droplet Collisions ◽  
Critical Capillary Number ◽  
Boltzmann Method

When droplets collide in a shear flow, they may coalesce or remain separate after the collision. At low Reynolds numbers, droplets coalesce when the capillary number does not exceed a critical value. We present three-dimensional simulations of droplet coalescence in a simple shear flow. We use a free-energy lattice Boltzmann method (LBM) and study the collision outcome as a function of the Reynolds and capillary numbers. We study the Reynolds number range from 0.2 to 1.4 and capillary numbers between 0.1 and 0.5. We determine the critical capillary number for the simulations (0.19) and find that it is does not depend on the Reynolds number. The simulations are compared with experiments on collisions between confined droplets in shear flow. The critical capillary number in the simulations is about a factor of 25 higher than the experimental value.

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.

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 Numerical Simulation of Drops in Three Dimensional Viscoelastic Simple Shear Flows

2001 ◽  
Author(s):  
Shriram B. Pillapakkam ◽  
Pushpendra Singh
Keyword(s):  
Numerical Simulation ◽  
Shear Flow ◽  
Direct Numerical Simulation ◽  
Viscoelastic Fluid ◽  
Simple Shear ◽  
Polymer Concentration ◽  
Three Dimensional ◽  
Simple Shear Flow ◽  
Splitting Technique

Abstract A three dimensional finite element scheme for Direct Numerical Simulation (DNS) of viscoelastic two phase flows is implemented. The scheme uses the Level Set Method to track the interface and the Marchuk-Yanenko operator splitting technique to decouple the difficulties associated with the governing equations. Using this numerical scheme, the shape of Newtonian drops in a simple shear flow of viscoelastic fluid and vice versa are analyzed as a function of Capillary number, Deborah number and polymer concentration. The viscoelastic fluid is modeled via the Oldroyd-B model. The role of viscoelastic stresses in deformation of a drop subjected to simple shear flow and its effect on the steady state shape is analyzed. Our results compare favorably with existing experimental data and also help in understanding the role of viscoelastic stresses in drop deformation.

Rotation of small non-axisymmetric particles in a simple shear flow

1979 ◽  
Vol 92 (3) ◽  
pp. 591-607 ◽  
Author(s):  
E. J. Hinch ◽  
L. G. Leal
Keyword(s):  
Shear Flow ◽  
Simple Shear ◽  
Numerical Solutions ◽  
Reynolds Numbers ◽  
Order System ◽  
General Nature ◽  
Simple Shear Flow ◽  
Third Order ◽  
Low Reynolds Numbers ◽  
Planar Rotation

The equations for the rotation of non-axisymmetric ellipsoids in a simple shear flow at low Reynolds numbers are derived in terms of Euler angles. Numerical solutions of this third-order system of equations show a doubly periodic structure to the rotation, with a change in the general nature of the solutions when a certain planar rotation of the particle becomes unstable. Some analytic progress can be made for nearly spherical ellipsoids and for nearly axisymmetric ellipsoids. The near spheres show the same qualitative behaviour as the general ellipsoids. Quite small deviations from axial symmetry are found to produce large changes in the rotation.

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