scholarly journals Dynamics of sedimentation of particle in a viscous fluid in the presence of two flat walls

2018 ◽  
Vol 20 (3) ◽  
pp. 318-326
Author(s):  
Sergey I. Martynov ◽  
Tatyana V. Pronkina ◽  
Natalya V. Dvoryaninova ◽  
Tatyana V. Karyagina
Keyword(s):  
Viscous Fluid ◽  
Particle Deposition ◽  
Reynolds Numbers ◽  
Particle Sedimentation ◽  
Planar Surfaces ◽  
Angular Velocities ◽  
Small Reynolds Numbers ◽  
Oriented Parallel ◽  
Limiting Case ◽  
Number Of Particles

The model problem of sedimentation of a solid spherical particle in a viscous fluid bordering two solid planar surfaces is considered. To find the solution of the hydrodynamic equations in the approximation of small Reynolds numbers with boundary conditions on a particle and on two planes, a procedure developed for numerical simulation of the dynamics of a large number of particles in a viscous fluid with one plane wall is used. The procedure involves usage of fictive particles located symmetrically to real ones with respect to the plane. To solve the problem of the real particle’s sedimentation in the presence of two planes, a system of fictive particles is introduced. An approximate solution was found using four fictive particles. Basing on this solution, numerical results are obtained on dynamics of particle deposition for the cases of planes oriented parallel and perpendicular to each other. In particular, the values of linear and angular velocities of a particle are found, depending on the distance to each plane and on the direction of gravity. In the limiting case, when one of the planes is infinitely far from the particle, we obtain known results on the dynamics of particle sedimentation along and perpendicular to one plane.

scholarly journals Dynamics of sedimentation of particle in a viscous fluid in the presence of two flat walls

2018 ◽  
Vol 20 (3) ◽  
pp. 318-326
Author(s):  
S. I. Martynov ◽  
T. V. Pronkina ◽  
N. V. Dvoryaninova ◽  
T. V. Karyagina
Keyword(s):  
Viscous Fluid ◽  
Particle Deposition ◽  
Reynolds Numbers ◽  
Particle Sedimentation ◽  
Planar Surfaces ◽  
Angular Velocities ◽  
Small Reynolds Numbers ◽  
Oriented Parallel ◽  
Limiting Case ◽  
Number Of Particles

The model problem of sedimentation of a solid spherical particle in a viscous fluid bordering two solid planar surfaces is considered. To find the solution of the hydrodynamic equations in the approximation of small Reynolds numbers with boundary conditions on a particle and on two planes, a procedure developed for numerical simulation of the dynamics of a large number of particles in a viscous fluid with one plane wall is used. The procedure involves usage of fictive particles located symmetrically to real ones with respect to the plane. To solve the problem of the real particle’s sedimentation in the presence of two planes, a system of fictive particles is introduced. An approximate solution was found using four fictive particles. Basing on this solution, numerical results are obtained on dynamics of particle deposition for the cases of planes oriented parallel and perpendicular to each other. In particular, the values of linear and angular velocities of a particle are found, depending on the distance to each plane and on the direction of gravity. In the limiting case, when one of the planes is infinitely far from the particle, we obtain known results on the dynamics of particle sedimentation along and perpendicular to one plane.

scholarly journals Force distribution on a slender body close to an interface

1981 ◽  
Vol 24 (1) ◽  
pp. 27-36 ◽  
Author(s):  
J.R. Blake ◽  
G.R. Fulford
Keyword(s):  
Reynolds Numbers ◽  
Plane Wall ◽  
Slender Body ◽  
Force Distribution ◽  
Immiscible Liquids ◽  
Flat Interface ◽  
Small Reynolds Numbers ◽  
Rigid Plane ◽  
Limiting Case ◽  
Analytical Expressions

The motion of a slender body parallel and very close to a flat interface which separates two immiscible liquids of differing density and viscosity is considered for very small Reynolds numbers. Approximate analytical expressions are obtained for the distribution of forces acting on the slender body. The limiting case of a rigid plane wall yields results obtained previously.

Drag of a sphere in an unsteady flow of viscous fluid at small reynolds numbers

1988 ◽  
Vol 23 (1) ◽  
pp. 6-10 ◽  
Author(s):  
M. N. Gaidukov ◽  
V. G. Roman ◽  
Yu. I. Yalamov
Keyword(s):  
Viscous Fluid ◽  
Unsteady Flow ◽  
Reynolds Numbers ◽  
Small Reynolds Numbers

scholarly journals The steady flow of viscous fluid past a fixed spherical obstacle at small reynolds numbers

1929 ◽  
Vol 123 (791) ◽  
pp. 225-235 ◽  
Keyword(s):  
Viscous Fluid ◽  
Steady Flow ◽  
Kinematic Viscosity ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Great Distance ◽  
Small Reynolds Numbers

It was proposed by Oseen that, in considering the steady flow of a viscous fluid past a fixed obstacle, the velocity of disturbance should be considered small, and terms depending on its square neglected. This approximation is to be taken to hold not only at a great distance from the obstacle, but also right up to its surface; and involves the assumption that U d/v is small, where d is some representative length of the obstacle, which in the case of a sphere is taken to be its diameter, U is the undisturbed velocity of the stream, and v the kinematic viscosity of the fluid. With this approximation, the equations of motion become linear, and can be solved; the condition of no slip at the boundary is then applied to complete the solution. We take the obstacle to be a sphere of radius and take the origin of coordinates at its centre.

The slow motion of a sphere in a rotating, viscous fluid

1964 ◽  
Vol 20 (2) ◽  
pp. 305-314 ◽  
Author(s):  
Stephen Childress
Keyword(s):  
Reynolds Number ◽  
Angular Velocity ◽  
Viscous Fluid ◽  
Classical Problem ◽  
Slow Motion ◽  
Reynolds Numbers ◽  
Constant Angular Velocity ◽  
Axis Of Rotation ◽  
Small Reynolds Numbers ◽  
Analytical Result

The uniform, slow motion of a sphere in a viscous fluid is examined in the case where the undisturbed fluid rotates with constant angular velocity Ω and the axis of rotation is taken to coincide with the line of motion. The various modifications of the classical problem for small Reynolds numbers are discussed. The main analytical result is a correction to Stokes's drag formula, valid for small values of the Reynolds number and Taylor number and tending to the classical Oseen correction as the last parameter tends to zero. The rotation of a free sphere relative to the fluid at infinity is also deduced.

Torque Characteristics for Spherical Annulus Flow

1979 ◽  
Vol 101 (2) ◽  
pp. 284-286 ◽  
Author(s):  
A. M. Waked ◽  
B. R. Munson
Keyword(s):  
Reynolds Number ◽  
Viscous Fluid ◽  
Secondary Flow ◽  
Reynolds Numbers ◽  
Flow Effect ◽  
Spherical Annulus ◽  
Concentric Spheres ◽  
Annulus Flow ◽  
Angular Velocities

The torque needed to rotate concentric spheres when the spherical annulus gap between them is filled with a viscous fluid depends on the Reynolds number and the ratio of the angular velocities of the two spheres. Experimental torque results for low to moderate Reynolds numbers are presented. The secondary flow effect is evident.

Sign in / Sign up

Export Citation Format

Share Document