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.

Force on a Small Particle Attached to a Plane Wall in a Hiemenz Straining Flow

2012 ◽  
Vol 134 (11) ◽  
Author(s):  
A. B. Maynard ◽  
J. S. Marshall
Keyword(s):  
Reynolds Number ◽  
Flow Field ◽  
Reynolds Numbers ◽  
Lower Surface ◽  
Ring Structure ◽  
Plane Wall ◽  
Small Reynolds Numbers ◽  
Particle Force ◽  
Volume Method ◽  
Excellent Accuracy

The force acting on a spherical particle fixed to a wall and immersed in an axisymmetric straining flow is examined for small Reynolds numbers. The steady, incompressible flow field is computed using an axisymmetric finite-volume method over conditions spanning five decades in the Reynolds number. The flow is characterized by the formation of a vortex ring structure in the wedge region formed between the particle lower surface and the plane wall. A power law expression for the dimensionless particle force is obtained as a function of the Reynolds number, which is found to hold with excellent accuracy for Reynolds numbers below about 0.1.

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 along a slender body straddling an interface

1986 ◽  
Vol 27 (3) ◽  
pp. 295-315 ◽  
Author(s):  
G. R. Fulford ◽  
J. R. Blake
Keyword(s):  
Stokes Flow ◽  
Viscous Fluids ◽  
The Other ◽  
Slender Body ◽  
Asymptotic Approximations ◽  
Force Distribution ◽  
First Order ◽  
Flat Interface ◽  
Parallel Motion ◽  
Axis Of Symmetry

AbstractLine distributions of Stokes flow singularities are used to model the flow around a slender body which is straddling a flat interface between two viscous fluids. Motion of the slender body parallel to the interface and normal to the interface is considered where the axis of symmetry of the slender body is always perpendicular to the undisturbed interface. Asymptotic approximations to the force distributions on the slender body are evaluated and the relative contributions of that part of the slender body in one fluid to the force distribution in the other fluid and of the interface interaction to the force distribution are examined. It is observed that a shielding region exists about the interface which is due to the interaction with that part of the slender body in the other fluid. Finally, for parallel motion, the first order interface deformation is calculated.

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.

Pulsatile pipe flow pseudoplastic materials; The flow enhancement for Re ≪ 1

1983 ◽  
Vol 48 (6) ◽  
pp. 1579-1587 ◽  
Author(s):  
Ondřej Wein
Keyword(s):  
Small Parameter ◽  
Pipe Flow ◽  
Quantitative Estimation ◽  
Reynolds Numbers ◽  
Power Law Model ◽  
Viscosity Function ◽  
Small Reynolds Numbers ◽  
Title Problem ◽  
Flow Enhancement ◽  
Method Of Small Parameter

Solution of the title problem for the power-law model of viscosity function is constructed by the method of small parameter in the region of small Reynolds numbers. The main result of the paper is a quantitative estimation of the values of Re, when the influence of inertia on flow enhancement may be quite neglected.

scholarly journals Analytical solution of settling behavior of a particle in incompressible Newtonian fluid by using Parameterized Perturbation Method

2014 ◽  
Vol 33 (2) ◽  
pp. 145-160
Author(s):  
Reza Mohammadyari ◽  
Mazaher Rahimi Esboee ◽  
Majid Rahgoshay
Keyword(s):  
Perturbation Method ◽  
Newtonian Fluid ◽  
Mass Term ◽  
Reynolds Numbers ◽  
Added Mass ◽  
Unsteady Motion ◽  
High Rate ◽  
Settling Behavior ◽  
Analytical Expressions ◽  
Parameterized Perturbation Method

The problem of solid particle settling is a well known problem in mechanic of fluids. The parametrized Perturbation Method is applied to analytically solve the unsteady motion of a spherical particle falling in a Newtonian fluid using the drag of the form given by Oseen/Ferreira, for a range of Reynolds numbers. Particle equation of motion involved added mass term and ignored the Basset term. By using this new kind of perturbation method called parameterized perturbation method (PPM), analytical expressions for the instantaneous velocity, acceleration and position of the particle were derived. The presented results show the effectiveness of PPM and high rate of convergency of the method to achieve acceptable answers.

Sign in / Sign up

Export Citation Format

Share Document