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Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 2. Couette and Poiseuille flows

Published online by Cambridge University Press:  26 April 2006

J. Feng ,
H. H. Hu  and
D. D. Joseph
J. Feng
Affiliation:
Department of Aerospace Engineering and Mechanics and The Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, MN 55455–0153, USA
H. H. Hu
Affiliation:
Department of Mechanical Engineering and Applied Mechanics, University of Pennsylvania, Philadelphia, PA 19104–6315, USA
D. D. Joseph
Affiliation:
Department of Aerospace Engineering and Mechanics and The Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, MN 55455–0153, USA
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Abstract

This paper reports the results of a two-dimensional finite element simulation of the motion of a circular particle in a Couette and a Poiseuille flow. The size of the particle and the Reynolds number are large enough to include fully nonlinear inertial effects and wall effects. Both neutrally buoyant and non-neutrally buoyant particles are studied, and the results are compared with pertinent experimental data and perturbation theories. A neutrally buoyant particle is shown to migrate to the centreline in a Couette flow, and exhibits the Segré-Silberberg effect in a Poiseuille flow. Non-neutrally buoyant particles have more complicated patterns of migration, depending upon the density difference between the fluid and the particle. The driving forces of the migration have been identified as a wall repulsion due to lubrication, an inertial lift related to shear slip, a lift due to particle rotation and, in the case of Poiseuille flow, a lift caused by the velocity profile curvature. These forces are analysed by examining the distributions of pressure and shear stress on the particle. The stagnation pressure on the particle surface are particularly important in determining the direction of migration.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 277 , 25 October 1994 , pp. 271 - 301
Copyright
© 1994 Cambridge University Press

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