Direct Simulation of Initial Value Problems for the Motion of Solid Bodies in a Newtonian Fluid Part 2. Couette and Poiseuille Flows

J. Feng, H. H. Hu and D. D. Joseph^{ }

*J. Fluid Mech*. **277**, 271- 301
(1994)

**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 non-linear 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 centerline in a Couette flow, and exhibits the Segre-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 analyzed by interrogating the distributions of pressure and shear stress
on the particle. The stagnation pressures on the particle surface are
particularly important in determining the direction of migration.