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.