DIRECT SIMULATION OF INITIAL-VALUE PROBLEMS FOR THE MOTION OF SOLID BODIES IN A NEWTONIAN FLUID .2. COUETTE AND POISEUILLE FLOWS

This paper reports the results of a two-dimensional finite element sim ulation of the motion of a circular particle in a Couette and a Poiseu ille flow. The size of the particle and the Reynolds number are large enough to include fully nonlinear inertial effects and wall effects. B oth neutrally buoyant and non-neutrally buoyant particles are studied, and the results are compared with pertinent experimental data and per turbation theories. A neutrally buoyant particle is shown to migrate t o the centreline 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 differe nce between the fluid and the particle. The driving forces of the migr ation have been identified as a wall repulsion due to lubrication, an inertial lift related to shear slip, a lift due to particle rotation a nd, in the case of Poiseuille flow, a lift caused by the velocity prof ile curvature. These forces are analysed by examining the distribution s of pressure and shear stress on the particle. The stagnation pressur e on the particle surface are particularly important in determining th e direction of migration.