In this paper we report results of two-dimensional simulations of the motion of elliptic capsules carried by a Poiseuille flow in a channel. The numerical method allows computation of the capsule motion and the fluid flow around the capsule, and accurate evaluation of the lift force and torque. Results show that the motion of a capsule which is heavier than the carrying fluid may be decomposed into three stages: initial lift-off, transient oscillations and steady flying. The behaviour of the capsule during initial lift-off and steady flying is analysed by studying the pressure and shear stress distributions on the capsule. The dominant mechanism for the lift force and torque is lubrication or inertia or a combination of the two under different conditions. The lift-off velocity for the ellipse in two dimensions is compared with experimental values for cylindrical capsules in pipes. Finally, the mechanisms of lift for capsules are applied to flying core flows, and it is argued that inertial forces are responsible for levitating heavy crude oil cores lubricated by water in a horizontal pipeline.
On symmetry and anisotropy of Earth-core flows
