MOTION OF A SOLID SPHERE IN A GENERAL FLOW NEAR A PLANE BOUNDARY AT ZERO REYNOLDS-NUMBER

It is demonstrated how the hydrodynamic force and moment of force acti ng on a solid sphere may be calculated when it is placed at rest at an arbitrary position in a two dimensional flow at zero Reynolds number in which the region of how is bounded by either an undeformable planar free surface or by a plane solid wail. The results so obtained are us ed to calculate the motion of a freely moving solid sphere in an asymm etric vortex in the presence of an underformable free surface. It is s een that the sphere, depending on the direction of the undisturbed how will either spiral into or out of the vortex. This implies that when a dilute suspension of such spherical particles undergoes such a vorte x motion in the presence of the free surface, the vortex will either f ill up with particles from the surrounding flow or become devoid of pa rticles.