ANOMALOUS ROLLING OF SPHERES DOWN AN INCLINED PLANE

A sphere in air will roll down a plane that is tilted away from the ve rtical. The only couple acting about the point of contact between the sphere and the plane is due to the component of the weight of the sphe re along the plane, provided that air friction is negligible. If on th e other hand the sphere is immersed in a liquid, hydrodynamic forces w ill enter into the couples that turn the sphere, and the rotation of t he sphere can be anomalous, i.e., as if rolling up the plane while it falls. In this paper we shall show that anomalous rolling is a charact eristic phenomenon that can be observed in every viscoelastic liquid t ested so far. Anomalous rolling is normal for hydrodynamically levitat ed spheres, both in Newtonian and viscoelastic liquids. Normal and ano malous rolling are different names for dry and hydrodynamic rolling. S pheres dropped at a vertical wall in Newtonian liquids are forced into anomalous rotation and are pushed away from the wall while in viscoel astic liquids, they are forced into anomalous rotation, but are pushed toward the wall. If the wall is inclined and the fluid is Newtonian, the spheres will rotate normally for dry rolling, but the same spheres rotate anomalously in viscoelastic liquids when the angle of inclinat ion from the vertical is less than some critical value. The hydrodynam ic mechanisms underway in the settling of circular particles in a Newt onian fluid at a vertical wall are revealed by an exact numerical simu lation based on a finite-element solution of the Navier-Stokes equatio ns and Newton's equations of motion for a rigid body.