Motion of a sphere down a rough plane in a viscous fluid

When a sphere moves in a viscous fluid down an artificially roughened inclined plane with multiple roughness scales, its motion can be described as four successive stages: (i) descending toward the plane while in contact with a large asperity, (ii) descending toward the plane without contact, (iii) contacting the plane on small asperities, and (iv) ascending from the plane while in contact with a second large asperity. This process was analyzed by theory and experiment to provide the time variation of the translational and rotational velocities of the sphere and of its hydrodynamic separation from the plane. The translational velocity decreases weakly as the sphere descends toward the plane without contact, while the rotational velocity is nearly constant. When contact occurs, the translational velocity generally decreases, while the rotational velocity generally increases, due to solid–solid friction. For large angles of inclination of the plane from horizontal, or when the larger asperities are closely spaced or have large heights, then contact with the small asperities does not occur and the motion is dominated by contact with the large asperities and by no contact.