Hydrodynamic interactions between two spheres at contact

We develop a model of contact interactions between two spherical particles immersed in a viscous fluid, under a very low Reynolds number. This model allows us to interpret results of our experiment, in which the settling motion of a ball in the vicinity of another fixed sphere is accurately measured with laser interferometry. Due to the symmetry of the experimental setup and the reversibility of the Stokes equations describing the fluid flow, the trajectory and velocity of the moving sphere center are expected to exhibit symmetry with respect to reflection in the horizontal plane containing the fixed sphere center. However, no such symmetry is observed if the particles "touch" each other. Our model accounts for symmetry breaking by the contact friction between surfaces-such a force appears only when the moving sphere center is above the horizontal plane containing the center of the fixed particle. The model predicts two intervals of motion, at contact: pure rolling and rolling with slip. The existence of both types of motion, with a sharp transition from one to another, has been verified experimentally. [S1003-651X(99)05303-9].