Rolling Stones: The motion of a Sphere Down an Inclined Plane Coated with a Thin Liquid Film

by Bico, J., Ashmore-Chakrabarty, J., McKinley, G.H. and Stone, H.A.

A spherical bead deposited on a smooth tilted dry plane wall rolls down the slope under the uniform

acceleration of gravity. We describe an analogous experiment conducted using a plane wall that is

coated with a thin layer of order 50–100 m of a viscous liquid. The steady motion of the sphere

under gravity involves a combination of rotation and sliding. We examine the dependence of the

experimentally observed steady translational and rotational speeds on the physical parameters in the

system. In particular, the interplay between viscous forces and interfacial forces leads to nontrivial

exponents for the scaling of the speeds with the characteristics of the sphere and the viscous liquid.

The overhang situation, in which the sphere rolls down the underside of an inclined lubricated plane,

is also examined. In this case, the steady motion is still observed for a certain range of angles and

bead sizes; that is, the sphere does not always detach from the surface. The adhesive force arises

dynamically from the motion of the sphere and can exceed classical quasistatic capillary forces.

Such a force should also play a role in other problems of lubrication mechanics such as humid

granular flows.