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Rolling stones: The motion of a sphere down an inclined plane coated with a thin liquid film

Phys. Fluids 21, 082103 (2009); doi:10.1063/1.3207884

Published 26 August 2009

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J. Bico,1,2 J. Ashmore-Chakrabarty,3 G. H. McKinley,1 and H. A. Stone3
1Department of Mechanical Engineering, Hatsopoulos Microfluids Laboratory, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
2Physique et Mécanique des Milieux Hétérogènes, ESPCI-ParisTech, Paris 6, Paris 7, UMR CNRS 7635, Paris 75005, France
3School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
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  µm) 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. ©2009 American Institute of Physics
History: Received 4 March 2009; accepted 13 July 2009; published 26 August 2009
Permalink: http://link.aip.org/link/?PHFLE6/21/082103/1
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1070-6631 (print)   1089-7666 (online)
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