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The symmetry of mobility laws for viscous flow along arbitrarily patterned surfaces

Author(s)
Kamrin, Kenneth N.; Stone, Howard A.
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Abstract
Generalizations of the no-slip boundary condition to allow for slip at a patterned fluid-solid boundary introduce a surface mobility tensor, which relates the shear traction vector tangent to the mean surface to an apparent surface velocity vector. For steady, low-Reynolds-number fluid motions over planar surfaces perturbed by arbitrary periodic height and Navier slip fluctuations, we prove that the resulting mobility tensor is always symmetric, which had previously been conjectured. We describe generalizations of the results to three other families of geometries, which typically have unsteady flow.
Date issued
2011-03
URI
http://hdl.handle.net/1721.1/67891
Department
Massachusetts Institute of Technology. Department of Mechanical Engineering
Journal
Physics of Fluids
Publisher
American Institute of Physics
Citation
Kamrin, Ken, and Howard A. Stone. “The symmetry of mobility laws for viscous flow along arbitrarily patterned surfaces.” Physics of Fluids 23.3 (2011): 031701.© 2011 American Institute of Physics.
Version: Final published version
ISSN
1070-6631
1089-7666

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