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Effective slip boundary conditions for arbitrary periodic surfaces: the surface mobility tensor

Author(s)
Kamrin, Kenneth N.; Bazant, Martin Z.; Stone, Howard A.
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Abstract
In a variety of applications, most notably microfluidics design, slip-based boundary conditions have been sought to characterize fluid flow over patterned surfaces. We focus on laminar shear flows over surfaces with periodic height fluctuations and/or fluctuating Navier scalar slip properties. We derive a general formula for the ‘effective slip’, which describes equivalent fluid motion at the mean surface as depicted by the linear velocity profile that arises far from it. We show that the slip and the applied stress are related linearly through a tensorial mobility matrix, and the method of domain perturbation is then used to derive an approximate formula for the mobility law directly in terms of surface properties. The specific accuracy of the approximation is detailed, and the mobility relation is then utilized to address several questions, such as the determination of optimal surface shapes and the effect of random surface fluctuations on fluid slip.
Date issued
2010-09
URI
http://hdl.handle.net/1721.1/67016
Department
Massachusetts Institute of Technology. Department of Chemical Engineering
Journal
Journal of Fluid Mechanics
Publisher
Cambridge University Press
Citation
Kamrin, Ken, Martin Z. Bazant, and Howard A. Stone. “Effective Slip Boundary Conditions for Arbitrary Periodic Surfaces: The Surface Mobility Tensor.” Journal of Fluid Mechanics 658 (2010) : 409-437. © 2010 Cambridge University Press
Version: Final published version
ISSN
0022-1120
1469-7645

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