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Effective velocity boundary condition at a mixed slip surface

Published online by Cambridge University Press:  26 April 2007

M. SBRAGAGLIA  and
A. PROSPERETTI
M. SBRAGAGLIA
Affiliation:
Faculty of Applied Sciences, IMPACT, and Burgerscentrum, University of Twente, AE 7500 Enschede, The Netherlands
A. PROSPERETTI
Affiliation:
Faculty of Applied Sciences, IMPACT, and Burgerscentrum, University of Twente, AE 7500 Enschede, The Netherlands Department of Mechanical Engineering, The Johns Hopkins University, Baltimore, MD 21218, USA
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Abstract

This paper studies the nature of the effective velocity boundary condition for liquid flow over a plane boundary on which small free-slip islands are randomly distributed. It is found that an effective Navier partial-slip condition for the velocity emerges from a statistical analysis valid for arbitrary fractional area coverage β. As an example, the general theory is applied to the low-β limit and this result is extended heuristically to finite β with a resulting slip length proportional to aβ/(1 − β), where a is a characteristic size of the islands. A specification of the nature of the free-slip islands is not required in the analysis. They could be nano-bubbles, as suggested by recent experiments, or hydrophobic surface patches. The results are also relevant for ultra-hydrophobic surfaces exploiting the so-called ‘lotus effect’.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 578 , 10 May 2007 , pp. 435 - 451
Copyright
Copyright © Cambridge University Press 2007

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