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Effective velocity boundary condition at a mixed slip surface

Published online by Cambridge University Press:  26 April 2007

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

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
Copyright
Copyright © Cambridge University Press 2007

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