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The friction of a mesh-like super-hydrophobic surface

Phys. Fluids 21, 113101 (2009); doi:10.1063/1.3250947

Published 3 November 2009

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Anthony M. J. Davis and Eric Lauga
Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, California 92093-0411, USA
When a liquid droplet is located above a super-hydrophobic surface, it only barely touches the solid portion of the surface, and therefore slides very easily on it. More generally, super-hydrophobic surfaces have been shown to lead to significant reduction in viscous friction in the laminar regime, so it is of interest to quantify their effective slipping properties as a function of their geometric characteristics. Most previous studies considered flows bounded by arrays of either long grooves, or isolated solid pillars on an otherwise flat solid substrate, and for which therefore the surrounding air constitutes the continuous phase. Here we consider instead the case where the super-hydrophobic surface is made of isolated holes in an otherwise continuous no-slip surface, and specifically focus on the mesh-like geometry recently achieved experimentally. We present an analytical method to calculate the friction of such a surface in the case where the mesh is thin. The results for the effective slip length of the surface are computed, compared to simple estimates, and a practical fit is proposed displaying a logarithmic dependence on the area fraction of the solid surface. ©2009 American Institute of Physics
History: Received 15 June 2009; accepted 25 September 2009; published 3 November 2009
Permalink: http://link.aip.org/link/?PHFLE6/21/113101/1
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KEYWORDS and PACS

Keywords
PACS
  • 47.55.D-
    Drops and bubbles
  • 66.20.-d
    Viscosity of liquids; diffusive momentum transport
  • 46.55.+d
    Tribology and mechanical contacts
  • YEAR: 2009

PUBLICATION DATA

ISSN:
1070-6631 (print)   1089-7666 (online)
Publisher:
AIP is a member of CrossRef AIP

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