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Hydrodynamic friction of fakir-like superhydrophobic surfaces

Published online by Cambridge University Press:  23 August 2010

ANTHONY M. J. DAVIS  and
ERIC LAUGA
ANTHONY M. J. DAVIS
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA
ERIC LAUGA*
Affiliation:
Department of Mechanical and Aerospace Engineering, University of California San Diego, 9500 Gilman Drive, La Jolla, CA 92093-0411, USA
*
†Email address for correspondence: [email protected]
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Abstract

A fluid droplet located on a superhydrophobic surface makes contact with the surface only at small isolated regions, and is mostly in contact with the surrounding air. As a result, a fluid in motion near such a surface experiences very low friction, and superhydrophobic surfaces display strong drag reduction in the laminar regime. Here we consider theoretically a superhydrophobic surface composed of circular posts (so-called fakir geometry) located on a planar rectangular lattice. Using a superposition of point forces with suitably spatially dependent strength, we derive the effective surface-slip length for a planar shear flow on such a fakir-like surface as the solution to an infinite series of linear equations. In the asymptotic limit of small surface coverage by the posts, the series can be interpreted as Riemann sums, and the slip length can be obtained analytically. For posts on a square lattice, our analytical prediction of the dimensionless slip length, in the low surface coverage limit, is in excellent quantitative agreement with previous numerical computations.

JFM classification

Low-Reynolds-number flows: Low-Reynolds-number flows Micro-/Nano-fluid dynamics: Micro-/Nano-fluid dynamics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 661 , 25 October 2010 , pp. 402 - 411
Copyright
Copyright © Cambridge University Press 2010

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