Small-solid-fraction approximations for the slip-length tensor of micropillared superhydrophobic surfaces

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Title: Small-solid-fraction approximations for the slip-length tensor of micropillared superhydrophobic surfaces
Authors: Schnitzer, O
Yariv, E
Item Type: Journal Article
Abstract: Fakir-like superhydrophobic surfaces, formed by doubly periodic arrays of thin pillars that sustain a lubricating gas layer, exhibit giant liquid-slip lengths that scale as relative to the periodicity, being the solid fraction (Ybert et al., Phys. Fluids, vol. 19, 2007, 123601). Considering arbitrarily shaped pillars distributed over an arbitrary Bravais lattice, we employ matched asymptotic expansions to calculate the slip-length tensor in the limit . The leading slip length is determined from a local analysis of an ‘inner’ region close to a single pillar, in conjunction with a global force balance. This leading term, which is independent of the lattice geometry, is related to the drag due to pure translation of a flattened disk shaped like the pillar cross-section; its calculation is illustrated for the case of elliptical pillars. The slip length is associated with the excess velocity induced about a given pillar by all the others. Since the field induced by each pillar corresponds on the ‘outer’ lattice scale to a Stokeslet whose strength is fixed by the shear rate, the slip length depends upon the lattice geometry but is independent of the cross-sectional shape. Its calculation entails asymptotic evaluation of singular lattice sums. Our approximations are in excellent agreement with existing numerical computations for both circular and square pillars.
Issue Date: 25-May-2018
Date of Acceptance: 19-Feb-2018
URI: http://hdl.handle.net/10044/1/57298
DOI: https://dx.doi.org/10.1017/jfm.2018.187
ISSN: 0022-1120
Publisher: Cambridge University Press (CUP)
Start Page: 637
End Page: 652
Journal / Book Title: Journal of Fluid Mechanics
Volume: 843
Copyright Statement: © 2018 Cambridge University Press. This paper has been accepted for publication and will appear in a revised form, subsequent to peer-review and/or editorial input by Cambridge University Press.
Keywords: Science & Technology
Technology
Physical Sciences
Mechanics
Physics, Fluids & Plasmas
Physics
low-Reynolds-number flows
micro-
nano-fluid dynamics
STOKES-FLOW
01 Mathematical Sciences
09 Engineering
Fluids & Plasmas
Publication Status: Published
Online Publication Date: 2018-03-26
Appears in Collections:Mathematics
Applied Mathematics and Mathematical Physics
Faculty of Natural Sciences



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