Slip length for longitudinal shear flow over an arbitrary-protrusion-angle bubble mattress: The small-solid-fraction singularity

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Title: Slip length for longitudinal shear flow over an arbitrary-protrusion-angle bubble mattress: The small-solid-fraction singularity
Authors: Schnitzer, O
Item Type: Journal Article
Abstract: We study the effective slip length for unidirectional flow over a superhydrophobic mattress of bubbles in the small-solid-fraction limit . Using scaling arguments and utilising an ideal-flow analogy we elucidate the singularity of the slip length as : relative to the periodicity it scales as for protrusion angles and as for . We continue with a detailed asymptotic analysis using the method of matched asymptotic expansions, where ‘inner’ solutions valid close to the solid segments are matched with ‘outer’ solutions valid on the scale of the periodicity, where the bubbles protruding from the solid grooves appear to touch. The analysis yields asymptotic expansions for the effective slip length in each of the protrusion-angle regimes. These expansions overlap for intermediate protrusion angles, which allows us to form a uniformly valid approximation for arbitrary protrusion angles . We thereby explicitly describe the transition with increasing protrusion angle from a logarithmic to an algebraic small-solid-fraction slip-length singularity.
Issue Date: 12-May-2017
Date of Acceptance: 4-Apr-2017
URI: http://hdl.handle.net/10044/1/46266
DOI: https://dx.doi.org/10.1017/jfm.2017.224
ISSN: 1469-7645
Publisher: Cambridge University Press (CUP)
Start Page: 580
End Page: 603
Journal / Book Title: Journal of Fluid Mechanics
Volume: 820
Copyright Statement: © 2017 Cambridge University Press
Keywords: Fluids & Plasmas
01 Mathematical Sciences
09 Engineering
Publication Status: Published
Appears in Collections:Mathematics
Faculty of Natural Sciences



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