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Asymptotic formulae for flow in superhydrophobic channels with longitudinal ridges and protruding menisci

Published online by Cambridge University Press:  01 February 2018

Toby L. Kirk Open the ORCID record for Toby L. Kirk [Opens in a new window]
Toby L. Kirk*
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
*
†Email address for correspondence: tlk12@ic.ac.uk
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Abstract

This paper presents new asymptotic formulae for flow in a channel with one or both walls patterned with a longitudinal array of ridges and arbitrarily protruding menisci. Derived from a matched asymptotic expansion, they extend results by Crowdy (J. Fluid Mech., vol. 791, 2016, R7) for shear flow, and thus make no restriction on the protrusion into or out of the liquid. The slip length formula is compared against full numerical solutions and, despite the assumption of small ridge period in its derivation, is found to have a very large range of validity; relative errors are small even for periods large enough for the protruding menisci to degrade the flow and touch the opposing wall.

JFM classification

Flow Control: Drag reduction Drops and Bubbles: Drops and Bubbles Micro-/Nano-fluid dynamics: Microfluidics
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 839 , 25 March 2018 , R3
Copyright
© 2018 Cambridge University Press 

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