Asymptotic formulae for flow in superhydrophobic channels with longitudinal ridges and protruding menisci
Asymptotic formulae for flow in superhydrophobic channels with longitudinal ridges and protruding menisci
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.
drag reduction, drops and bubbles, microfluidics
R31-R312
Kirk, Toby L.
7bad334e-c216-4f4a-b6b3-cca90324b37c
25 March 2018
Kirk, Toby L.
7bad334e-c216-4f4a-b6b3-cca90324b37c
Kirk, Toby L.
(2018)
Asymptotic formulae for flow in superhydrophobic channels with longitudinal ridges and protruding menisci.
Journal of Fluid Mechanics, 839, .
(doi:10.1017/jfm.2018.73).
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.
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Published date: 25 March 2018
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© 2018 Cambridge University Press.
Keywords:
drag reduction, drops and bubbles, microfluidics
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Local EPrints ID: 495686
URI: http://eprints.soton.ac.uk/id/eprint/495686
ISSN: 0022-1120
PURE UUID: 402f0a85-9e37-4790-8258-2f636c204f33
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Date deposited: 20 Nov 2024 17:43
Last modified: 30 Nov 2024 03:17
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Author:
Toby L. Kirk
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