Slip length formulas for longitudinal shear flow over a superhydrophobic grating with partially filled cavities
File(s)
Accepted version
Author(s)
Crowdy, Darren
Type
Journal Article
Abstract
Explicit formulas are given for the hydrodynamic slip lengths associated with longitudinal shear flow over a superhydrophobic grating where the menisci have partially invaded the cavities and are only weakly curved. For flat menisci that have depinned from the top of the grating and have displaced downwards into the cavities, the axial velocity is determined analytically and the slip length extracted from it. This solution is then combined with an integral identity to determine the first-order correction to the slip length when the displaced menisci bow weakly into the cavity. It is argued that the new formulas provide useful upper bounds for quantifying slip in microchannel flows involving partially filled cavities. The new solutions are natural extensions of prior results due to Philip (Z. Angew. Math. Phys., vol. 23, 1972, pp. 353–372) for shear flow over mixed no-slip/no-shear surfaces and due to Bechert & Bartenwerfer (J. Fluid Mech., vol. 206, 1989, pp. 105–129) for shear flow over blade-shaped riblets.
Date Issued
2021-09-01
Date Acceptance
2021-07-30
Citation
Journal of Fluid Mechanics, 2021, 925, pp.1-11
ISSN
0022-1120
Publisher
Cambridge University Press
Start Page
1
End Page
11
Journal / Book Title
Journal of Fluid Mechanics
Volume
925
Copyright Statement
© The Author(s), 2021. Published by Cambridge University Press
Identifier
https://www.cambridge.org/core/journals/journal-of-fluid-mechanics/article/slip-length-formulas-for-longitudinal-shear-flow-over-a-superhydrophobic-grating-with-partially-filled-cavities/1DD5D9A5753228D6008479E9BD1C3A9C
Subjects
Science & Technology
Technology
Physical Sciences
Mechanics
Physics, Fluids & Plasmas
Physics
drag reduction
capillary flows
wetting and wicking
SURFACES
Fluids & Plasmas
01 Mathematical Sciences
09 Engineering
Publication Status
Published
Date Publish Online
2021-10-25