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Slip length formulas for longitudinal shear flow over a superhydrophobic grating with partially filled cavities

Published online by Cambridge University Press:  01 September 2021

Darren G. Crowdy Open the ORCID record for Darren G. Crowdy [Opens in a new window]
Darren G. Crowdy*
Affiliation:
Department of Mathematics, Imperial College London, 180 Queen's Gate, LondonSW7 2AZ, UK
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Flow Control: Drag reduction Interfacial Flows (free surface): Capillary flows
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 925 , 25 October 2021 , R2
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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