Longitudinal flow in superhydrophobic channels with partially invaded grooves
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Published version
Author(s)
MIYOSHI, Hiroyuki
Rodriguez-Broadbent, Henry
Curran, Anna
Crowdy, Darren
Type
Journal Article
Abstract
Analytical expressions are derived for the longitudinal flow in a super-
hydrophobic microchannel where flat menisci in the Cassie state have
partially invaded the grooves between no-slip blades. Using these solu-
tions, the effective slip lengths are computed and compared with recent
analytical results for unbounded shear flow over the same class of
surfaces. Expressions for the first-order corrections to these effective
slip lengths when the menisci are weakly curved are also derived.
A mathematical connection to superhydrophobic channel flows where
the flat menisci are still pinned to the tops of the pillars is also
made, resulting in novel analytical expressions for those solutions too.
hydrophobic microchannel where flat menisci in the Cassie state have
partially invaded the grooves between no-slip blades. Using these solu-
tions, the effective slip lengths are computed and compared with recent
analytical results for unbounded shear flow over the same class of
surfaces. Expressions for the first-order corrections to these effective
slip lengths when the menisci are weakly curved are also derived.
A mathematical connection to superhydrophobic channel flows where
the flat menisci are still pinned to the tops of the pillars is also
made, resulting in novel analytical expressions for those solutions too.
Date Issued
2022-10-25
Date Acceptance
2022-09-26
Citation
Journal of Engineering Mathematics, 2022, 137
ISSN
0022-0833
Publisher
Springer
Journal / Book Title
Journal of Engineering Mathematics
Volume
137
Copyright Statement
© The Author(s) 2022. This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
License URL
Sponsor
Engineering and Physical Sciences Research Council
Grant Number
EP/T51780X/1
Subjects
0102 Applied Mathematics
0103 Numerical and Computational Mathematics
0913 Mechanical Engineering
Applied Mathematics
Publication Status
Published
Article Number
ARTN 3