Longitudinal flow in superhydrophobic channels with partially invaded grooves

Analytical expressions are derived for the longitudinal flow in a superhydrophobic microchannel where flat menisci in the Cassie state have partially invaded the grooves between no-slip blades. Using these solutions, the effective slip lengths are computed and compared with recent analytical results...

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Bibliographic Details
Published inJournal of engineering mathematics Vol. 137; no. 1
Main Authors Miyoshi, Hiroyuki, Rodriguez-Broadbent, Henry, Curran, Anna, Crowdy, Darren
Format Journal Article
LanguageEnglish
Published Dordrecht Springer Netherlands 01.12.2022
Springer Nature B.V
Subjects
Applications of Mathematics
Channel flow
Computational Mathematics and Numerical Analysis
Exact solutions
Grooves
Hydrophobicity
Mathematical and Computational Engineering
Mathematical Modeling and Industrial Mathematics
Mathematics
Mathematics and Statistics
Menisci
Microchannels
Shear flow
Slip
Theoretical and Applied Mechanics
Conformal maps
Prime function
Mixed boundary value problem
Superhydrophobic surfaces
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Summary:Analytical expressions are derived for the longitudinal flow in a superhydrophobic microchannel where flat menisci in the Cassie state have partially invaded the grooves between no-slip blades. Using these solutions, 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.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:0022-0833
1573-2703
DOI:10.1007/s10665-022-10240-9