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Velocity amplification in pressure-driven flows between superhydrophobic gratings of small solid fraction

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Abstract

With diminishing fraction of their solid portion, compound gas–solid superhydrophobic surfaces exhibit a large amount of slip which allows for appreciable velocity amplification in pressure-driven microchannel flows. We address this small solid-fraction limit in the context of a grating-like configuration, where superhydrophobicity is provided by a periodic array of flat-meniscus bubbles which are trapped in a Cassie state within the grooved channel walls. Asymptotic analysis for both longitudinal and transverse flows reveals a logarithmic scaling of the effective slip length in the solid fraction of the compound boundaries, thus refuting earlier claims of an algebraic singularity. The logarithmic scaling in the longitudinal problem is explained using an analogy between the unidirectional velocity and the velocity potential in two-dimensional irrotational flows. In the transverse problem it has to do with the Stokes paradox. The mechanisms identified herein explain the absence of slip-length singularity in the comparable asymmetric configuration, where only one of the channel walls is superhydrophobic.

Graphical abstract: Velocity amplification in pressure-driven flows between superhydrophobic gratings of small solid fraction

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Publication details

The article was received on 02 Jul 2017, accepted on 01 Sep 2017 and first published on 12 Sep 2017


Article type: Communication
DOI: 10.1039/C7SM01311F
Citation: Soft Matter, 2017, Advance Article
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    Velocity amplification in pressure-driven flows between superhydrophobic gratings of small solid fraction

    E. Yariv, Soft Matter, 2017, Advance Article , DOI: 10.1039/C7SM01311F

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