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@article{Schnitzer:2017:10.1103/PhysRevFluids.2.072101,
author = {Schnitzer, O and Yariv, E},
doi = {10.1103/PhysRevFluids.2.072101},
journal = {Physical Review Fluids},
title = {Longitudinal pressure-driven flows between superhydrophobic grooved surfaces: large effective slip in the narrow-channel limit},
url = {http://dx.doi.org/10.1103/PhysRevFluids.2.072101},
volume = {2},
year = {2017}
}

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TY  - JOUR
AB  - The gross amplification of the fluid velocity in pressure-driven flows due to the introduction of superhydrophobic walls is commonly quantified by an effective slip length. The canonical duct-flow geometry involves a periodic structure of longitudinal shear-free stripes at either one or both of the bounding walls, corresponding to flat-meniscus gas bubbles trapped within a periodic array of grooves. This grating configuration is characterized by two geometric parameters, namely the ratio κ of channel width to microstructure period and the areal fraction Δ of the shear-free stripes. For wide channels, κ1, this geometry is known to possess an approximate solution where the dimensionless slip length λ, normalized by the duct semiwidth, is small, indicating a weak superhydrophobic effect. We here address the other extreme of narrow channels, κ1, identifying large O(κ−2) values of λ for the symmetric configuration, where both bounding walls are superhydrophobic. This velocity enhancement is associated with an unconventional Poiseuille-like flow profile where the parabolic velocity variation takes place in a direction parallel (rather than perpendicular) to the boundaries. Use of matched asymptotic expansions and conformal-mapping techniques provides λ up to O(κ−1), establishing the approximation λ∼κ−2Δ33+κ−1Δ2πln4+, which is in excellent agreement with a semianalytic solution of the dual equations governing the respective coefficients of a Fourier-series representation of the fluid velocity. No similar singularity occurs in the corresponding asymmetric configuration, involving a single superhydrophobic wall; in that geometry, a Hele-Shaw approximation shows that λ=O(1).
AU  - Schnitzer,O
AU  - Yariv,E
DO  - 10.1103/PhysRevFluids.2.072101
PY  - 2017///
SN  - 2469-990X
TI  - Longitudinal pressure-driven flows between superhydrophobic grooved surfaces: large effective slip in the narrow-channel limit
T2  - Physical Review Fluids
UR  - http://dx.doi.org/10.1103/PhysRevFluids.2.072101
UR  - http://hdl.handle.net/10044/1/49669
VL  - 2
ER  -

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