Comparisons between slip lengths predicted by a liquid-gas coupled model and that by an idealized zero-gas-shear model are presented in this paper. The problem under consideration is pressure-driven flow of a liquid through a plane channel bounded by two superhydrophobic walls which are patterned with longitudinal or transverse gas-filled grooves. Effective slip arises from lubrication on the liquid-gas interface and intrinsic slippage on the solid phase of the wall. In the mathematical models, the velocities are analytically expressed in terms of eigenfunction series expansions, where the unknown coefficients are determined by the matching of velocities and shear stresses on the liquid-gas interface. Results are generated to show the effects due to small but finite gas viscosity on the effective slip lengths as functions of the channel height, the depth of grooves, the gas area fraction of the wall, and intrinsic slippage of the solid phase. Conditions under which even a gas/liquid viscosity ratio as small as 0.01 may have appreciable effects on the slip lengths are discussed.
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October 2010
Research Article|
October 28 2010
On the effects of liquid-gas interfacial shear on slip flow through a parallel-plate channel with superhydrophobic grooved walls
Chiu-On Ng;
Chiu-On Ng
a)
1Department of Mechanical Engineering,
The University of Hong Kong
, Pokfulam Road, Hong Kong
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Henry C. W. Chu;
Henry C. W. Chu
1Department of Mechanical Engineering,
The University of Hong Kong
, Pokfulam Road, Hong Kong
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C. Y. Wang
C. Y. Wang
2Department of Mathematics,
Michigan State University
, East Lansing, Michigan 48824, USA
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Chiu-On Ng
1,a)
Henry C. W. Chu
1
C. Y. Wang
2
1Department of Mechanical Engineering,
The University of Hong Kong
, Pokfulam Road, Hong Kong
2Department of Mathematics,
Michigan State University
, East Lansing, Michigan 48824, USA
a)
Author to whom correspondence should be addressed. Electronic mail: [email protected].
Physics of Fluids 22, 102002 (2010)
Article history
Received:
April 26 2010
Accepted:
September 07 2010
Citation
Chiu-On Ng, Henry C. W. Chu, C. Y. Wang; On the effects of liquid-gas interfacial shear on slip flow through a parallel-plate channel with superhydrophobic grooved walls. Physics of Fluids 1 October 2010; 22 (10): 102002. https://doi.org/10.1063/1.3493641
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