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Change in drag, apparent slip and optimum air layer thickness for laminar flow over an idealised superhydrophobic surface

Published online by Cambridge University Press:  28 June 2013

A. Busse ,
N. D. Sandham ,
G. McHale  and
M. I. Newton
A. Busse*
Affiliation:
Faculty of Engineering and the Environment, University of Southampton, Highfield, Southampton SO17 1BJ, UK
N. D. Sandham
Affiliation:
Faculty of Engineering and the Environment, University of Southampton, Highfield, Southampton SO17 1BJ, UK
G. McHale
Affiliation:
Faculty of Engineering and Environment, Northumbria University, Newcastle upon Tyne NE1 8ST, UK
M. I. Newton
Affiliation:
School of Science and Technology, Nottingham Trent University, Clifton Lane, Nottingham NG11 8NS, UK
*
†Email address for correspondence: [email protected]
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Abstract

Analytic results are derived for the apparent slip length, the change in drag and the optimum air layer thickness of laminar channel and pipe flow over an idealised superhydrophobic surface, i.e. a gas layer of constant thickness retained on a wall. For a simple Couette flow the gas layer always has a drag reducing effect, and the apparent slip length is positive, assuming that there is a favourable viscosity contrast between liquid and gas. In pressure-driven pipe and channel flow blockage limits the drag reduction caused by the lubricating effects of the gas layer; thus an optimum gas layer thickness can be derived. The values for the change in drag and the apparent slip length are strongly affected by the assumptions made for the flow in the gas phase. The standard assumptions of a constant shear rate in the gas layer or an equal pressure gradient in the gas layer and liquid layer give considerably higher values for the drag reduction and the apparent slip length than an alternative assumption of a vanishing mass flow rate in the gas layer. Similarly, a minimum viscosity contrast of four must be exceeded to achieve drag reduction under the zero mass flow rate assumption whereas the drag can be reduced for a viscosity contrast greater than unity under the conventional assumptions. Thus, traditional formulae from lubrication theory lead to an overestimation of the optimum slip length and drag reduction when applied to superhydrophobic surfaces, where the gas is trapped.

JFM classification

Multiphase and Particle-laden Flows: Core-annular flow Low-Reynolds-number flows: Low-Reynolds-number flows Multiphase and Particle-laden Flows: Multiphase flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 727 , 25 July 2013 , pp. 488 - 508
Copyright
©2013 Cambridge University Press 

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