Busse, Angela, Sandham, Neil, McHale, Glen and Newton, Michael (2013) Change in drag, apparent slip and optimum air layer thickness for laminar flow over an idealised superhydrophobic surface. Journal of Fluid Mechanics, 727. pp. 488508. ISSN 00221120
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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 pressuredriven 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.
Item Type:  Article 

Uncontrolled Keywords:  drag, slip, superhydrophobic, Leidenfrost, Core Annular Flow 
Subjects:  F200 Materials Science F300 Physics H100 General Engineering 
Department:  Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering 
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Depositing User:  Glen Mchale 
Date Deposited:  02 Jan 2014 11:21 
Last Modified:  30 Oct 2017 13:57 
URI:  http://nrl.northumbria.ac.uk/id/eprint/14932 
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 Change in drag, apparent slip and optimum air layer thickness for laminar flow over an idealised superhydrophobic surface. (deposited 02 Jan 2014 11:21) [Currently Displayed]
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