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

Change in drag, apparent slip and optimum air layer thickness for laminar flow over an idealised superhydrophobic surface
Change in drag, apparent slip and optimum air layer thickness for laminar flow over an idealised superhydrophobic surface
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.
core-annular flow, low-Reynolds-number flows, multiphase flow
0022-1120
488-508
Busse, Angela
0430b320-341b-4c73-9cb5-f35632d562a4
Sandham, Neil D.
0024d8cd-c788-4811-a470-57934fbdcf97
McHale, Glen
8f4a9960-c9ac-4754-b219-40ce3a45c65e
Newton, Michael I.
0d2aa5ce-f5d7-4641-8192-ee6f96d8a1e3
Busse, Angela
0430b320-341b-4c73-9cb5-f35632d562a4
Sandham, Neil D.
0024d8cd-c788-4811-a470-57934fbdcf97
McHale, Glen
8f4a9960-c9ac-4754-b219-40ce3a45c65e
Newton, Michael I.
0d2aa5ce-f5d7-4641-8192-ee6f96d8a1e3

Busse, Angela, Sandham, Neil D., McHale, Glen and Newton, Michael I. (2013) Change in drag, apparent slip and optimum air layer thickness for laminar flow over an idealised superhydrophobic surface. Journal of Fluid Mechanics, 727, 488-508. (doi:10.1017/jfm.2013.284).

Record type: Article

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.

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More information

e-pub ahead of print date: 28 June 2013
Published date: July 2013
Keywords: core-annular flow, low-Reynolds-number flows, multiphase flow
Organisations: Aerodynamics & Flight Mechanics Group

Identifiers

Local EPrints ID: 354414
URI: http://eprints.soton.ac.uk/id/eprint/354414
ISSN: 0022-1120
PURE UUID: 228e8d77-75b9-41cd-9631-1b59924f01d6
ORCID for Neil D. Sandham: ORCID iD orcid.org/0000-0002-5107-0944

Catalogue record

Date deposited: 15 Jul 2013 09:15
Last modified: 21 Nov 2021 05:01

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Contributors

Author: Angela Busse
Author: Neil D. Sandham ORCID iD
Author: Glen McHale
Author: Michael I. Newton

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