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Nov 2009

Volume 21, Issue 11, Articles (11xxxx)

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Phys. Fluids 21, 115105 (2009); http://dx.doi.org/10.1063/1.3263703 (8 pages)

W. J. T. Bos, B. Kadoch, K. Schneider, and J.-P. Bertoglio
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back to top Viscous and Non-Newtonian Flows

The friction of a mesh-like super-hydrophobic surface

Anthony M. J. Davis and Eric Lauga

Phys. Fluids 21, 113101 (2009); http://dx.doi.org/10.1063/1.3250947 (8 pages) | Cited 10 times

Online Publication Date: 3 November 2009

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When a liquid droplet is located above a super-hydrophobic surface, it only barely touches the solid portion of the surface, and therefore slides very easily on it. More generally, super-hydrophobic surfaces have been shown to lead to significant reduction in viscous friction in the laminar regime, so it is of interest to quantify their effective slipping properties as a function of their geometric characteristics. Most previous studies considered flows bounded by arrays of either long grooves, or isolated solid pillars on an otherwise flat solid substrate, and for which therefore the surrounding air constitutes the continuous phase. Here we consider instead the case where the super-hydrophobic surface is made of isolated holes in an otherwise continuous no-slip surface, and specifically focus on the mesh-like geometry recently achieved experimentally. We present an analytical method to calculate the friction of such a surface in the case where the mesh is thin. The results for the effective slip length of the surface are computed, compared to simple estimates, and a practical fit is proposed displaying a logarithmic dependence on the area fraction of the solid surface.
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47.55.D- Drops and bubbles
66.20.-d Viscosity of liquids; diffusive momentum transport
46.55.+d Tribology and mechanical contacts

Optimal shapes for best draining

J. D. Sherwood

Phys. Fluids 21, 113102 (2009); http://dx.doi.org/10.1063/1.3262844 (7 pages) | Cited 2 times

Online Publication Date: 4 November 2009

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The container shape that minimizes the volume of draining fluid remaining on the walls of the container after it has been emptied from its base is determined. The film of draining fluid is assumed to wet the walls of the container, and is sufficiently thin so that its curvature may be neglected. Surface tension is ignored. The initial value problem for the thickness of a film of Newtonian fluid is studied, and is shown to lead asymptotically to a similarity solution. From this, and from equivalent solutions for power-law fluids, the volume of the residual film is determined. The optimal container shape is not far from hemispherical, to minimize the surface area, but has a conical base to promote draining. The optimal shape for an axisymmetric mixing vessel, with a hole at the center of its base for draining, is also optimal when inverted in the manner of a washed wine glass inverted and left to drain.
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47.15.Rq Laminar flows in cavities, channels, ducts, and conduits
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