The friction of a mesh-like super-hydrophobic surface

• Published in: Physics of fluids (1994) 2009-11, Vol.21 (11), p.113101-113101-8
• Main Authors: Davis, Anthony M. J., Lauga, Eric
• Format: Article
• Language: English
• Subjects: Condensed matter: structure, mechanical and thermal properties; Drops and bubbles; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Nonhomogeneous flows; Physics; Solid-fluid interfaces; Surfaces and interfaces; thin films and whiskers (structure and nonelectronic properties); Wetting
• ISSN: 1070-6631; 1089-7666
• DOI: 10.1063/1.3250947

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.