The friction of a mesh-like super-hydrophobic surface

When a liquid droplet is located above,I super-hydrophobic surface, it only barely touches the solid portion of the surface, and therefore slides very easily oil 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 ether long grooves. or isolated solid pillars oil 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 oil 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 oil the area fraction of the solid surface 0 2009 American Institute of Physics. [doi: 10.1063/1.3250947]