Eur. Phys. J. E (2013) 36: 104
https://doi.org/10.1140/epje/i2013-13104-2

Regular Article

Is superhydrophobicity robust with respect to disorder?

¹ Laboratory of Surface and Interfacial Physics, University of Mons, Avenue Maistriau, 19, 7000, Mons, Belgium
² Laboratory of Physics: Theory and Models, CNRS UMR 8089, Cergy-Pontoise University, 95302, Cergy-Pontoise, France

^* e-mail: francois.dunlop@u-cergy.fr

Received: 21 January 2013
Revised: 26 July 2013
Accepted: 19 August 2013
Published online: 26 September 2013

Abstract

We consider theoretically the Cassie-Baxter and Wenzel states describing the wetting contact angles for rough substrates. More precisely, we consider different types of periodic geometries such as square protrusions and disks in 2D, grooves and nanoparticles in 3D and derive explicitly the contact angle formulas. We also show how to introduce the concept of surface disorder within the problem and, inspired by biomimetism, study its effect on superhydrophobicity. Our results, quite generally, prove that introducing disorder, at fixed given roughness, will lower the contact angle: a disordered substrate will have a lower contact angle than a corresponding periodic substrate. We also show that there are some choices of disorder for which the loss of superhydrophobicity can be made small, making superhydrophobicity robust.