Dynamics of sliding drops on superhydrophobic surfaces

– We use a free energy lattice Boltzmann approach to investigate numerically the dynamics of drops moving across superhydrophobic surfaces. The surfaces comprise a regular array of posts small compared to the drop size. For drops suspended on the posts the velocity increases as the number of posts decreases. We show that this is because the velocity is primarily determined by the contact angle which, in turn, depends on the area covered by posts. Collapsed drops, which fill the interstices between the posts, behave in a very different way. The posts now impede the drop behaviour and the velocity falls as their density increases. Introduction. – The aim of this letter is to explore numerically how micron-scale drops move on superhydrophobic surfaces. If surfaces with contact angles greater than 90 are patterned with posts small compared to the drop dimensions the equilibrium contact angle is increased and can reach values close to 180. Such superhydrophobic surfaces are found in nature: for example the leaves of several plants, such as the lotus are covered in tiny bumps which may have evolved to aid the run-off of rain water. Recent microfabrication techniques have allowed superhydrophobic patterning to be mimicked and carefully controlled experiments on the behaviour of drops on superhydrophobic substrates are increasingly becoming feasible [1]. Drops on superhydrophobic surfaces can be in two states. Suspended drops lie on top of the posts with air pockets beneath them whereas collapsed drops fill the interstices between the posts. A suspended drop has a higher contact angle than the equivalent collapsed drop which in turn has a higher contact angle than a drop on a flat surface made of the same material. Several authors have shown that the equilibrium properties of the drops follow from thermodynamic arguments based on free energy minimisation [2–5]. Both the suspended and collapsed states can provide the global minimum of the free energy, with the phase boundary between them depending on the surface tension, the contact angle on the flat surface and the post geometries [6, 7]. The suspended drop may often exist as a metastable state as it has to cross a free energy barrier to fill the grooves [3, 8]. There is, however, no similar understanding of the way drops move across superhydrophobic surfaces. Several authors [9–11] have considered contact angle hysteresis in the context of