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Abstract

Hydrophobic substrates with topographic roughness possess the remarkable property of strong water-repellency, the so called super-hydrophobic behavior. When deposited on hydrophobic substrates decorated with a topographic pattern, liquid droplets typically are observed to occur in two distinct states: (i) the Cassie/Baxter (or fakir) state, where the droplet rests on top of the roughness structures, and (ii) the Wenzel state, where the droplet penetrates into the grooves and completely wets the substrate. While virtually all studies hitherto have been considering droplets much larger than the roughness scale of the substrate, we, for the first time, investigate the case where the size of the droplet is comparable to the surface asperities. This is a very natural situation that occurs whenever a liquid drop condenses or evaporates on such a substrate. We find a new stable state where the droplet is partially impaled, not yet contacting the bottom substrate. Contrary to the known curvature-driven impalement of a large droplet, the penetration depth decreases upon evaporation, effectively leading to a cleaning of the substrate by the recessing droplet. This new phenomenon is expected to occur in any hydrophobic capillary wetting situation where a spherical liquid reservoir is involved. The scale invariance of the predicted behavior is demonstrated. The new stable state can, therefore, be studied experimentally using relatively large (millimetric) drops thus facilitating the preparation of topographic patterns and circumventing problems related to the short lifetime of microdroplets.