Self-assembled levitating clusters of water droplets: pattern-formation and stability.

Water forms ordered hexagonally symmetric structures (snow crystals) in its solid state, however not as liquid. Typically, mists and clouds are composed of randomly moving small droplets lacking any ordered structure. Self-organized hexagonally patterned microdroplet clusters over locally heated water surfaces have been recently observed. However, many aspects of the phenomenon are far from being well understood including what determines droplets size, arrangement, and the distance between them. Here we show that the Voronoi entropy of the cluster tends to decrease indicating to their self-organization, while coupling of thermal effects and mechanical forces controls the stability of the clusters. We explain the balance of the long-range attraction and repulsion forces which stabilizes the cluster patterns and established the range of parameters, for which the clusters are stable. The cluster is a dissipative structure similar to self-organized Rayleigh-Bénard convective cells. Microdroplet formation plays a role in a variety effects from mist and clouds to aerosols. We anticipate that the discovery of the droplet cluster phenomenon and its explanation will provide new insights on the fundamental physical and chemical processes such as microdroplet role in reaction catalysis in nature as well as new tools for aerosol analysis and microfluidic applications.