Thermal conditions for the formation of self-assembled cluster of droplets over the water surface and diversity of levitating droplet clusters

The effect of temperature profile of the surface of a water layer on the formation and geometrical structure of a cluster of levitating droplets is studied in a series of laboratory experiments. The experiments show that a local temperature maximum of the water surface is a necessary condition for the droplet cluster formation. A quantitative criterion for the transformation of a monolayer of randomly placed microdroplets into a self-assembled cluster of relatively large droplets is obtained. A qualitative physical description of the formation of a flat levitating droplet cluster of an axisymmetric hexagonal structure is given, based on the experimentally verified concept of the decisive role of aerodynamic forces acting on water droplets from an upward vapor-air flow. Unusual droplet clusters resulting from high surfactant concentrations and rapidly changing or more intense local heating of the underlying water layer were observed. These are elegant ring clusters, small clusters of a controlled number of large droplets, and chain clusters with branching chains of droplets in their central part. The use of a recently developed experimental procedure based on the injection of initial microdroplets with a piezoelectric dispenser makes it possible to generate hierarchical clusters, which contain continuously transforming aggregates of several droplets held in contact by electrostatic interaction. An overview of various types of droplet clusters including relatively stable hexagonal clusters, emerging and rapidly breaking up ring-shaped clusters, small clusters of a desirable number of nearly identical droplets, chain clusters containing growing branched chains of water droplets, and hierarchical clusters with rearranged small groups of nearly merging droplets provides a complete picture not only of the transition from chaotically moving droplets to self-arranged clusters, but also of the diversity of droplet clusters.