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Modified Voronoi Analysis of Spontaneous Formation of Interfacial Droplets on Immersed Oil-Solid Substrates.

The nucleation and growth of liquid droplets on solid substrates have received much attention, due to the significant relevance of these multiphase processes in both nature and practical applications. There have been extensive studies on the condensation of water from air phase on solid substrates. Here we focus on water diffusion through oil phase and subsequent settlement on solid substrates, as such interfacial droplets form. Voronoi diagram analysis is proposed to statistically characterize the size distribution of the growing droplets. It is found that a modification of the standard Voronoi diagram is required for systems of interfacial droplets which have non-circular shape and/or whose centers change with time. The modified Voronoi analysis of the growing droplets provides an automatic quantification of droplet distribution and reveals that: (i) during the nucleation stage, the interfacial droplets do not nucleate at the same time, because the nucleation of newly-formed droplets competes with the growth of existing ones; (ii) the growth of interfacial droplets comes from water diffusion from the bulk water layer and/or from adjacent interfacial droplets, and/or coalescence of interfacial droplets; (ⅲ) the sizes of interfacial droplets become more polydispersed on P-glass but more monodispersed on OTS-glass as time goes. This work opens a new perspective on the formation of interfacial droplets at the interface between oil and solid substrate and demonstrates the capability of an automatic analysis method, which can be potentially applied to similar interfacial multiphase systems.