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 because of the significant relevance of these multiphase processes to both nature and practical applications. There have been extensive studies on the condensation of water from the air phase on solid substrates. Here, we focus on water diffusion through the oil phase and subsequent settlement on solid substrates because such interfacial droplets are formed. Voronoi diagram analysis is proposed to statistically characterize the size distribution of the growing droplets. It is found that modification of the standard Voronoi diagram is required for systems of interfacial droplets which have a noncircular shape and/or whose centers change with time. The modified Voronoi analysis of the growing droplets provides an automatic quantification of the 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 the 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 from coalescence of interfacial droplets; and (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 the solid substrate and demonstrates the capability of an automatic analysis method, which can be potentially applied to similar interfacial multiphase systems.