Coalescence of immiscible sessile droplets on a partial wetting surface

Abstract

Droplet coalescence is a common phenomenon and plays an important role in multidisciplinary applications. Previous studies mainly consider the coalescence of miscible liquids, even though the coalescence of immiscible droplets on a solid surface is a common process. In this study, we explore the coalescence of two immiscible droplets on a partial wetting surface experimentally and theoretically. We find that the coalescence process can be divided into three stages based on the time scales and force interactions involved, namely (I) the growth of a liquid bridge, (II) the oscillation of the coalescing sessile droplet and (III) the formation of a partially engulfed compound sessile droplet and the subsequent retraction. In stage I, the immiscible interface is found not to affect the scaling of the temporal evolution of the liquid bridge, which follows the same 2/3 power law as that of miscible droplets. In stage II, by developing a new capillary time scale considering both surface and interfacial tensions, we show that the interfacial tension between the two immiscible liquids functions as a non-negligible resistance to the oscillation which decreases the oscillation periods. In stage III, a modified Ohnesorge number is developed to characterize the visco-capillary and inertia-capillary time scales involved during the displacement of water by oil; a new model based on energy balance is proposed to analyse the maximum retraction velocity, highlighting that the viscous resistance is concentrated in a region close to the contact line.