  Droplet coalescence is a common phenomenon and plays an important role in
multi-disciplinary applications. Previous studies mainly consider the
coalescence of miscible liquid, 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 timescales and force interactions
involved, namely (I) the growth of the 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 timescale
considering both surface and interfacial tensions, we show that the interfacial
tension between the two immiscible liquids functions as a nonnegligible
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 timescales involved during the
displacement of water by oil; a new model based on energy balance is proposed
to analyze the maximum retraction velocity, highlighting that the viscous
resistance is concentrated in a region close to the contact line.
