Coalescence of immiscible droplets in liquid environments

Hypothesis: Droplet coalescence process is important in many applications and has been studied extensively when two droplets are surrounded by gas. However, the coalescence dynamics would be different when the two droplets are surrounded by an external viscous liquid. The coalescence of immiscible droplets in liquids has not been explored. Experiments: In the present research, the coalescence of two immiscible droplets in low- and high-viscosity liquids is investigated and compared with their miscible counterparts experimentally. The coalescence dynamics is investigated via high-speed imaging, and theoretical models are proposed to analyze the growth of the liquid bridge. Findings: We find that, the liquid bridge $r$ evolves differently due to the constraint from the triple line in the bridge region, which follows $r\propto {{t}^{{2}/{3}}}$ for low-viscosity surroundings. While for high-viscosity surroundings, the liquid bridge grows at a constant velocity ${{u}_{r}}$ which varies with the surrounding viscosity ${{\mu }_{s}}$ as ${{u}_{r}}\propto {{\mu }_{s}}^{{1}/{2}}$. In the later stage of the bridge growth, the bridge evolution again merges with the well-established power-law regime $r\propto {{t}^{{1}/{2}}}$, being either in low or high-viscosity liquids. Moreover, a new inertia-viscous-capillary timescale is proposed, which unifies the combined influence of inertia, viscous, and capillary forces on the evolution of the liquid bridge in liquid environments, highlighting the joint role of inertia and viscous resistance in the coalescence process.