Tunable structures of compound droplets formed by collision of immiscible microdroplets

We study the dynamics of a small water droplet colliding with an immiscible large sessile oil droplet in the air. Such a three-phase system forms compound microdroplets with tunable structures, depending on whether the small droplet can penetrate into the large one. A structure of penetrative-engulfing is distinguished from structures which are determined by balancing of the three interfacial tensions among the three phases, i.e., partial-engulfing and complete-engulfing. We develop a three-phase volume-of-fluid method to investigate the collision dynamics numerically, considering the evolution of the triple-line among the three interfaces. Regime maps of the structures for different spreading parameters and heights of the oil droplet are obtained regarding the impact velocity and the viscosity ratio of oil and water. We find that the oil droplet is impenetrable when the viscosity ratio is higher than a critical value. For lower ratio, the structure varies non-monotonically with the impact velocity to cause two transitions. We propose a simple model for the lower transition by incorporating droplet deformation, viscous resistance, and spreading condition. The upper transition boundary is influenced by the spreading of the oil droplet, resulting in an increase in the required penetration length to prevent penetrative-engulfing. Understandings from this work may provide valuable guidelines for generating compound microdroplets with desired structures.