Droplet encapsulating bubble: Investigation of droplet spreading dynamics and bubble encapsulation time

Abstract: Ternary interactions between hetero-fluid particles, particularly the dynamics of droplets spreading over curved fluid interfaces remain insufficiently understood compared to the two-phase coalescence. In this study, we combine lattice Boltzmann simulations, high-speed imaging, and theoretical scaling to investigate the collision and encapsulation of an air bubble by a rising oil droplet in an immiscible medium. We systematically vary fluid properties, droplet-to-bubble size ratios, and collision configurations to quantify their impact on encapsulation time and flow evolution. The process unfolds in four stages: collision/film drainage, encapsulation, reshaping, and compound rising. Results indicate that encapsulation time increases exponentially with viscosity and is strongly modulated by the spreading coefficient (So), which governs the imbalance of interfacial tensions. Higher So values enhance capillary-driven spreading and reduce engulfment time, while lower values yield coupled deformation-reshaping behavior, introducing oscillations in bubble velocity and shape evolution. For low viscosity drops (Oh<0.1), the neck growth rate follows the well-known power-low relation with an exponent of 0.44-0.5, dependent on the size ratio. The transition between the spherical and deformed regimes is identified. Our theoretical analysis reveals that in low Bond numbers (Bo<0.11), spreading speed scales with viscous-capillary velocity, while in the deformed regime (0.11<Bo<2.2), encapsulation time follows a capillary-gravitational timescale. Interestingly, smaller droplets expedite encapsulation in equal-sized collisions but delay it in size-mismatched pairs, despite a faster initial neck growth. These findings provide new mechanistic insight into three-fluid interactions and offer guidance for optimizing encapsulation processes in applications such as gas flotation and interfacial microfluidics.