Inertial droplet dynamics inside a quiescent liquid medium

Inspired by wastewater treatment technologies such as aeration, in this work, we have numerically investigated the dynamics of a collision between a single bubble and a droplet in a quiescent ambient liquid to establish limits required for a successful droplet capture onto a bubble surface (and vice versa). We have varied the bubble diameter to the droplet diameter (∆) in the range of 0.5 to 2 and the droplet Weber number, between 13 to 270, to achieve a head-on collision. An initially accelerated droplet in a viscous liquid can generate a vortex-based liquid jet that can deform the (primary) droplet into a dimpled one or to a toroidal ring with or without a secondary droplet generation. In the case of a bubble-droplet collision, based on the W e d -∆ map, we have identified four regimes, in which (I) the primary droplet attaches to the bubble surface without any secondary droplet generation, (II) instead of the primary one, the generated secondary tiny droplet attaches to the bubble, (III) the droplet deforms into a toroidal ring and attaches to the bubble surface, and (IV) both the droplet and the bubble deform into elongated toroidal rings and a sleeve like attachment takes place. We find the bubble-droplet collisional outcome has a co-existence of regimes I, II and III around We_d ≈ 23 and ∆ = 0.8. The transition from regime III to IV takes place at high Webre numbers, and the boundary separating the mentioned regimes follows W e d inversely proportional to ∆. Via the total energy balance approach, we have constructed a scaling law to describe the transition behaviour from regime III to IV.