Flow features and jet formation in droplet–bubble collision

We investigate head-on droplet–bubble collisions in a quiescent, surfactant-free viscous liquid using three-dimensional volume-of-fluid simulations. By systematically varying the bubble-to-droplet radius ratio (

) and Weber number (

3 less than or equals italic We less than or equals 270 3 ≤ We ≤ 270 $3\le \textit{We}\le 270$

) at small Ohnesorge number (

italic Oh less than 1 Oh < 1 $ \textit{Oh}\lt 1$

), we identify the mechanisms governing interfacial deformation, attachment, jet formation and vortex evolution during an isolated collision. Four distinct collision regimes emerge, ranging from oscillatory attachment to jet-mediated penetration and coupled toroidal deformations. A transition from weak- to inertia-dominated dynamics occurs at a critical Weber number of

italic We almost equals 23 We ≈ 23 $ \textit{We}\approx 23$

, nearly independent of

upper Delta Δ $\varDelta$

, whereas the onset of complete jet penetration depends strongly on the size ratio. Comparison with the unsteady Oseen solution for an impulsively accelerated rigid sphere establishes a hydrodynamic baseline that isolates the effects of interface mobility and deformation, revealing the progressive emergence of toroidal vortices, interfacial oscillations and jetting. An energy analysis demonstrates that jet formation is controlled by the conversion of impact kinetic energy into surface energy, yielding a characteristic jet velocity comparable to the impact speed, while viscous dissipation suppresses jetting above a critical Ohnesorge number scaling as

italic Oh Subscript c Baseline tilde upper W e Superscript negative 1 divided by 2 Oh c ∼ W e − 1 / 2 $ \textit{Oh}_c\sim We^{-1/2}$

. These results provide a unified physical framework linking inertia, capillarity and vortex dynamics in elementary droplet–bubble interactions, offering predictive insight into multiphase processes such as flotation, aeration, emulsification and liquid–liquid separation.