Deformation and breakup of bubbles interacting with single vortex rings

Abstract The turbulent breakup of bubbles is a complex phenomenon present in a large number of engineering applications and natural processes. Simplified models are essential to better understand the interaction between turbulent eddies and bubbles. Probably the simplest one is that given by a vortex ring colliding with a single bubble. With this motivation, in the present work we perform three-dimensional numerical simulations of a single vortex ring of initial circulation Γ 0 , radius R 0 and Reynolds number R e = Γ 0 / ν l = 15 , 000 , interacting with a bubble of radius R b immersed in a liquid of kinematic viscosity ν l . The temporal evolution of the vortex ring is compared with analytical models for the size of the vortex core, a ( t ) , the kinetic energy, E k ( t ) , and the enstrophy Ω ( t ) , looking for a concurrence of this magnitude with the rate of dissipation of E k . The dynamics of the bubble-vortex interaction process is described varying the vortex-to-bubble size ratio, R 0 / R b , and the Weber number, W e = ρ l ( Γ 0 / 2 π R 0 ) 2 / ( σ / R b ) . With respect to the bubble, the simulations show that vortices smaller or of the same size as the bubble are not able to break it up. However, vortices slightly larger, although of comparable sizes, can efficiently break the bubble after trapping it inside the vortex core. In these cases, if the Weber number is sufficiently large, the bubble migrates to the vortex core, where the strain is maximum, and elongates along the azimuthal direction to eventually break by a Rayleigh-Plateau mechanism. In fact, we observe that the bubbles always break if W e ⪆ 1 when R 0 / R b > 1 . The numerical results are corroborated experimentally for vortex-to-bubble diameter ratios in the range 2.28 ≤ R 0 / R b ≤ 7.5 . Regarding the vortex ring, it is observed that when the vortex decelerates the bubble while they interact, the vorticity contained in the bubble boundary layer is engulfed by the vortex core, destabilizing the vortex ring. This makes the total enstrophy to suddenly increase due to the vorticity generation by the vortex stretching mechanism that follows the lost of axial symmetry. This increase in enstrophy is associated to a rapid decrease of kinetic energy, especially at low Weber numbers.