Numerical investigation of central breakup of large bubble induced by liquid jet

A large spherical bubble rising in quiescent liquid generally leads to the formation of a toroidal bubble (central breakup). In this paper, we investigate the bubble dynamics during the central breakup process using the three dimensional Volume of Fluid method implemented in OpenFOAM. The potential energy of the large bubble is converted into the kinetic energy of the liquid jet, resulting in the formation of the toroidal bubble. Before the central breakup of the bubble, a high pressure zone is formed on the top of the bubble due to the collision of the liquid jet with the top of the bubble. We report for the first time that a protrusion is formed on the top of the toroidal bubble for a large spherical bubble rising in quiescent liquid. The velocity of the gas inside the toroidal bubble around the liquid jet is much faster than that in other places after the central breakup, which leads to the formation of the protrusion against the restriction of the surface tension force. We find that the bubble size, liquid viscosity, and density can influence the formation of the toroidal bubble, while the influence of surface tension is negligible. We summarize the above influencing factors into two dimensionless numbers: Galilei (Ga) number and Eötvös number (Eo). In the end, we discover a simple linear relation between the jet Reynolds number and the Ga number by analyzing all numerical experiments.