Study on splitting of a toroidal bubble near a rigid boundary

The splitting of a toroidal bubble near a rigid boundary is commonly observed in experiments, which is a quite complex phenomenon in bubble dynamics and still not yet well understood. In present study, the bubble splitting phenomenon is studied using the boundary integral method. The vortex ring model is extended to multiple vortex rings to simulate the interaction between two toroidal bubbles after splitting. Buoyancy and non-buoyancy cases are investigated numerically in this study. Numerical results with buoyancy effects show favorable agreement with the experimental observations, which validates the present model. Generally, the first split of the toroidal bubble occurs when an annular “sideways jet” collides with the other side of the bubble. After the toroidal bubble splitting, some new phenomena are found as follows: (i) An annular high pressure region is generated at the splitting location, and the maximum pressure is associated with the velocity differences between the two sides therein just before splitting. (ii) The total volume varies continuously, while the two sub-bubbles vary differently in volume after splitting. (iii) The sideways jet continues propagating on a sub-bubble surface, which would cause more splits or partial breakup of the splash film into droplets. This may be an important reason for the formation of bubble cloud and the rough bubble surface in the rebounding process.