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.
Experiments on the pulsation of the high-voltage electrical-spark bubbles near different boundaries are conducted by means of high-speed photography. Some intriguing details are observed clearly, such as the formation of the jet (especially the contact jet formed when a bubble is quite close to the rigid boundary) and bubble splitting. The variation of the maximum radius of the bubble, bubble period, jet tip velocity, and bubble center migration is investigated with the presence of different boundaries. In the study of the bubble period, two fitting curves are obtained from the data by the author and previous references; one is for the bubble generated beneath the free surface and the other is for the bubble generated above the rigid boundary. In the study of the maximum jet tip velocity, a possible trend line is proposed to describe the variation of the jet tip velocity with γb (the non-dimensional standoff distance from the bubble center to the rigid boundary). Finally, the critical value of γb is studied, at which the migration of the bubble center is inverted.
Highlights
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