Numerical investigation on the dynamics of two bubbles

•Two toroidal bubbles interaction is simulated by introducing the vortex rings model.•Experiment for two bubbles interaction is conducted to validate the numerical model.•Velocity and pressure fields are calculated to reveal the physical mechanisms.•The jetting laws in two-bubble interaction are investigated.•Two differently sized bubbles interaction is classified in a graph according to two parameters.

Two-bubble interaction has wide applications, such as cavitation, seabed exploration and underwater explosions, in which bubble collapse and jetting are the most focused issues. Based on the incompressible potential flow theory coupled with the boundary integral method, we investigate the dynamics of two differently sized bubbles. After jets penetrate the two bubbles, vortex rings model is introduced to simulate the subsequent evolution of two toroidal bubbles. To validate the present model, the results are compared with the experiment recorded by a high-speed camera and the data in a published literature. Favorable agreements of bubble shape history are observed. Then, the influence of the size ratiol(defined as l=Rm,1/Rm,2, Rm,1≤Rm,2; Rm is the maximum radius attained in a free field) on bubble behaviors is investigated numerically. Annular jet leading to bubble splitting, axial jet formation towards and away from the larger bubble are observed. It is also found that the minimum jet velocity of the smaller bubble and the strongest jet impact of the larger bubble are obtained when l is around 0.8. Finally, the two-bubble interaction is classified in a graph according to the size ratio and the inter-bubble distance. The splitting phenomenon occurs only when l≤0.5.