Dynamics of Gas Bubbles in a Plane Cluster under an Impulse Excitation

The dynamics of air bubbles in a square cluster in water under a cosinusoidal impulse of the water rarefaction has been studied. The impulse duration is 82.73 $$\mu$$ s. The dynamics of the bubbles is considered only until some of the bubbles is destroyed due to large deformations or collide. The cluster consists of 121 bubbles with their centers located at the nodes of a uniform square mesh with one bubble at the cluster center. Initially the bubbles and the liquid are at rest, all the bubbles are spherical, their radii are 0.1 mm, the distance between the neighboring bubbles is about 10 times their radii, the water pressure is 1 bar. A particle-model of interacting bubble dynamics allowing for the bubble translations and deformations is applied. It has been shown that three modes of the bubble dynamics can be distinguished, corresponding to the small, moderate and large values of the impulse amplitude. In the first mode, none of the bubbles is destroyed or collides with others, the radial oscillations of the bubbles, their deformations and translations are small and vanish asymptotically. In the second mode, some of the bubbles become destroyed due to large deformations, and in the third mode some bubbles collide. The maximum value of the pressure achieved inside the cluster bubbles is about 670 times their initial pressure.