Dynamics of bubbles in a spherical cluster under increasing liquid pressure

The response of gas (air) bubbles in a spherical cluster to an increase in the pressure of the surrounding liquid (water) is considered. Consideration is carried out only until a bubble in the cluster disintegrates or collides with another bubble. The influence of the amplitude of the increase in the liquid pressure, as well as the position of the bubbles in the cluster and the interaction between the bubbles, is studied. The centers of the cluster bubbles are located at the nodes of a cubic grid, one of which is in the center of the cluster. The effect of the interaction of bubbles is assessed by comparison with the response of a single bubble. The cluster consists of $123$ bubbles, the liquid pressure is $1$ bar. Initially, the bubbles are spherical with a radius of $0.1$ mm, the cluster radius is about $3$ mm. A discrete model is used, in which, together with the radial oscilations of bubbles, their movements in the liquid and their small deformations are also modeled. It is established that the maximum pressure in the bubbles, reached before the destruction or collision of any of them, is realized when the liquid pressure increases by $10$ bar and turns out to be approximately $6500$ times greater than their initial pressure and approximately $30$ times greater than the response of a single bubble.