Dynamics of spherical gas bubbles in a cluster under an increase in the surrounding liquid pressure

Abstract

The influence of the hydrodynamic interaction of spherical gas bubbles in linear, circular and ball-shaped clusters under a sudden increase in the surrounding liquid pressure is studied. The centers of the bubbles are located at the nodes of a uniform one-dimensional mesh on a segment of a straight line in the linear clusters, at the nodes of a uniform two-dimensional mesh inside a circular region of a plane in the circular clusters and at nodes of a uniform three-dimensional mesh inside a spherical region in the ball-shaped clusters. Initially, the liquid and the bubbles are at rest, the liquid pressure is 1 bar, the bubble radius is 0.25 mm, and the size of the mesh cells is 5 mm. The pressure rises by 0.8 bar. A mathematical model is applied, in which the dynamics of bubbles is described by the second-order ODEs in the radii of the bubbles and the position-vectors of their centers. It is shown that the radial oscillations of the bubbles in the clusters are significantly different from those of a single bubble. In particular, the period of their oscillations is longer, their damping is non-monotonic (with beats). The amplitudes of the oscillations and their beats are much greater in the central bubbles of the clusters than in the peripheral ones. The process of decay of the radial oscillations of the central bubbles in the circular and ball-shaped clusters begins with the phase of their amplification, during which the bubble pressure maximum becomes higher than the maximum achieved during the oscillations of a single bubble. Moreover, with growing number of bubbles in these clusters, the rate of damping of their oscillations decreases, and the oscillation beat frequency of both the central and peripheral bubbles increases.