Dynamics of Gas Bubbles in a Spherical Cluster Under a Single Harmonic Pulse of Liquid Compression

The response of initially spherical air bubbles (of the same radius) in a spherical cluster (with the radius of about 45 times the radius of the bubbles) to the variation of the liquid (water) pressure in the form of a single cosine-like liquid compression pulse is considered. The liquid compression pulse duration is equal to the period of the natural oscillations of the cluster. All bubbles are assumed to remain only weakly nonspherical during the response. The cluster is formed by bubbles with the centers at the nodes of a cubic mesh (one of which is located at the cluster center). The influence of the bubble-bubble interaction, the forcing pulse amplitude, the bubble position and the number of bubbles in the cluster is investigated. The effect of the interaction between bubbles is estimated by comparison with the dynamics of a single bubble under the same conditions. The dynamics of bubbles in the cluster is governed by the second-order ODEs in the radii of the bubbles, the position-vectors of their centers and the amplitudes of their non-sphericity in the form of spherical harmonics. It has been found that the maximum values of the number of bubbles in the cluster and the pulse amplitude under the condition that all bubbles during the response remain only weakly non-spherical, are about 81 and 0.16 times the liquid pressure, respectively. The maximum pressure attained in the cluster bubbles during the response in the corresponding ranges of the pulse amplitude and the number of bubbles in cluster is only about 33% higher than their initial pressure.