Response of Gas Bubbles in Spherical Clusters to a Single Underpressure Pulse

Abstract

The paper studies the response of gas (air) bubbles in a spherical cluster to a single pulsed cosine-shaped decrease and subsequent recovery of the pressure of the surrounding liquid (water–glycerin mixture) with a pulse duration in the vicinity of the period of natural oscillations of the cluster. It is assumed that, during the response, all bubbles remain weakly nonspherical. The effect of the duration and amplitude of the excitation pulse, the position of bubbles in the cluster, the distance between bubbles, and the number of bubbles in the cluster is studied. Cubic clusters in which the centers of the bubbles are located at the nodes of a cubic grid, as well as clusters with a random arrangement of bubbles and with bubbles located at the center and vertices of a number of regular polyhedra nested in each other are considered. To estimate the effect of the interaction between bubbles, comparison with the response of a single bubble is made. One of the variants of discrete models of the dynamics of bubbles in a cluster is used, in which, along with radial oscillations, their spatial displacements and small nonspherical deformations are simulated. It has been established that, if the nonspherical deformations of the bubbles during the response are small, the maximum increase in pressure in the bubbles relative to its initial value is at most several-fold. If this assumption is ignored, significantly higher degrees of bubble compression can be obtained. The reason is that, when the condition of smallness of deformations is violated, the ranges of the parameters under consideration expand significantly.