Dynamics of Gas Bubbles in a Spherical Cluster under Stochastic Distribution of Their Size and Position

The influence of the stochastic distribution of the size and position of the bubbles in a spherical cluster on the bubble dynamics is investigated. The cluster is excited by the decrease and subsequent increase of the liquid pressure in the form of a single cosine-like pulse with the duration equal to the period of the natural oscillations of the cluster. The stochastic clusters are produced from a cluster with the bubbles located at the nodes of a uniform cubic grid by corresponding deviation of the bubble size and position. All bubbles in the clusters are assumed to remain weakly nonspherical during the response.The dynamics of bubbles is described 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 shown that the stochastic deviation of the bubble size and position increases the translational motion of the bubbles and their maximum non-spherical deformations. With the stochastic deviation of the bubble size, the focus of the largest bubble compression is shifted from the cluster center. The influence of the stochastic deviation of the bubble position on the maximum compression of the central bubble in the cluster is weak. With the stochastic deviation of the bubble size, the maximum compression of the central bubble in the cluster tends to decrease, whereas the maximum compression over all bubbles tends to increase.