Collapse of a Cavitation Bubble Surrounded by a Ring of Similar Bubbles

Joint collapse of a cluster of equally sized spherical vapor bubbles in water is considered in the case one of the bubbles (the central one) is located at the center of the cluster, the others (the peripheral ones) are equidistant from it and uniformly distributed on a ring with the initial spacing of ten initial radii of the bubbles. With increasing the ring radius, the number of bubbles on the ring grows, provided their spacing remains the same. The effects of such coupling of the number of bubbles on the ring and its radius as well as the time delay in the bubble-bubble interaction are studied. The mathematical model takes into account the evaporation and condensation on the surfaces of bubbles. It has been shown that the mentioned coupling without allowing for the time delay mainly influences the collapse of the peripheral bubbles, which increasingly strengthens with growing the ring radius. The time delay leads to that at a ring radius value larger than a critical one, the central bubble collapse becomes independent of the peripheral bubble collapse, and vice versa but with another critical radius. At the ring radii less than the critical ones, the collapse intensity of the central and peripheral bubbles only slightly differs from that of a single bubble (no more than 10 $$\%$$ in terms of maximum vapor pressure inside the bubbles). A number of useful expressions using numerical data for a single bubble are presented.