Collapse of Equal Symmetrically Located Spherical Cavitation Bubbles

Joint collapse of \(2\) , \(3,\) and \(4\) equal spherical vapor bubbles in water has been studied. The bubbles are symmetrically distributed in liquid, so that their centers are positioned at the end points of a line segment, vertices of an equilateral triangle or a tetrahedron The distance between any two bubbles is the same and is sufficiently large. Such symmetrical configurations are of interest since their mathematical model is reduced to a system of equations for only one bubble because the dynamics of others is the same. The system includes ordinary differential equations in the liquid velocity on the bubble surface, the uniform vapor pressure in the bubble and the bubble radius, and the partial differential equations in the vapor and liquid temperature with the corresponding boundary and initial conditions. The liquid compressibility effect is divided into two aspects. The first one allows for the energy losses from the generation of the acoustic disturbances diverging from bubbles, the second one takes into account the time delay in the influence of acoustic disturbances coming from other bubbles. It has been shown that in the case of four bubbles ( \(N=4\) ), the influence of the liquid compressibility due to generating diverging disturbances and the heat conductivity of both phases on the ratio of the pressure maximum in the bubbles with and without allowing for their interaction is small. The maximum pressures in the bubbles during collapse with the time delay is lower than without it. Collapses of bubbles with and without the mass exchange on the bubble surface are rather different. In particular, when it is taken into account, the difference between maximum pressures in the bubbles with and without neglecting their interaction is rather small when the time delay is allowed for. All features of the bubble dynamics in the case of \(N=4\) with and without the time delay are also typical for the cases of \(N=2\) and \(3\) . And with decreasing \(N\) , all the results gradually approach those in the case of a single bubble.