Collapse behaviors of synchronous bubble clusters

In this work, we analyze the radius evolution during the collapse process of a synchronous bubble cluster in an ideal, infinite fluid. The governing equation is derived from a modified Rayleigh–Plesset equation under the assumption of a symmetric bubble configuration and identical initial conditions. By neglecting liquid viscosity and compressibility, we demonstrate that a general analytical solution can be obtained through the algebraic method or the Weierstrass elliptic function method. The resulting solution is expressed in terms of an implicit function or the Weierstrass elliptic function. As applications, we examine how the behaviors of the bubbles with different configurations depend on key physical parameters. The results show that, similar to the case of a single bubble, the surface tension also significantly affects the motion of bubbles in a multi-bubble system when the bubble size is less than 10 μm. The dynamic similarity between the motions of synchronous multi-bubble systems with different configurations is discussed. In addition, the prolongation factors of one bubble near a wall and of synchronous bubble clusters are obtained, respectively, by the theoretical method.