Radius evolution for the synchronous collapse of a circular vapor bubble cluster

The radius evolution for the synchronous collapse motion of a circular vapor bubble cluster in an ideal and infinite fluid is studied. With the assumption that all bubbles are evenly distributed around the circumference and have the same initial conditions, we establish the associated governing equation for this case from a modified Rayleigh–Plesset equation. The inverted analytical solution in the form of t=t(r) and analytical approximations in the form of r=r(t) for the radius evolution to the initial value problem of the dimensionless governing equation are derived. These novel analytical approximations extend the previous ones for a single bubble by adding the effects of surface tension and multiple bubbles. In addition, we point out that the analytical results and dynamic behaviors for multiple bubbles will degenerate into the corresponding ones for single bubbles when the radius of the bubble cluster approaches to infinity. •The governing equation for the synchronous collapse motion of a circular vapor bubble cluster is established.•The inverted analytical solution and analytical approximations are derived.•The effects of surface tension and multiple bubbles are included in the obtained solutions.•The limiting behaviors of the circular vapor bubble cluster are discussed.