Interactions by exchange of volume between two spherical bubbles

Abstract

In this paper, by using the system potential of two bubbles and with a special interest in the interaction by exchange of volume and without exchange of mass, a system of equations governing the evolution of two bubbles is proposed. This two-bubble model shows terms that do not appear in the models of interaction between bubbles. The twobubble model is compared with the modified Rayleigh–Plesset equation and a validation with the experimental study of Ohl [2002] is presented. The numerical results show that, on one hand, the development of small nearby bubbles can slow down the evolution of the biggest local one, while their disappearance can favor its growing. Furthermore, in the case of two bubbles in particular, the small bubble exchanges volume with the big one during their evolutions. On the other hand, contrary to the modified Rayleigh–Plesset model, the two-bubble model predicts appearance and disappearance of small bubbles in the neighborhood of the big bubble as it is observed in the experimental study of Ohl [2002]. The present findings show in particular that the interaction by exchange of volume can be very important in the cavitation born phase and it is necessary to take into account the interaction between bubbles as well as the disappearance of small ones on the evolution of the biggest local bubble. Also, this two-bubble model predicts an exchange of volume between both bubbles equal to zero when they are perfectly identical.