Effects triggered by singular solutions in single bubble collapse

The Rayleigh problem defined as the collapse of a cavity in a liquid at a higher ambient pressure is an idealized situation relevant in many applications related to cavitation, sonochemistry, sonoluminiscence, medical treatments and more in general inertially driven collapse processes. In the simplest model the bubble is assumed to remain spherical during the entire collapse process leading to an extreme concentration of the energy of the system. The solution of the bubble radius evolution for the particular case of an empty void has a singularity at a finite time that provides the well-know Rayleigh collapse time. This analysis can be extended to account for the presence of non-condensable gases providing theoretical estimates about the finite peak pressures and temperatures that can be reached. In this presentation we revisit the analytical expressions for the singular collapse of gas/vapor bubbles to discuss the importance of phase change and Rayleigh–Taylor instabilities on the peak pressures reached during the bubble collapse as well as the energy dissipated and released as an outgoing wave. These analyses are shown to be useful to understand the influence of non-condensable gases on the collapse of laser induced bubbles, where recent experiments carried out at EPFL show that contrary to the predictions from classical models, the presence of non-condensable gases can intensify the amount of energy of the shock
emitted during the bubble collapse.
In the second part of the talk we will extend the analyses to the investigation of the collapse of an spherical cap bubble initially in contact with a wall. In this case an additional singularity in the initial acceleration field is identified at the contact line when the contact angle is larger than 90 degrees. The appearance of this singularity clearly distinguishes two different regimes of bubble-wall interactions investigated by Direct Numerical Simulations. When the initial contact angle is smaller than 90 degrees, a classical jet resulting from the asymetries during bubble collapse is directed towards thewall (figure 1a and 1b) being this jet responsible of damage processes in the bubble surroundings. Interestingly, when the initial contact angle is larger than 90 degrees, the effects of the singularity present in the solution of the Euler equations become visible and a jet parallel to a wall develops (figure 1d), eventually leading to the formation of a vortex ring that propagates in the direction opposite to the wall. Theoretical arguments are provided to interpret the numerical results and the experiments carried out at ENSTA-Bretagne, where we show that these effects are behind the long range interactions between a free surface and the collapse of a bubble at the bottom of a water filled tank [1].

[1] M. Saini & E. Tanne & M. Arrigoni & S.Zaleski & D. Fuster, On the dynamics of a collapsing bubble
in contact with a rigid wall, Journal of Fluid Mechanics., 948, 1–19 (2022).

Figure 1: DNS results for collapse of spherical cap bubbles in contact with a wall with different initial contact angles. The top row shows the evolution of bubble shapes contours for (a) α = 0 (b) α = π/3 (c) α = π/2 (d) α = 2/3π. The snapshot of bubble at the instant of minimum volume is given in bottom row where the interface is shown with black curve ,the kinetic energy in liquid phase is shown with linear color map in right half and the velocity vectors in left half.