Effects triggered by singular solutions in the collapse of non-spherical bubbles

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• Daniel Fuster, Institut D'Alembert
• Thursday 13 February 2025, 11:30-12:30
• Open Plan Area, Institute for Energy and Environmental Flows, Madingley Rise CB3 0EZ.

If you have a question about this talk, please contact Catherine Pearson.

The Rayleigh collapse problem is defined as the implosion of a cavity in a liquid at a higher ambient pressure and represents an idealized problem relevant in applications related to cavitation, environmental science, medical treatment and many others 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 being possible to extend the analysis to account for the presence of non-condensable gases and obtain theoretical estimates about the finite peak pressures and temperatures that can be reached during the collapse process.

In this work we revisit the analytical expressions for the singular collapse of bubbles to discuss the importance of non-spherical effects for a spherical cap bubble initially in contact with a wall. We show that the solution of this problem presents a singularity in the initial acceleration field at the triple contact point when the initial contact angle is larger than 90 degrees. The appearance of this singularity clearly distinguishes two different regimes of bubble-wall interactions. When the initial contact angle is smaller than 90 degrees, a classical jet resulting from the interaction with the wall is directed towards the wall being responsible for the damage processes of the wall. 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 leading to the formation of a vortex ring that propagates in the direction opposite to the wall and that can travel significant distances. Theoretical arguments are provided to interpret the numerical results obtained from the DNS of the Navier-Stokes equations and experiments 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 (Saini et al, JFM , 2022). We also show that these non-spherical effects can lead to significant deviations on the scaling laws for the peak pressures and temperatures predicted by the spherically symmetric theory.

This talk is part of the Institute for Energy and Environmental Flows (IEEF) series.

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