The details of nonlinear oscillations and collapse of elongated bubbles, subject to large internal overpressure, are studied by a boundary integral method. Weak viscous effects on the liquid side are accounted for by integrating the equations of motion across the boundary layer that is formed adjacent to the interface¹.

For large internal overpressures and moderate elongations there is a critical value of the Ohnesorge number, Oh=μ/(σRρ)^1/2, below which the bubble collapses via two jets that enter the bubble through its two poles, propagate in the opposite direction along the axis of symmetry and eventually coalesce in a centered fashion at the equatorial plane. In this process a tiny microbubble is formed, occupying the center of the original bubble, that is surrounded by a larger toroidal bubble. Above this critical value of Ohnesorge the bubble eventually returns to its equilibrium spherical shape. For large overpressures, very large initial elongations and below the critical Ohnesorge number the jet walls are deflected and collapse in an off-centered fashion at the bubble walls, forming two smaller toroidal bubbles and a large one occupying the center of the original bubble. Above the critical Ohnesorge the centered collapse mode with the tiny microbubble at the center is recovered. In all cases of bubble collapse the time from collapse scaled with the 3/2 power of the minimum distance between the pinching parts of the interface. As the bubble size increases the bubble is destabilized and the above break-up mechanisms are observed for smaller initial elongations. In this case, for very large internal overpressures and small elongations the Rayleigh-Taylor instability appears and the bubble collapses via coalescence of two jets that propagate in opposite directions along the equator.
Simulations of experiments with LASER induced nanosecond² bubbles, initial radius on the order of one mm, exhibit a similar collapse mode. The severity of jet impact during collapse of such bubbles in pointed out. Simulations of experiments with laser induced femto-second² bubbles indicate asymmetric collapse and smaller jet velocities.

[1] Tsiglifis K. & Pelekasis N. (2005), Phys. Fluids 17(10): 1-18.

[2] R. Geisler (2004), Ph.D Thesis University of Goettingen.

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