Theory of the collapsing axisymmetric cavity

Abstract

We investigate the collapse of an axisymmetric cavity or bubble inside a fluid of small viscosity, like water. Any effects of the gas inside the cavity as well as of the fluid viscosity are neglected. Using a slender-body description, we show that the minimum radius of the cavity scales like $h_0\propto t^{\prime \alpha }$, where $t^{\prime }$ is the time from collapse. The exponent $\alpha$ very slowly approaches a universal value according to $\alpha =1/2+1/(4\sqrt{-\ln (t^{\prime })})$. Thus, as observed in a number of recent experiments, the scaling can easily be interpreted as evidence of a single non-trivial scaling exponent. Our predictions are confirmed by numerical simulations.

References in corpus (3)

• Axisymmetric bubble pinch-off at high Reynolds numbers
• Giant bubble pinch-off
• Breakup of Air Bubbles in Water: Memory and Breakdown of Cylindrical Symmetry

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