dorsal/arxiv
View SchemaTheory of the collapsing axisymmetric cavity
| Authors | J. Eggers, M. A. Fontelos, D. Leppinen, J. H. Snoeijer |
|---|---|
| Categories | |
| ArXiv ID | physics/0610139 |
| URL | https://arxiv.org/abs/physics/0610139 |
| DOI | 10.1103/PhysRevLett.98.094502 |
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 $h_0 \propto t'^{\alpha}$, where $t'$ is the time from collapse. The exponent $\alpha$ very slowly approaches a universal value according to $\alpha=1/2 + 1/(4\sqrt{-\ln(t')})$. 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.
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"abstract": "We investigate the collapse of an axisymmetric cavity or bubble inside a\nfluid of small viscosity, like water. Any effects of the gas inside the cavity\nas well as of the fluid viscosity are neglected. Using a slender-body\ndescription, we show that the minimum radius of the cavity scales like $h_0\n\\propto t\u0027^{\\alpha}$, where $t\u0027$ is the time from collapse. The exponent\n$\\alpha$ very slowly approaches a universal value according to $\\alpha=1/2 +\n1/(4\\sqrt{-\\ln(t\u0027)})$. Thus, as observed in a number of recent experiments, the\nscaling can easily be interpreted as evidence of a single non-trivial scaling\nexponent. Our predictions are confirmed by numerical simulations.",
"arxiv_id": "physics/0610139",
"authors": [
"J. Eggers",
"M. A. Fontelos",
"D. Leppinen",
"J. H. Snoeijer"
],
"categories": [
"physics.flu-dyn"
],
"doi": "10.1103/PhysRevLett.98.094502",
"title": "Theory of the collapsing axisymmetric cavity",
"url": "https://arxiv.org/abs/physics/0610139"
},
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