title: 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 compute the local scaling exponent alpha=dlnh_{0}/dlnt' of the minimum radius h_{0} of the cavity, where t' is the time from collapse. The exponent alpha very slowly approaches a universal value according to alpha=1/2+1/[4 square root [-ln(t')]]. Thus, as observed in a number of recent experiments, the scaling can easily be interpreted as evidence of a single nontrivial scaling exponent. Our predictions are confirmed by numerical simulations.
authors.affiliation: School of Mathematics, University of Bristol, University Walk, Bristol BS8 1TW, United Kingdom.
authors.forename: J
authors.initials: J
authors.lastname: Eggers
authors.forename: M A
authors.initials: MA
authors.lastname: Fontelos
authors.forename: D
authors.initials: D
authors.lastname: Leppinen
authors.forename: J H
authors.initials: JH
authors.lastname: Snoeijer