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Axisymmetric breakup of bubbles at high Reynolds numbers

Published online by Cambridge University Press:  14 August 2006

J. M. GORDILLO
Affiliation:
Área de Mecánica de Fluidos, Universidad de Sevilla. Avda. de los Descubrimientos s/n, 41092, Sevilla, Spainjgordill@us.es
M. PÉREZ-SABORID
Affiliation:
Área de Mecánica de Fluidos, Universidad de Sevilla. Avda. de los Descubrimientos s/n, 41092, Sevilla, Spainjgordill@us.es

Abstract

We have analysed the structure of the irrotational flow near the minimum radius of an axisymmetric bubble at the final instants before pinch-off. The neglect of gas inertia leads to the geometry of the liquid–gas interface near the point of minimum radius being slender and symmetric with respect to the plane $z\,{=}\,0$. The results reproduce our previous finding that the asymptotic time evolution for the minimum radius, $R_o(t)$, is $\tau\propto R^2_o\sqrt{-\,{\rm ln}\,R^2_o}$, $\tau$ being the time to breakup, and that the interface is locally described, for times sufficiently close to pinch-off, by $f(z,t)/R_o(t)\,{=}\,1\,{-}\,(6\,{\rm ln}\,R_o)^{-1}(z/R_o)^2$. These asymptotic solutions correspond to the attractor of a system of ordinary differential equations governing the flow during the final stages before pinch-off. However, we find that, depending on initial conditions, the solution converges to the attractor so slowly (with a logarithmic behaviour) that the universal laws given above may hold only for times so close to the singularity that they might not be experimentally observed.

Type
Papers
Copyright
© 2006 Cambridge University Press

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