Journal of Fluid Mechanics



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Axisymmetric breakup of bubbles at high Reynolds numbers


J. M. GORDILLO a1 and M. PÉREZ-SABORID a1
a1 Área de Mecánica de Fluidos, Universidad de Sevilla. Avda. de los Descubrimientos s/n, 41092, Sevilla, Spain jgordill@us.es

Article author query
gordillo jm   [Google Scholar] 
perez-saborid m   [Google Scholar] 
 

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.

(Published Online August 14 2006)
(Received January 31 2006)
(Revised June 13 2006)



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