科研之友
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摘要
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-0(t), is tau proportional to R-0(2) root-ln R-0(2), 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-0(t) = 1-(6 ln R-0)(-1)(z/R-0)(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.
- 出版日期2006-9-10
