Quasi-steady formation of bubbles and drops viewed as processes that break bifurcation
Résumé
Instabilities occurring during the quasi-steady formation of bubbles and drops at a circular orifice through a thin plate, which separates a cylindrical upper vessel of quiescent liquid from a lower air chamber maintained at constant pressure, are considered in connection with the Rayleigh-Taylor instability of a flat meniscus. The control parameters of the problem are the Eötvös number Eö, and the excess-pressure number $Δ$, which characterizes the pressure difference between gas and liquid across the orifice. The Rayleigh-Taylor case i.e., $Δ = 0$, can be viewed as a perfect bifurcating problem. A subcritical bifurcation emerges from the critical point, Eöc = 5 B783186, beyond which the flat meniscus is unstable for axisymmetric perturbations. Bubbles ($Δ > 0$), and drops ($Δ < 0$) appear as solutions that break bifurcation. When an appropriate measure of their magnitude $ε$ is introduced, it can be shown analytically that the equilibrium surface at the critical point is a cusp; its intermediate sheet is stable, while its two upper and lower sheets are unstable. The analytical bifurcation set onto the control parameters plane is valid only around the critical point.
Origine : Fichiers produits par l'(les) auteur(s)
Loading...
