Type: Master/Semester project
The dynamics of bubbles moving in small tubes exhibits a rich phenomenology depending of the precise flow configuration. Bretherton [1] was the first to investigate this problem. In a vertical tube, under the action of gravity, bubbles can rise, provided a certain condition is met on the two fluid properties and the tube radius.
Figure: Scheme of a bubble in an horizontal tube (from [1]).
In a recent work [2], the linear stability analysis of an axisymmetric bubble rising in a vertical fluid under the action of of a counter flow has been performed. The study shows the existence of modes breaking the axisymmetry. Axisymmetric modes however are found to be stable.
Yet, long air cylinder are a perfect candidate for Rayleigh-Plateau instability, which is an axisymmetric instability.
To rationalize this apparent paradoxe, we propose to investigate numerically the fate of small amplitude axisymmetric perturbations on the surface of an axisymmetric bubble. The study will be done using the free software Basilisk [3]. The amplitude of the perturbation will be monitored in time. We anticipate that a competition between advection by the flow and growth of the perturbation should be at stake.
[1] Bretherton, F. P. (1961). The motion of long bubbles in tubes. Journal of Fluid Mechanics, 10(2), 166-188.
[2] Herrada, M. A., Yu, Y. E., & Stone, H. A. (2023). Global stability analysis of bubbles rising in a vertical capillary with an external flow. Journal of Fluid Mechanics, 958, A45.
[3] basilisk.fr
Supervisor(s): Aliénor Riviere & François Gallaire