Visualization of low Reynolds boundary-driven cavity flows in thin liquid shells

Abstract

Classic examples of low-Reynolds recirculating cavity flows are typically generated from lid-driven boundary motion at a solid–fluid interface, or alternatively may result from shear flow over cavity openings. Here, we are interested in an original family of boundary-driven cavity flows occurring, in contrast to classic setups, at fluid–fluid interfaces. Particle image velocimetry (PIV) is used to investigate the structure of internal convective flows observed in thin liquid shells. Under the specific configuration investigated, the soap bubble’s liquid shell is in fact in motion and exhibits sporadic local “bursts”. These bursts induce transient flow motion within the cavity of order Re ∼ O(1). The combination of PIV and proper orthogonal decomposition (POD) is used to extract dominant flow structures present within bubble cavities. Next, we show that thermally induced Marangoni flows in the liquid shell can lead to forced, (quasi) steady-state, internal recirculating flows. The present findings illustrate a novel example of low-Reynolds boundary-driven cavity flows.

Graphical Abstract

Appendix

For a soap bubble of height, h, blown at an opening of radius, r _o, the volume, V, of the liquid shell is described by a spherical cap model such that (Harris and Stoker 1998):

$$ V = \pi \left({\frac{1}{6}}h^3+{\frac{1}{2}}hr^2_{\text{o}}\right), $$

(7)

where $h = R + \sqrt{R^2-r^2_{\text{o}}}.$ For a given bubble radius, R, in the range of volumes considered (0.2–0.7 ml), the difference in volume relative to that of a sphere, where V = 4/3 πR ³, remains below 10%.