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Daughter bubble cascades produced by folding of ruptured thin films

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Abstract

Thin liquid films, such as soap bubbles, have been studied extensively for over a century because they are easily formed and mediate a wide range of transport processes in physics, chemistry and engineering1,2,3. When a bubble on a liquid–gas or solid–gas interface (referred to herein as an interfacial bubble) ruptures, the general expectation is that the bubble vanishes. More precisely, the ruptured thin film is expected to retract rapidly until it becomes part of the interface, an event that typically occurs within milliseconds4,5,6. The assumption that ruptured bubbles vanish is central to theories on foam evolution7 and relevant to health8 and climate9 because bubble rupture is a source for aerosol droplets10,11. Here we show that for a large range of fluid parameters, interfacial bubbles can create numerous small bubbles when they rupture, rather than vanishing. We demonstrate, both experimentally and numerically, that the curved film of the ruptured bubble can fold and entrap air as it retracts. The resulting toroidal geometry of the trapped air is unstable, leading to the creation of a ring of smaller bubbles. The higher pressure associated with the higher curvature of the smaller bubbles increases the absorption of gas into the liquid, and increases the efficiency of rupture-induced aerosol dispersal.

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Figure 1: The daughter bubble cascade, with jets, droplets and daughter bubbles resulting from bursting bubbles.
Figure 2: Two-step mechanism to form daughter bubbles.
Figure 3: Numerical simulations for understanding film folding and air entrapment.
Figure 4: Dynamical characterization of the formation of daughter bubbles.

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Acknowledgements

We thank P. Howell for discussions regarding our numerical simulations, and E. Villermaux and M. Brenner for feedback. We are grateful to the NSF via the Harvard MRSEC for support of this research.

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Authors

Contributions

J.C.B., L.C. and H.A.S. designed the research; J.C.B., R.d.R. and L.C. performed the research; J.C.B., R.d.R., L.C. and H.A.S. analysed the data; J.C.B. wrote the manuscript and all authors commented on it.

Corresponding authors

Correspondence to James C. Bird or Howard A. Stone.

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The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Material and Methods, a Supplementary Discussion, Supplementary Figures S1-S2 with legends and References. (PDF 549 kb)

Supplementary Movie 1

This is the original movie of the bubble dynamics shown in Fig. 1E-G. The interfacial bubble ruptures, uncovering a dimple on the water surface. The high curvature of this dimple causes a jet to form; since this jet does not have enough kinetic energy to be propelled into the atmosphere it returns to the interface. Yet, around the jet, there is a ring of smaller bubbles formed during the film retraction. One of these daughter bubbles ruptures at 56 ms (left side of movie). (MOV 5849 kb)

Supplementary Movie 2

A smaller, daughter bubble created by the rupture of a larger bubble ruptures on a much faster timescale and also forms a jet. This jet breaks up into micron-sized droplets which are propelled into the atmosphere at speeds exceeding 5 m/s. Therefore the rupture of a centimeter-sized bubble can lead to the aerosolization of dozens of fine droplets into the atmosphere. (MOV 1416 kb)

Supplementary Movie 3

The two-step mechanism to form daughter bubbles (Fig. 2) is presented with simultaneous movies showing side and bottom perspectives. (MOV 1694 kb)

Supplementary Movie 4

Numerical simulations of the film retraction capture the folding dynamics of the film (MOV 837 kb)

Supplementary Movie 5

The film retraction of a highly viscous bubble (a million times the viscosity of water). This movie corresponds to the far-left point in Fig. 4 (MOV 1985 kb)

Supplementary Movie 6

The rupture of an air bubble on water shows how the rim of the film becomes unstable as it retracts. This movie is representative of the points on the far-right of Fig. 4. (MOV 1343 kb)

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Bird, J., de Ruiter, R., Courbin, L. et al. Daughter bubble cascades produced by folding of ruptured thin films. Nature 465, 759–762 (2010). https://doi.org/10.1038/nature09069

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