On the shape of giant soap bubbles

Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved January 19, 2017 (received for review October 14, 2016)
February 21, 2017
114 (10) 2515-2519

Significance

Surface tension dictates the spherical cap shape of small sessile drops, whereas gravity flattens larger drops into millimeter-thick flat puddles. In contrast with drops, soap bubbles remain spherical at much larger sizes. However, we demonstrate experimentally and theoretically that meter-sized bubbles also flatten under their weight, and we compute their shapes. We find that mechanics does not impose a maximum height for large soap bubbles, but, in practice, the physicochemical properties of surfactants limit the access to this self-similar regime where the height grows as the radius to the power 2/3. An exact analogy shows that the shape of giant soap bubbles is nevertheless realized by large inflatable structures.

Abstract

We study the effect of gravity on giant soap bubbles and show that it becomes dominant above the critical size =a2/e0, where e0 is the mean thickness of the soap film and a=γb/ρg is the capillary length (γb stands for vapor–liquid surface tension, and ρ stands for the liquid density). We first show experimentally that large soap bubbles do not retain a spherical shape but flatten when increasing their size. A theoretical model is then developed to account for this effect, predicting the shape based on mechanical equilibrium. In stark contrast to liquid drops, we show that there is no mechanical limit of the height of giant bubble shapes. In practice, the physicochemical constraints imposed by surfactant molecules limit the access to this large asymptotic domain. However, by an exact analogy, it is shown how the giant bubble shapes can be realized by large inflatable structures.

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Acknowledgments

We thank Tomas Bohr for organizing the 2013 Krogerup Summer School that initiated the collaboration between Paris and Twente. We also thank Isabelle Cantat for her input on the stability of soap films and for her constructive criticism of the initial version of our work.

Supporting Information

Supporting Information (PDF)

References

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Information & Authors

Information

Published in

Go to Proceedings of the National Academy of Sciences
Proceedings of the National Academy of Sciences
Vol. 114 | No. 10
March 7, 2017
PubMed: 28223485

Classifications

Submission history

Published online: February 21, 2017
Published in issue: March 7, 2017

Keywords

  1. soap bubbles
  2. Marangoni stress
  3. self-similarity

Acknowledgments

We thank Tomas Bohr for organizing the 2013 Krogerup Summer School that initiated the collaboration between Paris and Twente. We also thank Isabelle Cantat for her input on the stability of soap films and for her constructive criticism of the initial version of our work.

Notes

This article is a PNAS Direct Submission.

Authors

Affiliations

Caroline Cohen1
Laboratoire d’Hydrodynamique de l’X, UMR 7646 CNRS, École Polytechnique, 91128 Palaiseau Cedex, France;
Baptiste Darbois Texier1
Laboratoire d’Hydrodynamique de l’X, UMR 7646 CNRS, École Polytechnique, 91128 Palaiseau Cedex, France;
Etienne Reyssat2 [email protected]
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), UMR 7636 du CNRS, ESPCI Paris/Paris Sciences et Lettres (PSL) Research University/Sorbonne Universités/Université Paris Diderot, 75005 Paris, France;
Jacco H. Snoeijer
Physics of Fluids Group, University of Twente, 7500 AE Enschede, The Netherlands;
MESA+ Institute for Nanotechnology, University of Twente, 7500 AE Enschede, The Netherlands;
Department of Applied Physics, Eindhoven University of Technology, 5600 MB, Eindhoven, The Netherlands
David Quéré
Laboratoire de Physique et Mécanique des Milieux Hétérogènes (PMMH), UMR 7636 du CNRS, ESPCI Paris/Paris Sciences et Lettres (PSL) Research University/Sorbonne Universités/Université Paris Diderot, 75005 Paris, France;
Christophe Clanet
Laboratoire d’Hydrodynamique de l’X, UMR 7646 CNRS, École Polytechnique, 91128 Palaiseau Cedex, France;

Notes

2
To whom correspondence should be addressed. Email: [email protected].
Author contributions: C. Cohen, B.D.T., and C. Clanet designed research; C. Cohen, B.D.T., E.R., J.H.S., and C. Clanet performed research; C. Cohen, B.D.T., E.R., J.H.S., D.Q., and C. Clanet analyzed data; and C. Cohen, B.D.T., E.R., J.H.S., and C. Clanet wrote the paper.
1
C. Cohen and B.D.T. contributed equally to this work.

Competing Interests

The authors declare no conflict of interest.

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    On the shape of giant soap bubbles
    Proceedings of the National Academy of Sciences
    • Vol. 114
    • No. 10
    • pp. 2431-E2067

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