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Deformation and bursting of elastic capsules impacting a rigid wall

Abstract

From water balloons to cells and various organs, thin elastic shells enclosing liquid cores or capsules are ubiquitous. Although such capsules are rampant in nature and in engineering, the physics of their deformation upon rapid impact is virtually unexplored. Here we perform experiments and develop formal models to rationalize the deformation and possible bursting of elastic capsules impacting rigid walls. We discover an analogy to the impact of liquid drops, where the shell surface modulus plays the role of the drop surface tension. On the basis of this analogy, we propose an energy balance that quantitatively predicts the maximal deformation of the capsule in the inviscid limit, and for liquids with viscosities up to 1,000 cP (Reynolds numbers 10). Unlike drops, however, capsules can be pre-stretched and burst. Experiments show a substantial influence of the pre-stretch on the critical burst velocity, a feature also captured by our model. While we focus on macroscopic objects, our model could potentially be extended to account for the deformations of microcapsules in microfluidic channels. In addition, this work could have practical implications from the optimized detonation of fire-extinguishing balls to fight domestic fires and wildfires to the prevention of organ bursting in car crashes.

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Fig. 1: Elastic capsule impinging a flat wall.
Fig. 2: Influence of the shell on the capsule deformation.
Fig. 3: Influence of the filler liquid on the capsule deformation.
Fig. 4: Effect of pre-stretch on the deformation and capsule burst.

Data availability

The data represented in Figs. are available as Source Data. All other data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

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Acknowledgements

We thank H. Stone for sharing his rheometer and L. Cai for his help during the water balloon experiments. E.J.-P. was partially funded by the grant DMR-1420541 MRSCE: Princeton Center for Complex Materials-iSuperseed.

Author information

Affiliations

Authors

Contributions

E.J.-P. and P.-T.B. conceived the project. E.J.-P. and T.J.J. performed the experiments. E.J.-P. derived the model. All authors wrote the manuscript.

Corresponding author

Correspondence to P.-T. Brun.

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Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Physics thanks Thomas Séon and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Experimental methods, theory and calculations.

Supplementary Video 1

Three custom-made VPS-8 capsules filled with water, glycerol and honey shot at U ≈ 14 m s−1 from the air canon (as a scale, the capsule radii are R0 = 7.6 mm).

Supplementary Video 2

Water balloon impact at U ≈ 4 m s−1 and bursting (as a scale, the balloon width is 7.6 cm, λp = 4.35).

Supplementary Video 3

A custom-made VPS-8 capsule filled with water impacts a smooth, rough and adhesive surface at U ≈ 3 m s−1 (as a scale, the capsule radius is R0 = 11.5 mm).

Source data

Source Data Fig. 2

Experimental and processed data.

Source Data Fig. 3

Experimental and processed data.

Source Data Fig. 4

Experimental and processed data.

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Jambon-Puillet, E., Jones, T.J. & Brun, PT. Deformation and bursting of elastic capsules impacting a rigid wall. Nat. Phys. 16, 585–589 (2020). https://doi.org/10.1038/s41567-020-0832-x

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