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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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.
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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.
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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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DOI: https://doi.org/10.1038/s41567-020-0832-x
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