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Optimal wrapping of liquid droplets with ultrathin sheets

Nature Materials volume 14, pages 1206–1209 (2015)Cite this article

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Abstract

Elastic sheets offer a path to encapsulating a droplet of one fluid in another that is different from that of traditional molecular or particulate surfactants1. In wrappings of fluids by sheets of moderate thickness with petals designed to curl into closed shapes2,3, capillarity balances bending forces. Here, we show that, by using much thinner sheets, the constraints of this balance can be lifted to access a regime of high sheet bendability that brings three major advantages: ultrathin sheets automatically achieve optimally efficient shapes that maximize the enclosed volume of liquid for a fixed area of sheet; interfacial energies and mechanical properties of the sheet are irrelevant within this regime, thus allowing for further functionality; and complete coverage of the fluid can be achieved without special sheet designs. We propose and validate a general geometric model that captures the entire range of this new class of wrapped and partially wrapped shapes.

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Figure 1: Side and top views of a circular polystyrene (PS) sheet wrapping a water drop immersed in silicone oil.
Figure 2: Axisymmetry breaking probed by side-view profiles.
Figure 3: Theoretical wrapping shapes and their efficiency.
Figure 4: Polygonal partial wrapping by petals and folds.

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Acknowledgements

We thank M. Juszkiewicz for early contributions to this work and O. Agam for helpful discussions. Funding from the W. M. Keck Foundation is gratefully acknowledged.

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Authors and Affiliations

  1. Department of Physics, University of Massachusetts, Amherst, Massachusetts 01003, USA

    Joseph D. Paulsen, Vincent Démery, Christian D. Santangelo, Benny Davidovitch & Narayanan Menon

  2. Polymer Science and Engineering Department, University of Massachusetts, Amherst, Massachusetts 01003, USA

    Joseph D. Paulsen & Thomas P. Russell

  3. Materials Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA

    Thomas P. Russell

  4. WPI—Advanced Institute for Materials Research (WPI-AIMR), Tohoku University, 2-1-1 Katahira, Aoba, Sendai 980-8577, Japan

    Thomas P. Russell

Authors
  1. Joseph D. Paulsen
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  4. Thomas P. Russell
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  5. Benny Davidovitch
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  6. Narayanan Menon
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Contributions

All authors contributed to designing the research and writing the manuscript; J.D.P. and V.D. performed the research; J.D.P. conducted the experiments; J.D.P., T.P.R. and N.M. analysed the experimental data, V.D., C.D.S. and B.D. conducted the analytic and numerical computations.

Corresponding authors

Correspondence to Joseph D. Paulsen or Vincent Démery.

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The authors declare no competing financial interests.

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Paulsen, J., Démery, V., Santangelo, C. et al. Optimal wrapping of liquid droplets with ultrathin sheets. Nature Mater 14, 1206–1209 (2015). https://doi.org/10.1038/nmat4397

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