Deformable sheets are ubiquitous in nature and industry across a vast range of scales, from graphene to metal foil to the earth’s crust. A sheet that is much thinner than it is wide will more readily bend than stretch. This simple property leads to a wide variety of wrinkling and stress-focussing behaviors when a sheet is compressed, poked, crumpled, or twisted.

Top and side views of a circular polystyrene sheet wrapping a water drop immersed in silicone oil. The sheet is 39 nm thick and 3.0 mm in diameter.
Top and side views of a circular polystyrene sheet wrapping a water drop immersed in silicone oil. The sheet is 39 nm thick and 3.0 mm in diameter.

We recently studied how a thin sheet wraps itself around a liquid drop. Whereas thicker sheets spontaneously wrap by long-wavelength bending [Py et al., Phys. Rev. Lett. 98, 2007], thinner sheets deform more readily by forming small-scale wrinkles and stress-focussing patterns. Although predicting the wrapping shape involves very complex mechanics, we have shown that it reduces to a simple geometric problem for very thin sheets. In the end, the wrapper forms a three-dimensional shape that maximizes the enclosed volume for a given area of the sheet. In this way, a thin film on a drop is similar to a stuffed food like a calzone, which maximizes its filling while using minimal dough. But thin sheets on droplets are remarkable in that they find this shape all on their own.

Wrapping liquids in elastic sheets could be useful in applications where a liquid cargo needs to be protected in a solid barrier, or in creating droplets with particular shapes or mechanical properties.


Wrapping liquids, solids, and gases in thin sheets. J. D. Paulsen, Annual Review of Condensed Matter Physics vol. 10, 431 (2019).  pdf  link  bibtex

Geometry underlies the mechanical stiffening and softening of thin sheets. M. M. Ripp, V. Démery, T. Zhang, and J. D. Paulsen, arXiv 1804.02421 (2018).  pdf  link

Thickness dependence of the Young’s modulus of polymer thin films.
 J. Chang, K. B. Toga, J. D. Paulsen, Thomas P. Russell, and N. Menon
, Macromolecules 51, 6764 (2018).  link  bibtex

Wrapping with a splash: High-speed encapsulation with ultrathin sheets. D. Kumar, J. D. Paulsen, T. P. Russell, and N. Menon, Science 359, 775 (2018).  pdf  link  bibtex

Geometry-driven folding of a floating annular sheet. J. D. Paulsen, V. Démery, K. B. Toga, Z. Qiu, T. Russell, B. Davidovitch, and N. Menon, Physical Review Letters 118, 048004 (2017).  pdf  link  bibtex

Curvature-induced stiffness and the spatial variation of wavelength in wrinkled sheets. J. D. Paulsen, E. Hohlfeld, H. King, J. Huang, Z. Qiu, T. P. Russell, N. Menon, D. Vella, and B. Davidovitch. Proceedings of the National Academy of Sciences, USA (2016).  pdf  link  bibtex

Optimal wrapping of liquid droplets with ultrathin sheets. J. D. Paulsen, V. Démery, C. D. Santangelo, T. P. Russell, B. Davidovitch, and N. Menon, Nature Materials 14, 1206 (2015).  pdf  link  bibtex


Splash-wrapping synopsis by Science Magazine (2018).  link

Supplementary videos from the paper: Optimal wrapping of liquid droplets with ultrathin sheets, Paulsen et al., Nature Materials 14, 1206 (2015).  link

Wrapping a drop with a flat sheet. Gallery of Fluid Motion, APS Division of Fluid Dynamics Meeting (2014).  link