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Author Notes:

To whom correspondence should be addressed. Email: alberto.fernandez@physics.gatech.edu

Author contributions: A.A.F., E.P., E.B., P.N.S., and A.F.-N. designed research; A.A.F., E.P., E.B., P.N.S., and A.F.-N. performed research; A.A.F., E.P., E.B., P.N.S., and A.F.-N. analyzed data; and A.A.F. and A.F.-N. wrote the paper.

The authors declare no conflict of interest.


Research Funding:

We thank the National Science Foundation for financial support.


  • liquid tori
  • PIV
  • hydrodynamic instabilities
  • Stokes flow
  • stream function

Shrinking instability of toroidal droplets

Journal Title:

Proceedings of the National Academy of Sciences


Volume 114, Number 11


, Pages 2871-2875

Type of Work:

Article | Final Publisher PDF


Toroidal droplets are inherently unstable due to surface tension. They can break up, similar to cylindrical jets, but also exhibit a shrinking instability, which is inherent to the toroidal shape. We investigate the evolution of shrinking toroidal droplets using particle image velocimetry. We obtain the flow field inside the droplets and show that as the torus evolves, its cross-section significantly deviates from circular. We then use the experimentally obtained velocities at the torus interface to theoretically reconstruct the internal flow field. Our calculation correctly describes the experimental results and elucidates the role of those modes that, among the many possible ones, are required to capture all of the relevant experimental features.

Copyright information:

© 2017 National Academy of Sciences

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