Plateau's Rotating Drops
Euler-Lagrange Equations and Bifurcations

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Objective: Build the Plateau apparatus and duplicate Plateau's experiment with alcohol-water and a neutrally bouyant immiscible castor oil drop, as described in Soap-bubbles and the Forces which Mold Them by C. V. Boys. Discuss the bifurcations described in the papers of Brown and Scriven (The shape and stability of rotating liquid drops. Proc. Roy. Soc. London Ser. A, 371 (1980) no. 1746, 331-357) and Gulliver (Tori of prescribed mean curvature and the rotating drop. Variational methods for equilibrium problems of fluids (Trento, 1983), Asterisque no. 118 (1984) 167-179).




Fall 2001 (Birdwell, Nanda, Pruvenok) Were unable to reproduce the results described by Plateau experimentally. Were unable to reproduce the numerical results of Brown and Scriven. Described new experimental behavior.



Summer 2002

Students Jeffrey Elms, Ryan Hynd, and Roberto Lopez constructed an improved apparatus and were able to produce the annular drops shown below. Click here to see a movie of the Plateau rings.

We also analyzed all rotationally symmetric equilibria for the formal rotating drop equation (mean curvature is a quadratic function of distance from the axis) and found a surprising interpretation of the solutions as roulettes. We are presently writing a paper in order to publish our results.

The purpose of the experiment is to rotate an oil drop inside ethanol and distilled water solution at a variable speed.


Using castor oil. Do you want to see the same experiment using vegetable oil?


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Using vegetable oil.



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Castor oil drop