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Theory of rotating electrohydrodynamic flows in a liquid film

E. V. Shiryaeva*

V. A. Vladimirov†

M. Yu. Zhukov‡

  • Department of Mathematics, Mechanics and Computer Science, Southern Federal University, 344090 Rostov-on-Don, Russia

  • Department of Mathematics, York University, York YO10 5DD, United Kingdom

  • Department of Mathematics, Mechanics and Computer Science, Southern Federal University, 344090 Rostov-on-Don, Russia

  • *shir@ns.math.rsu.ru
  • †vv500@york.ac.uk
  • ‡zhuk@ns.math.rsu.ru
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Phys. Rev. E 80, 041603 – Published 16 October, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.041603

Abstract

The mathematical model of rotating electrohydrodynamic flows in a thin suspended liquid film is proposed and studied. The flows are driven by the given difference of potentials in one direction and constant external electric field Eout in another direction in the plane of a film. To derive the model, we employ the spatial averaging over the normal coordinate to a film that leads to the average Reynolds stress that is proportional to |Eout|3. This stress generates tangential velocity in the vicinity of the edges of a film that, in turn, causes the rotational motion of a liquid. The proposed model is used to explain the experimental observations of the liquid film motor.

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Phys. Rev. E 80, 041603– Published 16 October, 2009
  • Received 20 February 2009

© 2009 American Physical Society

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