### 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.

Original language | English |
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Article number | 041603 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 80 |

Issue number | 4 |

DOIs | |

Publication status | Published - Oct 16 2009 |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Statistical and Nonlinear Physics
- Statistics and Probability

### Cite this

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*,

*80*(4), [041603]. https://doi.org/10.1103/PhysRevE.80.041603

**Theory of rotating electrohydrodynamic flows in a liquid film.** / Shiryaeva, E. V.; Vladimirov, V. A.; Zhukov, M. Yu.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 80, no. 4, 041603. https://doi.org/10.1103/PhysRevE.80.041603

}

TY - JOUR

T1 - Theory of rotating electrohydrodynamic flows in a liquid film

AU - Shiryaeva, E. V.

AU - Vladimirov, V. A.

AU - Zhukov, M. Yu

PY - 2009/10/16

Y1 - 2009/10/16

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=70350589069&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=70350589069&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.80.041603

DO - 10.1103/PhysRevE.80.041603

M3 - Article

AN - SCOPUS:70350589069

VL - 80

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 4

M1 - 041603

ER -