### Abstract

The non-linear dynamics of a viscous film falling under gravity on the outside surface of a vertical circular cylinder are investigated. An electric field is imposed radially and the non-linear deformations of the liquid-air interface are modelled using thin film asymptotic analysis. The resulting equation extends other thin film models found in the literature. The electrostatic terms are a result of both normal and tangential Maxwell stresses, the latter made possible when the fluid is a leaky dielectric. The normal stresses produce non-local terms that destabilize the flow, whereas the tangential stresses can be either stabilizing or destabilizing. Numerical computations show that the electric field can be used to either suppress or enhance the instability by producing travelling wave structures with relatively larger amplitudes.

Language | English |
---|---|

Pages | 430-440 |

Number of pages | 11 |

Journal | IMA Journal of Applied Mathematics |

Volume | 77 |

Issue number | 3 |

DOIs | |

Publication status | Published - 29 May 2012 |

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### Keywords

- capillarity
- electric field
- interfacial instability
- leaky dielectric
- thin film

### Cite this

*IMA Journal of Applied Mathematics*,

*77*(3), 430-440. https://doi.org/10.1093/imamat/hxs027

}

*IMA Journal of Applied Mathematics*, vol. 77, no. 3, pp. 430-440. https://doi.org/10.1093/imamat/hxs027

**Non-linear waves in electrified viscous film flow down a vertical cylinder.** / Wray, A. W.; Matar, O.; Papageorgiou, D. T.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Non-linear waves in electrified viscous film flow down a vertical cylinder

AU - Wray, A. W.

AU - Matar, O.

AU - Papageorgiou, D. T.

PY - 2012/5/29

Y1 - 2012/5/29

N2 - The non-linear dynamics of a viscous film falling under gravity on the outside surface of a vertical circular cylinder are investigated. An electric field is imposed radially and the non-linear deformations of the liquid-air interface are modelled using thin film asymptotic analysis. The resulting equation extends other thin film models found in the literature. The electrostatic terms are a result of both normal and tangential Maxwell stresses, the latter made possible when the fluid is a leaky dielectric. The normal stresses produce non-local terms that destabilize the flow, whereas the tangential stresses can be either stabilizing or destabilizing. Numerical computations show that the electric field can be used to either suppress or enhance the instability by producing travelling wave structures with relatively larger amplitudes.

AB - The non-linear dynamics of a viscous film falling under gravity on the outside surface of a vertical circular cylinder are investigated. An electric field is imposed radially and the non-linear deformations of the liquid-air interface are modelled using thin film asymptotic analysis. The resulting equation extends other thin film models found in the literature. The electrostatic terms are a result of both normal and tangential Maxwell stresses, the latter made possible when the fluid is a leaky dielectric. The normal stresses produce non-local terms that destabilize the flow, whereas the tangential stresses can be either stabilizing or destabilizing. Numerical computations show that the electric field can be used to either suppress or enhance the instability by producing travelling wave structures with relatively larger amplitudes.

KW - capillarity

KW - electric field

KW - interfacial instability

KW - leaky dielectric

KW - thin film

UR - http://www.scopus.com/inward/record.url?scp=84864968104&partnerID=8YFLogxK

U2 - 10.1093/imamat/hxs027

DO - 10.1093/imamat/hxs027

M3 - Article

VL - 77

SP - 430

EP - 440

JO - IMA Journal of Applied Mathematics

T2 - IMA Journal of Applied Mathematics

JF - IMA Journal of Applied Mathematics

SN - 0272-4960

IS - 3

ER -