### Abstract

We examine the dynamics of a thin film flowing under gravity down the exterior of a vertically aligned inner cylinder, with a co-aligned, concentric cylinder acting as an outer electrode; the space between the outer cylinder and the film is occupied by an inviscid gas. The stability of the interface is studied when it is subjected to an electric field, applied by imposing a potential difference between the two cylinders. Leaky-dielectric theory is used in conjunction with asymptotic reduction, in the large-conductivity limit, to derive a single, two-dimensional evolution equation for the interfacial location, which accounts for gravity, capillarity, and electrostatic effects. A linear stability analysis is carried out which shows that non-axisymmetric modes become more dominant with increasing electric field strength. Our fully two-dimensional numerical solutions of the evolution equation demonstrate qualitative agreement between the trends observed in the nonlinear regime and those predicted by linear theory. These numerical solutions also show that, depending on the electric field strength and the relative proximity of the outer electrode, the interface either remains spatially uniform, or exhibits either axisymmetric or, importantly, non-axisymmetric travelling waves. The effect of wave formation on the interfacial area is investigated in connection with the use of electric fields to control thin film flows to enhance heat and mass transfer rates.

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

Journal | Journal of Fluid Mechanics |

Volume | 736 |

Early online date | 8 Nov 2013 |

DOIs | |

Publication status | Published - 10 Dec 2013 |

### Fingerprint

### Keywords

- electrohydrodynamic effects
- interfacial flows (free surface)
- thin films

### Cite this

*Journal of Fluid Mechanics*,

*736*. https://doi.org/10.1017/jfm.2013.543

}

*Journal of Fluid Mechanics*, vol. 736. https://doi.org/10.1017/jfm.2013.543

**Electrostatically controlled large-amplitude, non-axisymmetric waves in thin film flows down a cylinder.** / Wray, A. W.; Papageorgiou, D. T.; Matar, O. K.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Electrostatically controlled large-amplitude, non-axisymmetric waves in thin film flows down a cylinder

AU - Wray, A. W.

AU - Papageorgiou, D. T.

AU - Matar, O. K.

PY - 2013/12/10

Y1 - 2013/12/10

N2 - We examine the dynamics of a thin film flowing under gravity down the exterior of a vertically aligned inner cylinder, with a co-aligned, concentric cylinder acting as an outer electrode; the space between the outer cylinder and the film is occupied by an inviscid gas. The stability of the interface is studied when it is subjected to an electric field, applied by imposing a potential difference between the two cylinders. Leaky-dielectric theory is used in conjunction with asymptotic reduction, in the large-conductivity limit, to derive a single, two-dimensional evolution equation for the interfacial location, which accounts for gravity, capillarity, and electrostatic effects. A linear stability analysis is carried out which shows that non-axisymmetric modes become more dominant with increasing electric field strength. Our fully two-dimensional numerical solutions of the evolution equation demonstrate qualitative agreement between the trends observed in the nonlinear regime and those predicted by linear theory. These numerical solutions also show that, depending on the electric field strength and the relative proximity of the outer electrode, the interface either remains spatially uniform, or exhibits either axisymmetric or, importantly, non-axisymmetric travelling waves. The effect of wave formation on the interfacial area is investigated in connection with the use of electric fields to control thin film flows to enhance heat and mass transfer rates.

AB - We examine the dynamics of a thin film flowing under gravity down the exterior of a vertically aligned inner cylinder, with a co-aligned, concentric cylinder acting as an outer electrode; the space between the outer cylinder and the film is occupied by an inviscid gas. The stability of the interface is studied when it is subjected to an electric field, applied by imposing a potential difference between the two cylinders. Leaky-dielectric theory is used in conjunction with asymptotic reduction, in the large-conductivity limit, to derive a single, two-dimensional evolution equation for the interfacial location, which accounts for gravity, capillarity, and electrostatic effects. A linear stability analysis is carried out which shows that non-axisymmetric modes become more dominant with increasing electric field strength. Our fully two-dimensional numerical solutions of the evolution equation demonstrate qualitative agreement between the trends observed in the nonlinear regime and those predicted by linear theory. These numerical solutions also show that, depending on the electric field strength and the relative proximity of the outer electrode, the interface either remains spatially uniform, or exhibits either axisymmetric or, importantly, non-axisymmetric travelling waves. The effect of wave formation on the interfacial area is investigated in connection with the use of electric fields to control thin film flows to enhance heat and mass transfer rates.

KW - electrohydrodynamic effects

KW - interfacial flows (free surface)

KW - thin films

UR - http://www.scopus.com/inward/record.url?scp=84938153676&partnerID=8YFLogxK

U2 - 10.1017/jfm.2013.543

DO - 10.1017/jfm.2013.543

M3 - Article

VL - 736

JO - Journal of Fluid Mechanics

T2 - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -