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

Published online by Cambridge University Press:  08 November 2013

A. W. Wray ,
D. T. Papageorgiou  and
O. K. Matar
A. W. Wray
Affiliation:
Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
D. T. Papageorgiou
Affiliation:
Department of Mathematics, Imperial College London, South Kensington Campus, London SW7 2BZ, UK
O. K. Matar*
Affiliation:
Department of Chemical Engineering, Imperial College London, South Kensington Campus, London SW7 2AZ, UK
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Drops and Bubbles: Electrohydrodynamic effects Interfacial Flows (free surface): Interfacial Flows (free surface) Interfacial Flows (free surface): Thin films
Type
Rapids
Information
Journal of Fluid Mechanics , Volume 736 , 10 December 2013 , R2
Copyright
©2013 Cambridge University Press 

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