Long-wavelength, small-amplitude disturbances on the surface of a fluid layer subject to a normal electric field are considered. In our model, a dielectric medium lies above a layer of perfectly conducting fluid, and the electric field is produced by parallel plate electrodes. The Reynolds number of the fluid flow is taken to be large, with viscous effects restricted to a thin boundary layer on the lower plate. The effects of surface tension and electric field enter the governing equation through an inverse Bond number and an electrical Weber number, respectively. The thickness of the lower fluid layer is assumed to be much smaller than the disturbance wavelength, and a unified analysis is presented allowing for the full range of scalings for the thickness of the upper dielectric medium. A variety of different forms of modified Korteweg-de Vries equation are derived, involving Hilbert transforms, convolution terms, higher order spatial derivatives, and fractional derivatives. Critical values are identified for the inverse Bond number and electrical Weber number at which the qualitative nature of the disturbances changes.
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January 2014
Research Article|
January 27 2014
The effect of a normal electric field on wave propagation on a fluid film
P. W. Hammerton;
P. W. Hammerton
a)
1School of Mathematics,
University of East Anglia
, Norwich Research Park, Norwich NR4 7TJ, United Kingdom
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Andrew P. Bassom
Andrew P. Bassom
b)
2School of Mathematics and Statistics,
The University of Western Australia
, Crawley 6009, Australia
Search for other works by this author on:
P. W. Hammerton
1,a)
Andrew P. Bassom
2,b)
1School of Mathematics,
University of East Anglia
, Norwich Research Park, Norwich NR4 7TJ, United Kingdom
2School of Mathematics and Statistics,
The University of Western Australia
, Crawley 6009, Australia
a)
Electronic mail: [email protected]
b)
Electronic mail: [email protected]
Physics of Fluids 26, 012107 (2014)
Article history
Received:
July 20 2013
Accepted:
December 05 2013
Citation
P. W. Hammerton, Andrew P. Bassom; The effect of a normal electric field on wave propagation on a fluid film. Physics of Fluids 1 January 2014; 26 (1): 012107. https://doi.org/10.1063/1.4862975
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