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The effect of a normal electric field on wave propagation on a fluid film

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posted on 2023-05-18, 15:44 authored by Hammerton, PW, Andrew BassomAndrew Bassom
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.

History

Publication title

Physics of Fluids

Volume

26

Article number

012107

Number

012107

Pagination

1-13

ISSN

1070-6631

Department/School

School of Natural Sciences

Publisher

Amer Inst Physics

Place of publication

Circulation & Fulfillment Div, 2 Huntington Quadrangle, Ste 1 N O 1, Melville, USA, Ny, 11747-4501

Rights statement

Copyright 2014 AIP Publishing LLC

Repository Status

  • Open

Socio-economic Objectives

Expanding knowledge in the mathematical sciences

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