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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.

Item Type:	Refereed Article
Research Division:	Mathematical Sciences
Research Group:	Applied Mathematics
Research Field:	Theoretical and Applied Mechanics
Objective Division:	Expanding Knowledge
Objective Group:	Expanding Knowledge
Objective Field:	Expanding Knowledge in the Mathematical Sciences
Author:	Bassom, AP (Professor Andrew Bassom)
ID Code:	105699
Year Published:	2014
Web of Science® Times Cited:	3
Deposited By:	Mathematics and Physics
Deposited On:	2016-01-13
Last Modified:	2016-08-11
Downloads:	14 View Download Statistics