Analysis of a static undulation on the surface of a thin dielectric liquid layer formed by dielectrophoresis forces

Brown, C. V., McHale, G. and Mottram, N. J. (2011) Analysis of a static undulation on the surface of a thin dielectric liquid layer formed by dielectrophoresis forces. Journal of Applied Physics, 110(2), 024107. (doi: 10.1063/1.3606435)

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Abstract

A layer of insulating liquid of dielectric constant ɛ Oil ɛOil and average thickness h − h− coats a flat surface at y = 0 at which a one-dimensional sinusoidal potential V(x,0)=V O cos(πx/p) V(x,0)=VOcos(πx/p) is applied. Dielectrophoresis forces create a static undulation (or “wrinkle”) distortion h(x) of period p at the liquid/air interface. Analytical expressions have been derived for the electrostatic energy and the interfacial energy associated with the surface undulation when h(x)=h − −(1/2)Acos(2πx/p) h(x)=h−-(1/2)Acos(2πx/p) yielding a scaling relationship for A as a function of h ⎯ ⎯ ⎯ h− , p, V O VO , ɛ Oil ɛOil and the surface tension. The analysis is valid as A/p → 0, and in this limit convergence with numerical simulation of the system is shown.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Mottram, Professor Nigel
Authors: Brown, C. V., McHale, G., and Mottram, N. J.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Applied Physics
Publisher:American Institute of Physics
ISSN:0021-8979
ISSN (Online):1089-7550
Published Online:22 July 2011

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