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

Mottram, Nigel and Brown, Carl and McHale, Glen (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). pp. 1-5. ISSN 0021-8979

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Abstract

A layer of insulating liquid of dielectric constant epsilon(Oil) and average thickness (h) over bar coats a flat surface at y = 0 at which a one-dimensional sinusoidal potential V(x, 0) = V(O) cos(pi x/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) over bar - (1/2)A cos(2 pi x/p) yielding a scaling relationship for A as a function of (h) over bar, p, V(O), epsilon(Oil) 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.