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

A layer of insulating liquid of dielectric constant ɛOil and average thickness coats a flat surface at y = 0 at which a one-dimensional sinusoidal potential 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) = -(1/2)Acos(2πx/p) yielding a scaling relationship for A as a function of , p, VO, 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.