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

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

Developing interface localized liquid dielectrophoresis for optical applications

“…2b). The energies involved in changes at the liquid-vapor interface can be explained using detailed calculations or a simple scaling argument 21,25 . The equilibrium shape is then found by minimizing the total energy change with respect to changes in wrinkle amplitude, A,…”

“…2c). Calculations of the higher frequency components can be performed and the relative amplitudes of components calculated 21 .…”

Boundary integral solution of potential problems arising in the modelling of electrified oil films

“…We test our boundary integral model and numerical solution scheme using the same boundary condition for (4) as employed in [5] for a static applied potential f (x) = A cos(πx/L), where A is a constant amplitude term. Note that one can then derive the half-space solution φ H , either using separation of variables or directly from the boundary integral formula (16), to get φ H (x) = A cos(πx/L) exp(−πy/L).…”

“…In addition we set the parameter ǫ 1 = 8 and ǫ 2 = 1 to reflect the values for oil and air in our application of interest [5]. For the interface position h(x) we consider three possibilities: I1 A constant profile h(x) = h 0 since in this case the results can be checked against an exact solution.…”

“…Proposition 1 Consider the transmission problem (1) to (5) with 2L−periodic boundary condition f ∈ C(R) and 2L−periodic interface 0 < h ∈ C k (R) for some integer k ≥ 2. If a solution φ α ∈ BC 2 (Ω α ), α = 1, 2 of this problem exists, then it is unique.…”