Electric fields as a means of controlling thin film flow over topography

Gravity-driven, steady-state flow of a thin liquid film over a substrate containing topography in the presence of a normal electric field is studied numerically. The liquid is assumed to be a perfect conductor and the air above it an ideal dielectric. The Navier-Stokes equations are solved using a new depth-averaged approximation that is capable of analyzing film flows with inertia with the flow coupled to the electric field via a Maxwell normal stress term that results from the solution of Laplace’s equation for the electric potential above the film. The latter is solved analytically using separation of variables and Fourier series. The coupled solver is used to analyse the interplay between inertia and electric field effects for flow over one-dimensional step and trench topographies and to predict the effect of an electric field on three-dimensional Stokes flow over a two-dimensional trench topography. Sample results are given which investigate the magnitude of the electric fields needed to suppress free surface disturbances induced by topography in each of the cases considered.