The effect of electric fields on the rupture of thin viscous films by van der Waals forces

We examine the stability of a thin two-dimensional incompressible liquid film when an electric field is applied in a direction parallel to the initially flat bounding fluid interfaces, and study the competition between surface tension, van der Waals, viscous, and electrically induced forces. The film is assumed to be sufficiently thin, and the surface tension and electrically induced forces are large enough that gravity can be ignored to the leading order. We analyze the nonlinear stability of the flow by deriving and numerically solving a set of nonlinear evolution equations for the local film thickness and the horizontal velocity. We find that the electric field forces enhance the stability of the flow and can remove rupture. If rupture occurs then the form of the singularity, to leading order, is that found in the absence of an electric field.