Dynamics and rupture of planar electrified liquid sheets

We investigate the stability of a thin two-dimensional liquid film when a u niform electric field is applied in a direction parallel to the initially f lat bounding fluid interfaces. We consider the distinct physical effects of surface tension and electrically induced forces for an inviscid, incompres sible nonconducting fluid. The film is assumed to be thin enough and the su rface forces large enough that gravity can be ignored to leading order. Our aim is to analyze the nonlinear stability of the flow. We achieve this by deriving a set of nonlinear evolution equations for the local film thicknes s and local horizontal velocity. The equations are valid for waves which ar e long compared to the average film thickness and for symmetrical interfaci al perturbations. The electric field effects enter nonlocally and the resul ting system contains a combination of terms which are reminiscent of the Ko rtweg-de-Vries and the Benjamin-Ono equations. Periodic traveling waves are calculated and their behavior studied as the electric field increases. Cla sses of multimodal solutions of arbitrarily small period are constructed nu merically and it is shown that these are unstable to long wave modulational instabilities. The instabilities are found to lead to film rupture. We pre sent extensive simulations that show that the presence of the electric fiel d causes a nonlinear stabilization of the flow in that it delays singularit y (rupture) formation. (C) 2001 American Institute of Physics.