Effect of the electric field on the wave flow regimes of a thin film of a viscous dielectric fluid

Waves on the surface of a thin film of a viscous dielectric fluid flowing down the inner surface of one plate of a plane capacitor with alternating voltage applied is considered. It is shown that the volume forces acting from the inhomogeneous electric field are negligibly small in the case of long waves, and the influence of the electric field reduces to the influence of additional pressure onto the film surface. A model equation for determining the deviation of the film thickness from the undisturbed value is derived in the long-wave approximation. Some numerical solutions of this equation are given.