Nonlinear electrohydrodynamic waves on films falling down an inclined plane

The stability of a perfectly conducting viscous film, falling down an inclined plane, is considered for the case of an applied uniform normal electric field. A highly nonlinear evolution equation for the deformation of the free surface of the film is derived. The study of the linear stability of the system shows the destabilizing effect of the electric forces. A weakly nonlinear analysis leads to a Ginsburg-Landau equation, which predicts that the destabilization induced by the electric field in an otherwise stable film occurs in the form of traveling waves of finite amplitude.