Nonlinear electrohydrodynamics of free surfaces

Electrical stresses acting at electrified interfaces govern the dynamics of fluids in many situations of practical relevance. In order to understand the electrohydrodynamics of these systems, a knowledge of the forces acting at interfaces is necessary. We will review the balance equations for the forces and the charge density. The relevant nondimensional numbers will be derived and illustrated with some particular cases. The problems of shallow horizontal layers and inclined thin films of perfectly conducting liquids will be examined in some detail