Wave flows in a thin layer of a viscous liquid. Influence of a constant electric field

The influence of a constant transverse electric field on the dynamics of longwave, weakly nonlinear flow of a viscous dielectric liquid film down a vertical wall is studied. An amplitude integrodifferential equation in partial derivatives of the Kuramoto–Sivashinskii equation type, which describes the behavior of the free surface of the layer, is derived using the method of multiscale stretching. In the case considered, the potential energy of the electric field is a source of longwave perturbations, but, on the whole, secondary regimes are apparently nonlinearly steady. Probably, the electric polarization effects studied can be used as a factor that governs the dynamics of film flow.