Long-wavelength structure on a charged liquid surface

The problem of the equilibrium form of a charged surface of a dielectric li quid in a strong electric field, such that a flat surface becomes unstable, is studied. A periodic long-wavelength structure with a small amplitude ca n arise when the gap between the surface and a charged electrode is small c ompared with the capillary length and the charge completely screens the ele ctric field. The equilibrium form of the surface is calculated assuming tha t the resulting wave is one-dimensional. The effect of the boundary conditi ons at the vessel walls on the dependence of the amplitude of the standing wave on the applied voltage is estimated. It is shown that this dependence is very sensitive to the conditions of contact between the vessel walls and the liquid. The possibility is discussed of using the theory developed in this paper to explain the experimental results obtained with a charged liqu id-hydrogen surface. (C) 1999 American Institute of Physics. [S1063-7761(99 )00401-1].