CAPILLARY OSCILLATIONS AND TONKS-FRENKEL INSTABILITY OF A LIQUID LAYER OF FINITE THICKNESS

A dispersion relation is derived and analyzed for the spectrum of capi llary motion at a charged hat surface of viscous liquid covering a sol id substrate with a layer of finite thickness. It is shown that for wa ves whose wavelengths are comparable with the layer thickness, viscous damping at the solid bottom begins to play an important role. The spe ctrum of capillary liquid motion established in this system has high a nd low wave number limits. The damping rates of the capillary liquid m otion with wave lengths comparable with the layer thickness are increa sed considerably and the Tonks-Frenkel instability growth rates are re duced compared with those for a liquid of infinite depth. (C) 1997 Ame rican Institute of Physics.