Capillary oscillations of a thin film of viscous liquid on a solid substrate and its instability against surface charge

In a numerical analysis of the dispersion relation describing capillary motions in a thin film of a viscous, surface-charged liquid with fluctuation forces taken into account, it is found that the critical conditions of instability of the free surface of the liquid for a fixed thickness d of the liquid film in the region where the influence of the fluctuation forces is large (d<100 nm) depend strongly on the wave number and do not depend on the viscosity of the liquid, that the fluctuation forces strongly affect the wave number of the most unstable wavelength and decrease the instability growth rate, and that the capillary motions of the liquid admit an analogy with gravity-capillary motion and can be interpreted as fluctuation-capillary motions. Zh. Tekh. Fiz. 68, 27–31 (October 1998)