Instability of a charged layer of a viscous liquid on the surface of a solid spherical core

Abstract

The dispersion relation for the spectrum of capillary waves of a spherical layer of a viscous liquid coating a solid spherical core with a layer of finite thickness is introduced and analyzed. It is shown that the existence of two mechanisms for the viscous dissipation of the energy of the capillary-wave motions of the liquid, viz., damping in the bulk of the layer and on the solid core, leads to restriction of the spectrum of the realizable capillary waves of the liquid on both the high-and low-mode sides. At a fixed value of the system charge which is supercritical for the first several capillary modes, the maximum growth rates in the case of a small solid core are possessed by modes from the middle of the band of unstable modes, while in thin liquid layers the highest of the unstable modes have the largest growth rates. This points out differences in the realization of the instability of the charged surface of the spherical layer for small and large relative sizes of the solid core.