INSTABILITY OF A CHARGED LAYER OF A VISCOUS-LIQUID ON THE SURFACE OF A SOLID SPHERICAL CORE

The dispersion relation for the spectrum of capillary waves of a spher ical layer of a viscous liquid coating a solid spherical core with a l ayer of finite thickness is introduced and analyzed. It is shown that the existence of two mechanisms for the viscous dissipation of the ene rgy 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 s pectrum of the realizable capillary waves of the liquid on both the hi gh- and low-mode sides. At a fixed value of the system charge which is supercritical for the first several capillary modes, the maximum grow th 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 c harged surface of the spherical layer for small and large relative siz es of the solid core. (C) 1997 American Institute of Physics.