Stability of capillary waves on charged surface of water layer on electrically driven solid cylindrical rod

Abstract

Analytically, in a linear approach on the dimensionless amplitude of oscillation, the dispersion equation for capillary waves is obtained on the charged liquid layer surfaces on a conductive cylindrical firm bar of the final thickness. It is shown that the firm core has a stabilization effect on capillary waves and reduces the destabilizing influence of a radial electric field. The influence of the core becomes substantial only at values of the radius comparable with the outer radius of the cover. The higher the density of the superficial charge, the wider the range of unstable wave numbers and the higher the values of the instability increase increments.