The extended Rayleigh theory of the oscillation of liquid droplets

Abstract

The Rayleigh theory of oscillation of liquid drops is extended to include the effects of viscosity and a uniform external electric field. The resonant frequencies of the modes of the drop are shown to be shifted by the electric field. The magnitude and sign of the frequency shift depends on the dielectric constant of the drop. The condition for instability of drops in large electric fields is given and found to differ from that given by previous workers. This difference is attributed to the assumption by previous workers that the drops, under the influence of an electric field, distort into ellipsoids of revolution about the field direction. The dynamical equations are derived and the solution for small oscillations is given in an oscillating field and in an amplitude-modulated optical field.