Electrohydrodynamic oscillation and stability of a charged drop

Abstract

Small amplitude oscillations of a charged fluid globule immersed in a viscous dielectric are studied with special regard for the processes of surface charge relaxation and convection. Perfect dielectrics and conductors behave in identical fashion insofar as oscillation frequencies and stability are concerned whenever viscous effects are small. This similarity is due to interfacial charge convection, in the case of a perfect dielectric, and charge conduction, with a perfect conductor. The damping of stable oscillations depends, however, on the rate of interfacial charge relaxation: With instantaneous relaxation the damping rates are the same as those found with uncharged droplets, while with slower relaxation rates the dissipation is concentrated in an electrohydrodynamic boundary layer outside the drop. If viscous effects predominate then the existence of charge relaxation introduces oscillatory behavior in place of the aperiodic damping characteristic of uncharged drops. Several special circumstances are examined in detail.