The stability of a water drop oscillating with finite amplitude in an electric field

Abstract

By assuming that an uncharged drop situated in a uniform electric field E retains a spheroidal shape while oscillating about its equilibrium configuration, two approximate equations of motion are derived for the deformation ratio γ expressed as the ratio a/b of the major and minor axis of the drop. Solutions of these equations of motion indicate that the stability of a drop of undistorted radius R and surface tension T depends upon E(R/T) ½ and the initial displacement of γ from its equilibrium value. The predictions of the two equations are compared to assess the accuracy of the spheroidal assumption as applied to such a dynamical situation. The analysis is used to determine the stability criterion of a drop subject to a step function field. Finally, the limit of validity of the spheroidal assumption is discussed in terms of Rayleigh's criterion for the stability of charged spherical drops. By applying Rayleigh's criterion to the poles of a spheroidal drop, the stage at which the drop departs from spheroidal form to form conical jets was approximately determined.