On nonlinear deformation correction to oscillations frequencies of a strongly charged drop in an electrostatic suspension

Abstract

In fourth-order nonlinear asymptotic calculations for eccentricity (which measures the stationary deformation of a charged drop in an external electrostatic field) and first-order calculations for the dimensionless amplitude of its oscillations, the frequency of a strongly charged drop in a weaker external uniform electrostatic field is calculated. The deformation corrections to the frequency related to the change in the equilibrium shape of a drop in comparison with its spherical shape are found. As the surface area of a drop in an external field increases, the oscillation frequency of the drop decreases and the deformation correction has one sign (negative). When the drop charge tends to critical (to the limit, om the sense of stability with respect to the superposition of its own and induced charges), the value of the correction is comparable to the frequency in order of magnitude.