Instability of the $n$th oscillation mode of a charged droplet in the presence of a uniform electrostatic field

The stability of the nth oscillation mode of a charged droplet in the presence of a uniform electro-static field is studied using nonlinear asymptotic calculations with the aid of the expansion in terms of two small parameters (dimensionless equilibrium deformation of a droplet and the ratio of the oscillation amplitude to radius). It is demonstrated that identical effects determine the droplet instability in the presence of electrostatic field for an uncharged droplet and a droplet with a charge that is less than the critical Rayleigh charge. The critical field parameter is saturated when the mode number increases but the corresponding asymptotic level that is parallel to the abscissa axis decreases with an increase in the droplet charge.