Nonlinear oscillations of the free surface of a charged drop of a highly viscous liquid

An analytical expression for the shape of a charged drop of a highly viscous, incompressible conducting liquid performing nonlinear axisymmetric oscillations upon a small multimode initial deformation have been obtained by direct expansion within the second order of smallness. Using the obtained expression, it is possible to study the temporal evolution of the shape of initially deformed viscous drops bearing charges that are both sub-and supercritical from the standpoint of the Rayleigh criterion of stability.