Nonlinear capillary vibrations of a charged drop placed in a dielectric medium: Single-mode initial deformation of the drop shape

The nonlinear vibrations of the equilibrium spherical shape of a charged drop placed in a perfect incompressible dielectric medium are asymptotically calculated in the second-order approximation in single-mode initial deformation of the drop surface. The drop is assumed to be a perfect incompressible liquid. It is shown that the nonlinear vibration amplitudes, as well as the energy distribution between nonlinearly excited modes, depend significantly on the parameter rho, where rho is the ratio of the environmental density to that of the drop. It is also demonstrated that an increase in rho raises the amplitude of the highest of the vibration modes excited due to second-order nonlinear interaction. In the second order of smallness, the amplitude of the zeroth mode is independent of the density ratio. As rho grows, the effect of the self-charge of the drop, the interfacial tension, and the permittivity of the environment on the nonlinear oscillations increases. (C) 2003 MAIK "Nauka / Interperiodica".