Deformation and nonlinear corrections to critical conditions of charged drop instability in an electrostatic suspension

Nonlinear asymptotic analysis of a charged drop placed in electrostatic and gravitational fields reveals a correction to the oscillation frequency and, accordingly, to the critical Rayleigh parameter. The analysis uses approximations quadratic in oscillation amplitude and linear in dimensionless equilibrium deformation of the drop. The correction is found to be proportional to the product of the oscillation amplitude and deformation. It is natural to name this correction deformational. In computations of the third order of smallness in oscillation dimensionless amplitude, a correction to the frequency and Rayleigh parameter appears, which is due to a nonlinear interaction between oscillation modes. This correction is larger than the deformational one in magnitude. Deformational corrections can be eliminated by experimenting under no-gravity conditions, but corrections due to the nonlinearity of hydrodynamic equations cannot be eliminated in this way. It is these corrections that are responsible for a critical Rayleigh parameter measurement inaccuracy.