Weakly nonlinear EHD stability of slightly viscous jet

A weakly nonlinear approach is utilized here to study the electrohydrodynamic (EHD) instability of an incompressible viscous liquid jet stressed by an axial electric field. The linear motion equations is solved in the light of nonlinear boundary conditions. The viscosity is assumed to be small. The study takes into account both the shear and radial components of the stresses at the interface. In the linear theory, we discuss the breakup phenomena of liquid jets. Also, it is found that, the electrical shearing stresses have no effect at the linear marginal state, while the linear cutoff wavenumber depends on the electrical shearing stresses. A nonlinear perturbation method is introduced. This method can be described our problem precisely. The nonlinear stability is compared with the linear stability condition in the weak viscosity case. It is found that, the weak viscosity has effect on the nonlinear stability condition, in contrast with the linear analysis, whereas the nonlinear cutoff wavenumber doesn't depend on the weak viscosity in both the linear and nonlinear theory.