Nonlinear spatio-temporal instability regime for electrically forced viscous jets

This paper considers the problem of nonlinear instability in electrically driven viscous axisymmetric jets with respect to spatial and temporal growing disturbances in the presence of a uniform or non-uniform applied electric field. The mathematical modeling for the jets, which uses the original electrohydrodynamics equations (Melcher and Taylor, 1969) [8], is based on the nonlinear mechanics that govern the liquid jet due to tangential electric field effects. At the linear stage, we found that a particular jet of fluid could exhibit the Rayleigh and Conducting flow Instabilities for the spatial and temporal evolution of the disturbance. For the nonlinear regime of the problem, we studied the resonant instability and nonlinear wave interactions of certain modes that satisfy the dyad resonant condition. The nonlinear wave interactions in the jet provided a significant change in the fluid flow properties that extend notably the available understanding of the problem at the linear stage. It was found that the nonlinear resonant instability provides an amplifying effect on the magnitude of the disturbances which evolves the jet to reduce significantly its radius at a shorter axial location. For the case of higher viscosity fluid, the electric field in the jet was found to be increasing spatially and temporally when nonlinear wave interactions were taken into account during the resonant instability. The resulting nonlinear solutions for the jet thickness, jet׳s electric field, jet׳s surface charge and jet velocity are presented and discussed.