Nonlinear electroviscoelastic potential flow instability theory of two superposed streaming dielectric fluids

The nonlinear electrohydrodynamic Kelvin–Helmholtz instability of two superposed viscoelastic Walters B′ dielectric fluids in the presence of a tangential electric field is investigated in three dimensions using the potential flow analysis. The method of multiple scales is used to obtain a dispersion relation for the linear problem, and a nonlinear Ginzburg–Landau equation with complex coefficients for the nonlinear problem. The linear and nonlinear stability conditions are obtained and discussed both analytically and numerically. In the linear stability analysis, we found that the fluid velocities and kinematic viscosities have destabilizing effects, and the electric field, kinematic viscoelasticities, and surface tension have stabilizing effects; and that the system in the three-dimensional disturbances is more stable than in the corresponding case of two-dimensional disturbances. While in the nonlinear analysis, for both two- and three-dimensional disturbances, we found that the fluid velocities, surface tension, and kinematic viscosities have destabilizing effects, and the electric field, kinematic viscoelasticities have stabilizing effects, and that the system in the three-dimensional disturbances is more unstable than its behavior in the two-dimensional disturbances for most physical parameters except the kinematic viscosities.