Abstract
The electrohydrodynamic Kelvin–Helmholtz instability of the interface between two uniform superposed Rivlin–Ericksen viscoelastic dielectric fluid-particle mixtures in porous medium is investigated. The considered system is influenced by a uniform horizontal electric field. Perturbations transverse to the direction of streaming are found to be unaffected by either streaming and applied electric fields for the potentially stable configuration as long as perturbations in the direction of streaming are ignored, and the system remains stable in this case. For the potentially unstable configuration, the system is found to be stable or unstable for a certain wavenumber range depending on acceleration due to gravity, surface tension, and fluid velocities. For perturbations in all other directions, there exists instability for a certain wavenumber range, and the instability of the system can be delayed by the applied electric field. Numerical results show that Stokes' drag coefficient, electric field, kinematic viscosity have stabilizing effects; and mass density of the particles, porosity of the porous medium, kinematic viscoelasticity, fluid velocity, number density of the particles have destabilizing effects; while permeability of the medium has a dual role in the stability of the considered system, and the porosity of the porous medium has no effect on the stability for large wavenumbers. The limiting case of Rayleigh–Taylor instability is also discussed, and stability conditions are obtained.