Longwave instability of two-layer dielectric fluid flows in a transverse electrostatic field

Abstract

Some aspects of the problem of the stability and the nature of the secondary regimes of a plane two-layer Poiseuille flow of viscous dielectric fluids between horizontal electrodes with a constant potential difference are considered. A linear analysis shows that the electrostatic field can induce the growth of perturbations with an asymptotically small wavenumber when the dielectric permeabilities of the fluids are different. On the assumption that the perturbation wavelength is large as compared with the thickness of one of the layers and comparable with the thickness of the other in order of magnitude, one of the possible mechanisms of development of finite fluctuations is investigated. Within the framework of this mechanism the initial mathematical mdoel can be reduced to an integrodifferential evolutionary Kuramoto-Sivashinsky-type equation describing the behavior of the fluid interface. The periodic solutions of this equation, which are investigated numerically, are bounded and fairly diverse.