Abstract
The effect of an applied electric field on the stability of the interface between two thin viscous leaky dielectric fluid films in porous medium is analyzed in the long-wave limit. A systematic asymptotic expansion is employed to derive coupled nonlinear evolution equations of the interface and interfacial free charge distribution. The linearized stability of these equations is determined and the effects of various parameters are examined in detail. For perfect-perfect dielectrics, the various parameters affect only for small wavenumber values. For dielectrics, the various parameters affect only for small wavenumber values. For effect for small wavenumbers, and a stabilizing effect afterwards, and for high wavenumber values for the other physical parameters, new regions of stability or instability appear. For leaky-leaky dielectrics, the conductivity of upper fluid has a destabilizing effect for small or high wavenumbers, while it has a dual role on the stability of the system in a wavenumber range between them. The effects of all other physical parameters behave in the same manner as in the case of perfect-leaky dielectrics, except that in the later case, the stability or instability regions occur more faster than the corresponding case of leaky-leaky dielectrics.
Highlights
The effect of electric fields on the stability and dynamics of fluid-fluid interfaces has been an area of extensive research, beginning from the classic works of Taylor and McEwan 1 and Melcher and Smith 2
Mohamed et al 5 concentrated on two superposed viscous fluids in a channel subjected to a normal electric field, where the upper fluid is highly conducting, while the lower fluid is dielectric, and they performed the long-wave linear stability analysis, 6, 7, and showed that the electric field always has a destabilizing effect on the flow
The system of interest consists of two leaky dielectric fluids in porous medium of arbitrary viscosities occupying the regions −H < y < 0 fluid 2 and 0 < y < βH fluid 1 in the initial unperturbed state, see Figure 1, where β is the ratio of the thicknesses of top and bottom fluids
Summary
The effect of electric fields on the stability and dynamics of fluid-fluid interfaces has been an area of extensive research, beginning from the classic works of Taylor and McEwan 1 and Melcher and Smith 2. Abdella and Rasmussen 8 studied Couette flow of two viscous fluids with different viscosities, densities, conductivities and permittivities, in an unbounded domain subjected to a normal electric field They studied, following Melcher 9 , two special cases in detail: the electrohydrodynamic free-charge configuration EH-If and the electrohydrodynamic polarization charge configuration EH-If. They studied, following Melcher 9 , two special cases in detail: the electrohydrodynamic free-charge configuration EH-If and the electrohydrodynamic polarization charge configuration EH-If These studies have largely considered systems in which gravitational effects are important, and a critical applied voltage is required to cause the instability, very long waves are stabilized by interfacial tension, and waves of intermediate lengths become unstable.
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