Role of insoluble surfactant on electrohydrodynamic stability of a two-layer plane Poiseuille flow: An asymptotic analysis

The electrohydrodynamic stability of a two-layer plane Poiseuille flow has been considered under the influence of an electric field acting normally to the interface of the two viscous immiscible fluids. The two fluids considered here for the asymptotic stability analysis are leaky dielectrics. The study on the influence of a monolayer of insoluble surfactant at the fluid-fluid interface reveals that the interfacial surfactant further enhances or suppresses the electric field-induced instability. The long-wave linear stability analysis is carried out in the framework of Orr–Sommerfeld analysis for leaky dielectrics. In the context of long-wave linear stability study, the phase speed is expressed as a function of the ratio of viscosities ($m$), layer thicknesses ($d$), densities ($r$), permittivities ($\varepsilon$) and conductivities ($l$) of the two fluids. The electric field is observed to have either a destabilizing or a stabilizing effect, primarily non-monotonic, depending upon the ratios of permittivities and conductivities of the two fluids. It is found that when $m>d^2$, the region of instability in the $\varepsilon -l$ plane increases with increasing Marangoni number ($Ma$); however, when $m<d^2$, the scenario reverses. The electrohydrodynamic interface instability among two viscous fluids with varying electrical properties in plane Poiseuille flow has applications in microfluidic devices for mixing and droplet formation. Therefore, the present study aims to propose a control mechanism for the instability occurring at the interface through the modified interface tension.