Electrohydrodynamic stability of a two-layer plane Poiseuille flow in the presence of interfacial surfactant: Energy budget analysis

The electrohydrodynamic stability of a two-layer plane Poiseuille flow has been examined under the influence of an electric field acting normally to the unperturbed interface of two viscous immiscible fluids. The presence of insoluble surfactant at the interface is considered to achieve passive control over the instability that naturally comes into play in such flows. The fluids considered here for the asymptotic and numerical stability analyses are treated as leaky dielectrics, which are allowed to have different viscosities, densities, permittivities, and conductivities. An asymptotic analysis shows that the two opposite influences from the electrical stresses and the Marangoni stresses in competition at the interface give rise to remarkably different patterns of neutral curves depending upon the ratios of viscosities and thicknesses of the fluid layers. A linear stability analysis utilizing the Chebyshev spectral collocation method for disturbances of all wave numbers is employed numerically to obtain various types of dispersion curves and neutral stability diagrams originating from the associated Orr–Sommerfeld eigenvalue problem. Our results suggest that increasing the electrical conductivity ratio leads to an increase in the growth rate of disturbances, whereas an increase in the electrical permittivity ratio stabilizes the flow as the interfacial surface tension resists the growth of perturbations that are otherwise promoted by electrical stresses. The energy budget calculations show that the presence of the insoluble surfactant is primarily responsible for the viscosity-induced instability triggered by the modified interface deformation. The comparisons with pertinent studies are performed to enhance the quantitative reliability of the present work.