Electric modification of mode competition in viscous films with insoluble surfactants on vertical fibers

Abstract

This study investigates the coupled effects of an insoluble surfactant and a radial electric field on the stability of a viscous liquid film flowing down a vertical fiber. Starting from the governing equations in two dimensions, a reduced model in one dimension is derived using the long wave approximation to describe the coupled evolution of the interface and surfactant transport. Linear stability analysis identifies two distinct unstable modes: the Rayleigh-Plateau mode, which dominates at lower values of the Marangoni number $Ma$, and the Marangoni mode, which becomes dominant at higher values of $Ma$. The influence of the radial electric field is determined by the position of the outer electrode $β$. When $β<\mathrm{e}$, the electric field enhances both instabilities and narrows the stable interval in $Ma$ between the two modes. When $β>\mathrm{e}$, the electric field suppresses both modes and can completely eliminate the unstable region associated with the Marangoni mode even at a relatively small electric Weber number $E_b$. Continuation of the traveling wave solutions further shows that, when $β<\mathrm{e}$, the magnitude of the relative interfacial motion $I_{RP}$, generally increases with $E_b$. By contrast, the intensity of Marangoni convection $I_{M}$ varies only weakly at smaller values of $E_b$ and increases appreciably only when the electric field becomes sufficiently strong. Analysis of the stream function and the relative interfacial velocity reveals that the electric stress primarily intensifies the recirculation beneath the wave crest and reshapes the spatial distribution of the relative interfacial velocity.