Instability of liquid film flow inside of a vertical tube in presence of an interfacial surfactant.

Liquid film coating inside a tube becomes unstable to surface-tension-driven Rayleigh-Plateau (RP) instability. The presence of interfacial surfactant reduces the growth rate of RP instability but is unable to completely eliminate it. Further, it is known that the surfactant mode, an eigenmode emerging because of the presence of surfactant, remains stable for such liquid films. However, the above two observations hold true only when the liquid film remains stationary (i.e., in the absence of base flow). Here, we investigate the linear stability of surfactant-laden liquid film inside of the tube with base flow included in the analysis. We observed a complete suppression of Rayleigh-Plateau instability because of the presence of surfactant when the basic flow is included in the analysis. However, the surfactant mode, which otherwise remains stable in the absence of base flow, is found to be unstable when the basic flow is taken into account in the stability analysis. More importantly, depending on the base flow strength, the wave number corresponding to maximum growth rate and cutoff wave number for surfactant mode are greater than unity for a wide variety of parameters. This is unlike the (RP) instability observed for surfactant-covered stationary films where the cutoff wave number is always less than unity. Further, we show that the growth rate observed for this surfactant-mode instability in the presence of sufficiently strong basic flow is significantly higher than the growth rate of RP instability observed for a stationary liquid film. These observations imply that depending on the strength of basic flow, the effect of presence of surfactant is destabilizing for such film flows as opposed to a stabilizing effect observed for stationary liquid films in earlier studies.