Stability of a liquid film hanging underneath a large horizontal cylinder

Abstract

Here we investigate stability of a film of viscous liquid hanging under a large horizontal cylinder. The liquid film is restricted by two straight contact lines; it is hold by the capillary force balancing the action of gravity. However, Rayleigh-Taylor instability of perturbations along the cylinder may destabilize the film and cause liquid dripping. Here we develop quasi-two-dimensional model for growth and propagation of perturbations in such a film. Linear stability analysis is carried out and the dispersion relationships are obtained. It is found that the width of the film is crucial for film stability: when the width is thinner than certain level, the film remains stable. Above this level, Rayleigh-Taylor instability develops. The wavelength of the fastest growth also depends on the film width. The cases of periodic perturbation and nonlinear localized perturbations are considered; in the latter case, the initial perturbation gets deformed into a new signal dominated by the wavelength of maximum growth.