Numerical study of liquid film drainage around a vertical cylinder

For a thin liquid film around a vertical solid cylinder, this study aims to understand the flow phenomenon while it falls down the cylinder assisted by gravity, using a three-dimensional finite volume scheme. The problem is described broadly in three stages of development, i.e., film dynamics, convergence of film into a jet, and jet behavior. The interplay between inertia, gravity, and surface tension dictates these evolutions: gravity promotes vertical drainage, inertia stabilizes the jet, and surface tension minimizes the interface area, leading to Rayleigh–Plateau instability, which ultimately produces droplet breakup. The film flow is described with a self-similar scaling. Pressure distributions and velocity vectors are employed to understand convergence. Correlations are developed for the dripping/jet responses to the globally defined parameters. The jet formation is represented as a direct consequence of the propagation of wave patterns on the film, highlighting that the spatial and temporal evolution of film disturbances sets the parameters for the jet's velocity profile, diameter, and breakup phenomenon, summarized in a parametric regime map. Finally, a Lagrangian analogy is constructed between interwoven beads falling down a vertical pole and the draining liquid moieties, where the attractive inter-bead forces, mimicking surface tension, overcome the inertial resistance to effectively pinch the layer to capillary length scale.