Dynamics of thin liquid films on vertical cylindrical fibers*

Recent experiments of thin films flowing down a vertical fiber with varying nozzle diameters present a wealth of new dynamics that illustrate the need for more advanced theory. We present a detailed analysis for a full lubrication model that includes slip boundary conditions, nonlinear curvature terms, and generalized van der Waals physics. This study brings to focus the presence of a stable liquid substrate playing an important role in the full dynamics. We propose a combination of these physical effects to explain the observed velocity and stability of traveling droplets in the experiments and their transition to isolated droplet. This is also supported by stability analysis of the traveling wave solution of the model.