  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 using a full lubrication
model that includes slip boundary conditions, nonlinear curvature terms, and a
film stabilization term. This study brings to focus the presence of a stable
liquid layer 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 droplets. This is also supported by stability analysis of the
traveling wave solution of the model.
