Instabilities of a thin liquid film in a funnel

We explore flow of a completely wetting fluid in a funnel, with particular focus on contact line instabilities at the fluid front. While the flow in a funnel may be related to a number of other flow configurations as limiting cases, understanding its stability is complicated due to the presence of additional azimuthal curvature, as well as due to convergent flow effects imposed by the geometry. Convergent nature of the flow leads to thickening of the film, therefore influencing its stability properties. In this work, we analyze these stability properties by combining physical experiments, asymptotic modeling, self-similar type of analysis and numerical simulations. We show that appropriate long-wave based model supported by the input from experiments, simulations and linear stability analysis origination from the flow down an incline plane provides a basic insight allowing to understand the development of contact line instability and emerging lengthscales.