Wave interactions on a viscous film coating a vertical fibre: Formation of bound states

Fibre coating has attracted considerable attention over the past years due to its engineering applications as well as fundamental interest generated by the fascinating complexity of the resulting flow. A liquid film coating axisymmetrically a vertical fibre and flowing under the action of gravity spontaneously breaks up into a regular drop-like wave train. This instability results primarily from the capillary pressure induced by the azimuthal curvature (Rayleigh-Plateau instability) while the pressure induced by the axial curvature has a stabilising effect. Streamwise viscous diffusion plays a dispersive role that dramatically affects the waves selection, speeds and shapes. When both surface tension and viscosity effects are strong, complex wave interactions lead to the formation of bound states. In this study, we investigate experimentally the details of those interactions and show that regular patterns of bound states can be obtained by external forcing. A qualitative theoretical explanation of the experimental findings is provided with a simple model for the flow.