Thin films flowing on vertical fibers

We describe annular films flowing and thinning along vertical fibers. According to the film thickness and to the radius of the fiber, two different kinds of behaviour can be observed: i) when the film is thick, drops develop because of the Rayleigh instability and flow downward. Some of them grow by swallowing the other ones, and quickly fall, leaving behind them a thick film which breaks in turn into droplets. ii) For a thin film on a large fiber, the instability cannot grow because of the flow. We present a quantitative study of the conditions under which drops do not appear, and show that these conditions are compatible with a scenario of nonlinear saturation of the Rayleigh instability.