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Coating Liquid Films down a Vertical Fibre

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Previous experimental study by Kliakhandler et al. (JFM 429:381-390, 2001) reported three different flow patterns of a liquid film flowing down a vertical cylinder. The film flow is unstable due to the famous Plateau-Rayleigh mechanism, which evolves into organised droplets flow patterns. When the flow rate is high, steady moving droplets separated by a long-thin film were observed. When the flow rate is reduced, necklace-like flow structure was seen. When the flow rate is very small, droplets of multi-scales were observed and complex dynamical interactions between these droplets cause an unsteady flow. However, no previous theoretical model correctly predicted the droplet dynamics in the three regimes. In this talk, I will discuss the reasons accounting for poor predictions of liquid film dynamics down a vertical fibre. Then, we solve the Navier-Stokes problem and our results show excellent agreements with the experimental data by Kliakhandler et al.

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