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We present a control-volume approach for deriving a simplified model for thegravity-driven flow of an axisymmetric liquid film along a vertical fiber. Themodel accounts for gravitational, viscous, inertial and surface tension effectsand results in a pair of coupled one-dimensional nonlinear partial differentialequations for the film profile and average downward velocity as functions oftime and axial distance along the fiber. Two versions of the model areobtained, one assuming a plug-flow velocity profile and a constant thinboundary layer thickness to model the drag force on the fluid, the otherapproximating the drag using the fully-developed laminar velocity profile for alocally uniform film. A linear stability analysis shows both models to beunstable to long waves or short wavenumbers, with a specific wavenumber in thatrange having a maximal growth rate. Numerical simulations confirm thisinstability and lead to nonlinear periodic traveling wave solutions which canbe thought of as chains of identical droplets falling down the fiber. Physicalexperiments are also carried out on such a system using safflower oil as theworking liquid and a taut fishing line as the fiber. A machine learning schemeis used to find the best set of parameters in the laminar flow model to matchthe experimental results to the simulations. Good agreement is found betweenthe two, with parameter values that are quite close to their original estimatesbased on the approximate values of the physical parameters.

Liquid films falling down a vertical fiber: modeling, simulations and experiments