Liquid Films Falling Down a Vertical Fiber: Modeling, Simulations and Experiments

We provide a new framework for analyzing the flow of an axisymmetric liquid film flowing down vertical fiber, applicable to fiber coating flows and those in similar geometries heat exchangers, water treatment, desalination processes. The problem considered is that viscous falling under influence gravity surface tension on solid cylindrical fiber. Our approach different from existing ones we derive our mathematical model by using control-volume express conservation mass axial momentum simple intuitively appealing forms, resulting pair equations are reminiscent Saint-Venant shallow-water equations. Two versions obtained, one assuming plug-flow velocity profile with linear drag force expression, other fully-developed laminar locally uniform approximate drag. These can, respectively, high- low-Reynolds number regimes flow. Linear stability analyses fully nonlinear numerical simulations presented show emergence traveling wave solutions representing chains identical droplets Physical experiments safflower oil fishing line also undertaken match theoretical predictions well when machine learning methods used estimate parameters.