Modelling droplet coalescence on a tilted superhydrophilic cylindrical wire

Transporting droplets along cylindrical wires is an emerging focus area with various practical applications such as fog collection and filtration. Recent experiments by Feng et al. (2022) have revealed a wealth of new droplet coalescence dynamics on a superhydrophilic cylindrical wire, illustrating the need for more advanced theory. In this study, we present a mathematical model using lubrication theory and weighted residual modeling techniques for a thin liquid film flowing on a tilted superhydrophilic cylinder. This model incorporates key physical factors such as gravity, low-to-moderate inertia effects, viscous dissipation, surface tension, and disjoining pressure. This model explains the observed phenomenon of directional self-propelled transport during droplet coalescence, where the large droplet moves towards the small one. Moreover, we identify two distinct coalescence modes that result in either droplet oscillations or quasi-static droplet collapses. Stability analysis and numerical simulation agree well with the experimental observations.