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.