Droplet detachment from a vertical filament with one end clamped

Understanding whether a droplet adheres to or detaches from a flexible filament upon axial impact is of significant interest, particularly in the context of raindrop impact on natural surfaces. This process involves dynamic buckling followed by mode coarsening, dissipating the initial droplet kinetic energy and converting the remaining into elastic energy of the filament. To elucidate this phenomenon, we construct two phase diagrams, one while fixing the filament height and the other the droplet diameter. Notably, we observe that the energy conversion rate is inversely proportional to a Cauchy number, defining the transition between attached and detached droplet in the filament length-falling height diagram. This enables us to derive an expression for the critical falling height as a function of the filament parameters, accounting for the energy conversion rate, which emerges as a key factor for droplet detachment.