Droplet at the Corner of a V-Shaped Fiber

Abstract

A fundamental question in the physics of droplet--fiber interactions is: What is the maximum droplet volume a fiber can retain? While this problem has been studied for horizontal fibers and at the apex $\Lambda$-shaped bent fibers, it remains less explored for V-shaped bent fibers, despite their demonstrated advantages in engineering applications such as fog harvesting. This work investigates the capability of V-shaped fibers in retaining droplets against gravity. An analytical model to predict the maximum droplet volume on V-shaped fibers is developed based on free energy analysis, and validated against experimental data from five liquid--fiber pairs. The dependence of the maximum droplet volume on $\alpha$ can be reasonably captured by the function $\cos\beta/\cos\left(\beta-\alpha/2\right)$, where $\beta$ denotes the droplet's off-axis angle. As $\alpha$ increases from $0^\circ$ to $180^\circ$, the maximum droplet volume slightly decreases before entering a broad transition region around $\alpha \approx 40^\circ$--$100^\circ$, and then increases at larger $\alpha$.