(318i) The Effect of Gravity on the Shape of a Droplet on a Fiber in the Limit of Small Bond Numbers: Nearly Axisymmetric Profiles with Experimental Validation

We study the effect of gravity on static, barrel-shaped droplets on fibers using theoretical analyses, numerical simulations, and experiments. We propose a nearly axisymmetric solution to describes the shape of the droplet by conducting a regular perturbation analysis in the limit of small Bond numbers. The leading-order solution from perturbation analysis yields an axisymmetric profile whereas the first-order correction captures the effect of gravity. We report the droplet shape as a function of dimensionless droplet volume, contact angle and Bond number. We find that, due to gravity, the contact line position varies sinusoidally with the azimuthal angle around the fiber. We validate our solution by comparing droplet shape and contact line predictions with experiments and numerical simulations.