Effect of gravity on the shape of a droplet on a fiber: Nearly axisymmetric profiles with experimental validation

We study the effect of gravity on barrel-shaped droplets on fibers using theoretical analyses, numerical simulations, and experiments. By performing a perturbation analysis in the limit of small Bond numbers and small dimensionless droplet volumes, we formulate a nearly axisymmetric solution that describes the shape of the droplet. The leading-order solution yields the axisymmetric profile and the first-order correction incorporates the effect of gravity. Thus, 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.