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. We validate our solution by comparing droplet shape and contact line predictions with experiments and Surface Evolver simulations.