  We investigate theoretically and numerically the diffusion-limited
evaporation of a liquid deposited on a fiber in two configurations: a sleeve
and a axisymmetric barrel-shaped droplet. For a sleeve, the local flux depends
on both the aspect ratio and the smallest length of the problem. By using
analytical calculations and 3D finite elements simulations, we predict a
divergence of this flux further localized at the edge as the aspect ratio
increases. The evaporation of axisymmetric drops on a fiber is studied with
numerical simulations. For sufficiently large volumes, we evidence that the
evaporation rate is almost independent of the wetting properties of the liquid,
even for small contact angles, and that the droplets evaporate as spheres of
the same volume.
