The Shape and Stability of Small Liquid Drops on Fibers

The shape of a small liquid drop on a small diameter fiber may be either an axisymmetric barrel shape or it may be a non-axisymmetric clam-shell shape. Experiments show that when the reduced volume, given by the volume of droplet divided by the fiber radius, is large the barrel shape is the preferred conformation, but that as the volume reduces a transition to a clam-shell (pearl) shape occurs. The volume at which this stability transition occurs depends upon the equilibrium contact angle. In this work we review the known solution to Laplace's equation for the barrel shape and consider the link between the profile, the inflexion in the profile and the stability of the droplet. No known solution of Laplace's equation exists for the clam-shell shape droplet. We therefore consider a finite element approach to determining the possible shapes of a droplet on a fiber and give numerical results for the clam-shell profile. The surface free energies for the two types of droplet conformation on a fiber are computed for several droplet volumes and equilibrium contact angles and the implications of this for droplet stability are discussed.