Global geometry and the equilibrium shapes of liquid drops on fibers

The wetting of a planar surface depends upon both the chemical nature of the surface and the local geometry. On a chemically identical solid surface in the form of a fiber the wetting is significantly different due to the global geometry of the cylindrical shape. A fluid that fully wets a material in the form of a smooth planar surface may not wet the same material when presented as a smooth fiber surface. On a fiber, a vanishing contact angle is not a sufficient condition for the formation of a wetting film; a macroscopic barrel shaped droplet with a vanishing equilibrium contact angle can exist. Moreover, two distinctly different geometric shapes of droplet are possible: a barrel and a clam-shell. In this work, these two shapes are considered using an analytical result for the barrel shape and a finite element calculation for the clam-shell shape. The surface free energies for these two conformations are evaluated for contact angles between 14 and 70degrees and for a wide range of droplet volumes. The results show that when the droplet volume is large or the contact angle is small, an axisymmetric barrel shape is the energetically preferred conformation, but that as the volume reduces or the contact angle increases the clam-shell shape becomes lower in energy. These results are compared to literature data for the roll-up (barrel-to-clam-shell) transition and to a previously published criterion for metastability of the barrel shaped droplet. A conjecture on the role of the inflection angle in the barrel-shape droplet profile is also considered. For the contact angle range considered, the finite element results show that all barrel-shaped droplets that are lower in energy than clam-shell droplets, are stable according to the metastability condition and also possess an inflection angle. (C) 2002 Elsevier Science B.V. All rights reserved.