Profiles of Liquid Drops at the Tips of Cylindrical Fibers

In 1976, B. J. Carroll derived the equation to show that a symmetric liquid droplet sitting on a thin cylindrical fiber would acquire a bell shape at equilibrium. We have extended his derivation to describe a drop located at the top end of a vertical, cylindrical fiber. By minimizing the Gibbs free energy of the drop at the fiber tip, it was found that the drop consists of two portions, a spherical cap on the fiber tip and a full, symmetrical bell located on the fiber body adjacent to the fiber tip. The experimental verification of the predicted shapes was performed using water, ethylene glycol, and Kaydol drops on nylon cylindrical fibers. Only four parameters are required to obtain agreement between the theoretical shape and the observed shape: the drop volume, the fiber radius, the surface tension of the liquid, and the Young contact angle of the liquid on a flat surface of the same composition as the fiber.