Symmetric and asymmetric capillary bridges between a rough surface and a parallel surface.

Although the formation of a capillary bridge between two parallel surfaces has been extensively studied, the majority of research has described only symmetric capillary bridges between two smooth surfaces. In this work, an instrument was built to form a capillary bridge by squeezing a liquid drop on one surface with another surface. An analytical solution that describes the shape of symmetric capillary bridges joining two smooth surfaces has been extended to bridges that are asymmetric about the midplane and to rough surfaces. The solution, given by elliptical integrals of the first and second kind, is consistent with a constant Laplace pressure over the entire surface and has been verified for water, Kaydol, and dodecane drops forming symmetric and asymmetric bridges between parallel smooth surfaces. This solution has been applied to asymmetric capillary bridges between a smooth surface and a rough fabric surface as well as symmetric bridges between two rough surfaces. These solutions have been experimentally verified, and good agreement has been found between predicted and experimental profiles for small drops where the effect of gravity is negligible. Finally, a protocol for determining the profile from the volume and height of the capillary bridge has been developed and experimentally verified.

Profiles of liquid drops at the bottom of cylindrical fibers standing on flat substrates.

Based on Carroll's derivation that describes a symmetric liquid drop sitting on an infinite cylindrical fiber and the shape of the drop, we have extended the derivation to describe a drop located at the bottom of cylindrical fibers standing on flat substrates. According to our derivation, the shape of the drop forms a bell as predicted by Carroll but is cut off by the flat substrate. This theoretical prediction was verified experimentally using water, ethylene glycol, and Kaydol drops on glass, nylon and polypropylene cylindrical fibers, and on polytetrafluoroethylene (PTFE) and polyester (PET) flat substrates. We found that only four parameters are required to obtain agreement between the theoretical shape and the observed shape: the drop volume, the fiber radius, the liquid-fiber contact angle, and liquid-flat substrate contact angle.

Gibbs free energy of liquid drops on conical fibers.

Small drops can move spontaneously on conical fibers. As a drop moves along the cone, it must change shape to maintain a constant volume, and thus, it must change its surface energy. Simultaneously, the exposed surface area of the underlying cone must also change. The associated surface energies should balance each other, and the drop should stop moving when it reaches a location where the free energy is a minimum. In this paper, a minimum Gibbs free energy analysis has been performed to predict where a drop will stop on a conical fiber. To obtain the Gibbs free energies of a drop at different locations of a conical fiber, the theoretical expressions for the shape of a droplet on a conical fiber are derived by extending Carroll's equations for a drop on a cylindrical fiber. The predicted Gibbs free energy exhibits a minimum along the length of the cone. For a constant cone angle, as the contact angle between the liquid and the cone increases, the drop will move toward the apex of the cone. Likewise, for a constant contact angle, as the cone angle increases, the drop moves toward the apex. Experiments in which water and dodecane were placed on glass cones verify these dependencies. Thus, the final location of a drop on a conical fiber can be predicted on the basis of the geometry and surface energy of the cone, the surface tension and volume of the liquid, and the original location where the drop was deposited.

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.