Measurement of inflection angle and correlation of shape factor of barrel-shaped droplets on horizontal fibers

Abstract

Abstract The properties and shapes of drops attached to fibers are important for understanding the movements of drops on fibers in applications such as coalescing filters. One of the features of the shape of a drop attached to a cylindrical fiber is an inflection in the curvature of the drop profile near the contact line between the drop and the fiber surface. Depending on the drop volume, the point of inflection may occur very close to the drop-fiber contact line, and the angle at the inflection point could mistakenly be interpreted as the intrinsic contact angle. Measurement of the angle at the inflection point improves the characterization of the drop profile for a drop-on-fiber system. Many studies provide methods that apply droplet geometric symmetry to extract the profile of drops on flat surfaces. However, none of these methods can be easily applied to drops on fibers due to the curvature of the fiber surface and its effect on the shape of the drop. In the case of drops on fibers, drop properties such as drop length, thickness, inflection angle and volume are useful to obtain the wetting properties of the fiber surfaces without knowing the liquid properties. To determine inflection angles and volumes of axisymmetric barrel-shaped droplets on fibers from 2D images of droplets profiles a polynomial fitting method for fibers (PFMF) was applied. The strategy employed detects the location of the droplet boundary, fits a polynomial to the boundary, and calculates the inflection angle and the volume of the droplet. Volume measurements using the PFMF were consistent with calculations from Surface Evolver™ program. Using the PFMF, a new correlation was generated for a shape factor characterizing the asymmetry of barrel-shaped droplets as a function of liquid properties, fiber radius, and droplet volume.