Spreading of Annular Droplets on a Horizontal Fiber

This paper investigates an annular droplet on a horizontal fiber. The static state and the dynamic spreading process of the droplet is analyzed. A full model describing the profile of a static droplet is derived from the energy variation principle. To study the dynamical spreading of the droplet, we derive a lubrication model which is verified by the full model. It indicates that the lubrication model is valid for a thin droplet. Results of the static droplet reveal that, when the fiber radius is very small, the droplet tends to have a spherical shape; if the fiber radius is very large, the droplet approaches to a parabolic profile. Furthermore, the time-evolution study is carried out to investigate the dynamical spreading of the droplet. It is highlighted that when the fiber radius is small, the droplet can breakup into small droplets or contract into a sharp shape. For a large fiber radius, the droplet spreads to a steady profile. In addition, the liquid viscosity is found to retard the deformation of the droplet and the motion of the contact lines.