Motion of Droplets in Lyophilic Axially Varying Geometry-Gradient Tubes

Droplet transport occurs frequently in nature and has a wide range of applications. We studied the droplet motion in a lyophilic axially varying geometry-gradient tube (AVGGT). The motion of the AVGGT in two directions─from the large opening side (L) to the small opening side (S) and from S to L─was theoretically and experimentally analyzed. The droplet dynamic behaviors, such as the self-transport behavior and the droplet stuck behavior, are explored from the view points of mechanics and energy. We found that the surface tension force of a three-phase contact line can be either a driving or an impeding force depending on the various droplet geometries in different AVGGTs. An important contributing factor to the self-transport behavior of a droplet moving from L to S in an AVGGT is the bridge liquid force caused by negative pressure inside the droplet, which is always pointing in the direction of S. As a result of experiments, we investigated the relationship between droplet motion and correlated parameters. The theoretical model based on the simplified Navier-Stokes equation was developed to explain the corresponding mechanism of the droplet motion. Additionally, dimensional analysis was carried out for the droplet stuck behavior of a droplet moving from S to L in an AVGGT to investigate the relationship between the droplet stopping location and the correlated parameters and thus obtain the required geometry for the droplet stopping location.