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.