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.