Interacting Droplets: Collective Dynamics - Towards Autonomous Soft Matter Systems - page 105

Fig. 7.10 Rectification of droplet squirmers by spatial asymmetry. A 2-dimensional chamber is
separated by V-shaped walls with gaps of 75 microns between them. The mean droplet size is 50
microns. To p A time lapse image showing typical squirmer interactions with walls. Droplet in the
bottom half of the chamber are guided through the gaps, while those that start at the top bounce back
from the walls, leading to an effective rectification. Bottom Squirmer trajectories over a duration of
10min are overlayed on the image. Red trajectories are for those droplets which were in the bottom
half of the chamber at the start of the experiment. Similarly blue trajectories represent droplet that
started in the top half. The rectification effect can be seen by the number of the red trajectories that
go through to the other side compared with the blue ones
wall (marked in blue in the image) of the V-shaped barrier, it may be expected that
a similar guiding effect allows droplets from the top half to reach the bottom. This
does indeed happen, as we will see below. However, since the length of this side wall
is much smaller compared to the long arm of the V and thus the probability of this
event is comparitively lower.
The rectification of the droplet motion can be seen very convincingly in the bottom
panel of Fig. 7.10 where the trajectories of the droplets are overlayed on the wall
geometry. The trajectories shown in red correspond to those droplets that were in the
bottom half of the chamber at the start of the experiment and the blue trajectories are
correspondingly those of the droplets that started in the top half. At the start of the
experiment, corresponding to the trajectories shown, there were 263 droplets in the
bottom half and 253 droplets in the top half of chamber. It can be seen very clearly
that while more droplets move from bottom to top, and stay there, very few make
the transition from the other side. And among the few that do, a majority of them
are guided back to the top half due to the rectifying effect. It was counted from the
trajectories that 23 droplets transitioned from the bottom to the top half and remained
there at the end of the experiment. 5 droplets transitioned from the top to the bottom
out of which 2 travelled back (not counted among the 23 mentioned earlier) and 3
remained in the bottom half at the end of the experiment. While the initial droplet
distribution ratio in the top to bottom half of the chamber was 0.96, at the end of the
experiment it was 1.1. Therefore, we conclude that there is a rectifying effect resulting
in directional motion of the droplet population. Thus, from these experiments we can
see that the purely physical mechanism described above is sufficient to create passive