Chemistry Reference
In-Depth Information
7.3 Results
7.3.1 Hydrodynamic Interactions of Swimmer Populations
It is a long standing debate whether physical effects, like hydrodynamic interactions,
are sufficient to explain textures observed in the swarming behaviour of bacteria
and other microorganisms, without having to invoke chemotaxis or other genuinely
biological effects [
6
-
8
,
19
]. Using our model squirmers instead of bacteria, we can
tackle this problem from the reverse side, asking for the textures we can observe in
dense populations of model squirmers, which are guaranteed to exhibit no biological
interactions. As we will see, there is indeed considerable structure to unveil even for
such simple systems.
We restrict ourselves to effectively two-dimensional systems here, not only for
the sake of simplicity, but also because most studies so far have concentrated on the
two-dimensional case. Our samples were prepared by creating shallow wells of a
few millimeters diameter and a depth just slightly larger than the droplet diameter
in poly-dimethyl-siloxane (PDMS) rubber by standard soft lithography techniques.
Bonding the PDMS to a glass slide resulted in a compartment, which in addition
was connected by a narrow channel to a step emulsification unit, where droplets
were produced and subsequently transported through the channel into the sample
well. Figure
7.1
shows a typical sample. The red arrows indicate the direction of
motion of each droplet. As time proceeds, the formation of rather long-lived clusters
of different size is observed. The most striking feature, however, is the significant
polar alignment of the velocities of neighboring droplets. In order to quantify this
alignment, we use the angular correlation function,
C
θ
(
r
)
=
δ(
r
−|
r
i
−
r
j
|
)
cos
θ
t
ij
(7.1)
which describes the propensity of velocities of neighboring particles to align with
respect to each other. On the basis of earlier theoretical work, we might under certain
circumstances expect a significant polar correlation of the velocities of neighboring
Fig. 7.1
Velocity vectors
overlayed on droplets
