Chemistry Reference
In-Depth Information
Fig. 7.3
The ensemble averaged mean square displacement (MSD) for a 2- dimensional monolayer
of squirmer population at different area fractions. Each population has between 50 and 500 squirmer
droplets
Fig. 7.4
Diffusivity as a function of area fraction.
L
eft Results froma simulation done byHernandez
et al. [
6
]
R
ight Diffusivities calculated from the long time statistics of theMSDplots shown in Fig.
7.3
off of the diffusivity at increased swimmer densities. In fact, the same behaviour
has been seen recently in simulations by Hernandez et. al [
6
] where they see a
reduction in the diffusivitywith until a threshold of
0.3 at which swimmer density
they see an increase in the effective diffusivity. They attribute this to the collective
swimming that results due to the hydrodynamic interactions at higher swimmer
densities. Indeed, as we have discussed above, hydrodynamic interactions lead to
collective swimming states in the droplet swimmers, thus explaining the levelling
off of the diffusivities at higher swimmer densities. In the simulations however, the
effective diffusivity increases sharply after the threshold of
φ
∼
0.3, which is not seen
in the experiments. This is not surprising since the simulations were done without
monolayer confinement of the swimmers as we have in the experiments. As a result
of the monolayer confinement, the long range hydrodynamic interactions may be
screened, thus having a reducing effect on the large scale flows of the swimmers,
φ
∼
