Chemistry Reference
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Fig. 7.2
The angular correlation of the droplet motion,
C
ϑ
, as a function of the scaled distance
of the droplet centers, r
/
d. d
=
2R is the droplet diameter. The red curve correspond to an areal
droplet density of 0.46, the black curve to a density of 0.78. The black arrows are at multiples of
1.08 droplet diameters. The inset shows a semi-logarithmic plot of the decay of the correlation data.
The red line corresponds to a decay length of 0.6 droplet diameters, the straight asymtote of the
black line represents a decay length of 2.5 droplet diameters. An oscillation with a period of 1.08
droplet diameters (decaying over 0.9 droplet diameter) has been superimposed to fit the data
droplets [
10
,
7
], just from the hydrodynamic interaction of the squirmers with each
other.
That this is indeed the case can be seen in Fig.
7.2
. The red curve corresponds to
a moderate areal density of 0.46, which we define as the fraction with respect to the
density corresponding to a hexagonal close packing. We see that there is significant
correlation for small distances. More specifically, the angular correlation function
decays approximately exponentially away from the contact distance (which is equal
to one droplet diameter, d
2R), as can be seen from the inset. The decay constant
is about 0.6 droplet diameters (dashed line in the inset). The angular correlation thus
decays almost completely over one interparticle distance, suggesting that the correla-
tion of the velocities is mediated by the pair interaction of the particles. In fact, it has
been predicted theoretically that two adjacent droplets which are propelling them-
selves by means of low order spherical harmonic flow fields may attract themselves
into a bound state in which they are swimming with virtually parallel velocities [
10
].
We provide here a first experimental corroboration of this prediction using a purely
'physical' system. There are, however, also pronounced differences with simulation
data. Ishikawa and Pedley [
7
] have performed simulations of the collective behaviour
of spherical droplets with full hydrodynamic interactions, swimming in a monolayer.
This system is very similar to ours, but the monolayer in the simulation was freely
suspended in the three-dimensional liquid, such that there was no nearby wall as in
our case. This gives rise to long-range hydrodynamic interactions, and provides a
=
