Oscillating Droplets: Chemical Micro-Oscillators - Towards Autonomous Soft Matter Systems - page 71

In order to verify this interpretation, we can estimate the contact angle forming
at the three phase contact line, from the height of the jump in the droplet center
distance. If R is the radius of the droplet after the membrane has formed, i.e., the
radius of an ideal sphere fitted to the free droplet surface, it is easily shown that the
volume of the flattened droplet is given by

2

(θ) = π R
3

3 cos 2 − cos 3 2 V + (5.1)

where is defined as above. If D is the distance of the sphere centers after membrane

formation, we furthermore have D

θ

2 R cos . Denoting by R the radius of the

droplets before membrane formation, we finally obtain using volume conservation

= θ

4 R
D

3

2
cos 3

3
cos 2

+ = 1 + (5.2)

θ θ

From the height of the jump in the black curve in Fig. 5.8 , we obtain 2R/D ≈ 1.107

51 ◦ , in reasonable agreement with the value found in Chaps. 2 and 4 .
Here we are particularly interested in the change in coupling induced by the
membrane formation. Clearly, we see that after the jump in the black curve, all
three transmittance traces are firmly coupled. It seems that due to the presence of
the mono-olein double bonds in the oil phase, an efficient transport of bromine as
a messenger through the oil phase is prevented effectively. Transport through the
mono-olein bilayer membrane, however, is obviously still possible.

and thus θ ≈

5.3.3 Synchronization Patterns

Patterns such as pacemaker driven target waves, travelling waves and spirals are
most commonly seen in large assemblies of coupled oscillators. The BZ droplet
oscillators, connected by bilayer membranes, also give rise to such a rich range of
collective dynamics. In the present section, we discuss, qualitatively, the various
patterns that emerge in connected networks of oscillators and the dependance on
the network topology of the type of behaviour that emerges. The discreteness of
the droplet oscillators allows us to find clear trigger locations in the networks. All
the following experiments are done with a BZ reaction mixture as described in the
experimental section, with a malonic acid concentration of 500 mM.
First, we discuss the formation of target waves. Target waves are characterised
by a pacemaker core which periodically tiggers excitatory waves that spread from
the core center outward. In our system, we observe that pacemakers spontaneously
emerge in the center of connected droplet 'islands' or 'peninsulas'. An 'island' is
comprised of connected droplets as shown in the left panel of Fig. 5.9 with the
outer edges of the 'island' open to the mono-olein filled oil phase. A 'peninsula' is