  The simplest microfluidic network (a loop) comprises two parallel channels
with a common inlet and a common outlet. Recent studies, that assumed constant
cross-section of the channels along their length, have shown that the sequence
of droplets entering left (L) or right (R) arm of the loop can present either a
uniform distribution of choices (e.g. RLRLRL...) or long sequences of repeated
choices (RRR...LLL), with all the intermediate permutations being dynamically
equivalent and virtually equally probable to be observed. We use experiments
and computer simulations to show that even small variation of the cross-section
along channels completely shifts the dynamics either into the strong preference
for highly grouped patterns (RRR...LLL) that generate system-size oscillations
in flow, or just the opposite - to patterns that distribute the droplets
homogeneously between the arms of the loop. We also show the importance of
noise in the process of self-organization of the spatio-temporal patterns of
droplets. Our results provide guidelines for rational design of systems that
reproducibly produce either grouped or homogeneous sequences of droplets
flowing in microfluidic networks.
