  Understanding the fluid-structure interaction is crucial for an optimal
design and manufacturing of soft mesoscale materials. Multi-core emulsions are
a class of soft fluids assembled from cluster configurations of deformable
oil-water double droplets (cores), often employed as building-blocks for the
realisation of devices of interest in bio-technology, such as drug-delivery,
tissue engineering and regenerative medicine. Here, we study the physics of
multi-core emulsions flowing in microfluidic channels and report numerical
evidence of a surprisingly rich variety of driven non-equilibrium states (NES),
whose formation is caused by a dipolar fluid vortex triggered by the sheared
structure of the flow carrier within the microchannel. The observed dynamic
regimes range from long-lived NES at low core-area fraction, characterised by a
planetary-like motion of the internal drops, to short-lived ones at high
core-area fraction, in which a pre-chaotic motion results from multi-body
collisions of inner drops, as combined with self-consistent hydrodynamic
interactions. The onset of pre-chaotic behavior is marked by transitions of the
cores from one vortex to another, a process that we interpret as manifestations
of the system to maximize its entropy by filling voids, as they arise
dynamically within the capsule.
