  Multiple emulsions are a class of soft fluid in which small drops are
immersed within a larger one and stabilized over long periods of time by a
surfactant. We recently showed that, if a monodisperse multiple emulsion is
subject to a pressure-driven flow, a wide variety of nonequilibrium steady
states emerges at late times, whose dynamics relies on a complex interplay
between hydrodynamic interactions and multibody collisions among internal
drops. In this work, we use lattice Boltzmann simulations to study the dynamics
of polydisperse double emulsions driven by a Poiseuille flow within a
microfluidic channel. Our results show that their behavior is critically
affected by multiple factors, such as initial position, polydispersity index,
and area fraction occupied within the emulsion. While at low area fraction
inner drops may exhibit either a periodic rotational motion (at low
polydispersity) or arrange into nonmotile configurations (at high
polydispersity) located far from each other, at larger values of area fraction
they remain in tight contact and move unidirectionally. This decisively
conditions their close-range dynamics, quantitatively assessed through a
time-efficiency-like factor. Simulations also unveil the key role played by the
capsule, whose shape changes can favor the formation of a selected number of
nonequilibrium states in which both motile and nonmotile configurations are
found.
