  One of the most distinctive hallmarks of many-body systems far from
equilibrium is the spontaneous emergence of order under conditions where
disorder would be plausibly expected. Here, we report on the self-transition
between ordered and disordered emulsions in divergent microfluidic channels,
i.e. from monodisperse assemblies to heterogeneous polydisperse foam-like
structures, and back again to ordered ones. The transition is driven by the
nonlinear competition between viscous dissipation and surface tension forces as
controlled by the device geometry, particularly the aperture angle of the
divergent microfluidic channel. An unexpected route back to order is observed
in the regime of large opening angles, where a trend towards increasing
disorder would be intuitively expected.
