Flow of emulsions in heterogeneous media*

We elucidate the collective dynamics of particles hydrodynamically driven through disordered environments. We build on model microfluidic experiments where we track the individual dynamics of hundreds of thousands oil droplets advected by an aqueous fluid through random lattices of pinning sites. Increasing the driving flow, we identify a sharp transition between a creeping regime and a mobilization regime where a finite fraction of the droplets proceed through a sparse network of branched and reconnected rivers. This dynamical transition is a critical phenomenon characterised by diverging time and length scales at the onset of mobilization.
We however demonstrate that criticality is not accompanied by the correlated motion of particles in avalanches events. Mobilization requires at most the coordinated motion of ten particles at a time, but these erratic rearrangements are geometrically correlated over system spanning scales along a smectic river network.
We conclude by commenting on the similarities and profound deifferences with the plastic depinning transition of flux lines in super conductors, or grains in eroded sand beds.