Emergence of scale-free smectic rivers and critical depinning in emulsions driven through disorder

During the past 60 min, oil companies have extracted 6 trillion liters of oil from the ground, thereby giving a striking illustration of the impact of multiphase flows on the world economy. From a fundamental perspective, we largely understand the dynamics of interfaces separating immiscible fluids driven through heterogeneous environments. In stark contrast, the basic mechanisms ruling the transport of fragmented fluids, such as foams and emulsions, remain elusive with studies mostly limited to isolated droplets and bubbles. Here, we demonstrate that the mobilization of emulsion driven through model disordered media is a critical plastic depinning transition. To elucidate this collective dynamics, we track the trajectories of hundreds of thousands of microfluidic droplets advected through random lattices of pinning sites. Their dynamics reveals that macroscopic mobilization only requires the coordinated motion of small groups of particles and does not involve any large-scale avalanches. Criticality arises from the interplay between contact and hydrodynamic interaction, which channel seemingly erratic depinning events along smectic river networks correlated over system spanning scales. Beyond the specifics of emulsion transport, we close our article discussing the similarities and profound differences with the plastic depinning transitions of driven flux lines in high-Tcsuperconductors, charged colloids, and grain transport in eroded sand beds.

Majority-vote model on directed Small-World-Voronoi–Delaunay random lattices

We investigate the critical properties of the nonequilibrium majority-vote model in two-dimensions on directed small-world lattice with quenched connectivity disorder. The disordered system is studied through Monte Carlo simulations: the critical noise ([Formula: see text]), as well as the critical exponents [Formula: see text], [Formula: see text], and [Formula: see text] for several values of the rewiring probability [Formula: see text]. We find that this disordered system does not belong to the same universality class as the regular two-dimensional ferromagnetic model. The majority-vote model on directed small-world lattices presents in fact a second-order phase transition with new critical exponents which do not depend on [Formula: see text] ([Formula: see text]), but agree with the exponents of the equilibrium Ising model on directed small-world Voronoi–Delaunay random lattices.