We examine a minimal model for an active colloidal fluid in the form of self-propelled Brownian spheres that interact purely through excluded volume with no aligning interaction. Using simulations and analytic modeling, we quantify the phase diagram and separation kinetics. We show that this nonequilibrium active system undergoes an analog of an equilibrium continuous phase transition, with a binodal curve beneath which the system separates into dense and dilute phases whose concentrations depend only on activity. The dense phase is a unique material that we call an active solid, which exhibits the structural signatures of a crystalline solid near the crystal-hexatic transition point, and anomalous dynamics including superdiffusive motion on intermediate time scales.

http://absimage.aps.org/image/MAR13/MWS_MAR13-2012-003161.pdf

Structure and Dynamics of a Phase-Separating Active Colloidal Fluid

In simple fluids, such as water, invariance under parity and time-reversal symmetry imposes that the rotation of constituent ‘atoms’ is determined by the flow and that viscous stresses damp motion. Activation of the rotational degrees of freedom of a fluid by spinning its atomic building blocks breaks these constraints and has thus been the subject of fundamental theoretical interest across classical and quantum fluids. However, the creation of a model liquid that isolates chiral hydrodynamic phenomena has remained experimentally elusive. Here, we report the creation of a cohesive two-dimensional chiral liquid consisting of millions of spinning colloidal magnets and study its flows. We find that dissipative viscous ‘edge-pumping’ is a key and general mechanism of chiral hydrodynamics, driving unidirectional surface waves and instabilities, with no counterpart in conventional fluids. Spectral measurements of the chiral surface dynamics suggest the presence of Hall viscosity, an experimentally elusive property of chiral fluids. Precise measurements and comparison with theory demonstrate excellent agreement with a minimal chiral hydrodynamic model, paving the way for the exploration of chiral hydrodynamics in experiment. A chiral fluid comprising spinning colloidal magnets exhibits macroscopic dynamics reminiscent of the free surface flows of Newtonian fluids, together with unique features suggestive of Hall—or odd—viscosity.

The odd free surface flows of a colloidal chiral fluid

Elasticity typically refers to a material's ability to store energy, whereas viscosity refers to a material's tendency to dissipate it. In this review, we discuss fluids and solids for which this is not the case. These materials display additional linear response coefficients known as odd viscosity and odd elasticity. We first introduce odd viscosity and odd elasticity from a continuum perspective, with an emphasis on their rich phenomenology, including transverse responses, modified dislocation dynamics, and topological waves. We then provide an overview of systems that display odd viscosity and odd elasticity. These systems range from quantum fluids and astrophysical gases to active and driven matter. Finally, we comment on microscopic mechanisms by which odd viscosity and odd elasticity arise.

https://www.annualreviews.org/doi/pdf/10.1146/annurev-conmatphys-040821-125506

Odd Viscosity and Odd Elasticity

The self-organized motion of vast numbers of creatures in a single direction is a spectacular example of emergent order. Here, we recreate this phenomenon using actuated nonliving components. We report here that millimetre-sized tapered rods, rendered motile by contact with an underlying vibrated surface and interacting through a medium of spherical beads, undergo a phase transition to a state of spontaneous alignment of velocities and orientations above a threshold bead area fraction. Guided by a detailed simulation model, we construct an analytical theory of this flocking transition, with two ingredients: a moving rod drags beads; neighbouring rods reorient in the resulting flow like a weathercock in the wind. Theory and experiment agree on the structure of our phase diagram in the plane of rod and bead concentrations and power-law spatial correlations near the phase boundary. Our discovery suggests possible new mechanisms for the collective transport of particulate or cellular matter.

/pdf/flocking-at-a-distance-in-active-granular-matter-stmprxkj02.pdf

Flocking at a distance in active granular matter

Due to its inherent out-of-equilibrium nature, active matter in confinement may exhibit collective behavior absent in unconfined systems. Extensive studies have indicated that hydrodynamic or steric interactions between active particles and boundary play an important role in the emergence of collective behavior. However, besides introducing external couplings at the single-particle level, the confinement also induces an inhomogeneous density distribution due to particle-position correlations, whose effect on collective behavior remains unclear. Here, we investigate this effect in a minimal chiral active matter composed of self-spinning rotors through simulation, experiment, and theory. We find that the density inhomogeneity leads to a position-dependent frictional stress that results from interrotor friction and couples the spin to the translation of the particles, which can then drive a striking spatially oscillating collective motion of the chiral active matter along the confinement boundary. Moreover, depending on the oscillation properties, the collective behavior has three different modes as the packing fraction varies. The structural origins of the transitions between the different modes are well identified by the percolation of solid-like regions or the occurrence of defect-induced particle rearrangement. Our results thus show that the confinement-induced inhomogeneity, dynamic structure, and compressibility have significant influences on collective behavior of active matter and should be properly taken into account.

https://www.pnas.org/content/pnas/117/22/11901.full.pdf

Oscillating collective motion of active rotors in confinement.

We experimentally investigate internal coastal Kelvin waves in a two-layer fluid system on a rotating table. Waves in our system propagate in the prograde direction and are exponentially localized near the boundary. Our experiments verify the theoretical dispersion relation of the wave and show that the wave amplitude decays exponentially along the propagation direction. We further demonstrate that the waves can robustly propagate along boundaries of complex geometries without being scattered and that adding obstacles to the wave propagation path does not cause additional attenuation.

Robust propagation of internal coastal Kelvin waves in complex domains

We perform experiments on an active chiral fluid system of self-spinning rotors in a confining boundary. Along the boundary, actively rotating rotors collectively drive a unidirectional material flow. We systematically vary rotor density and boundary shape; boundary flow robustly emerges under all conditions. Flow strength initially increases then decreases with rotor density (quantified by area fraction ϕ); peak strength appears around a density ϕ=0.65. Boundary curvature plays an important role: flow near a concave boundary is stronger than that near a flat or convex boundary in the same confinements. Our experimental results in all cases can be reproduced by a continuum theory with single free fitting parameter, which describes the frictional property of the boundary. Our results support the idea that boundary flow in active chiral fluid is topologically protected; such robust flow can be used to develop materials with novel functions.

Robust boundary flow in chiral active fluid.

Internal coastal Kelvin waves were experimentally generated in a two-layer fluid system on a rotating table. Waves are exponentially localized near the tank boundary and propagate in the same direction as the table rotation along boundaries of complex geometries without being scattered. Our experiments suggest a connection between these unusual wave characteristics and topological properties of the underlying governing equations.

pdf/robust-propagation-of-internal-coastal-kelvin-waves-in-52k4hgejpk.pdf

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Robust propagation of internal coastal Kelvin waves in complex domains

Robust boundary flow in chiral active fluid.

Robust propagation of internal coastal Kelvin waves in complex domains