Cooperative Motion of Active Brownian Spheres in Three-Dimensional Dense Suspensions

The structural and dynamical properties of suspensions of self-propelled Brownian particles of spherical shape are investigated in three spatial dimensions. Our simulations reveal a phase separation into a dilute and a dense phase, above a certain density and strength of selfpropulsion. The packing fraction of the dense phase approaches random close packing at high activity, yet the system remains fluid. Although no alignment mechanism exists in this model, we find long-lived cooperative motion of the particles in the dense regime. This behavior is probably due to an interface-induced sorting process. Spatial displacement correlation functions are nearly scale-free for systems with densities close to or above the glass transition density of passive systems. Introduction. – Assemblies of intrinsically active objects, sometimes called living fluids, represent an exceptional class of non-equilibrium systems. Examples range from the macroscopic scale of human crowds to the microscopic scale of cells and motile microorganisms such as bacteria [1, 2]. A generic phenomenon of dense living fluids is the emergence of self-organized large-scale dynamical patterns like vortices, swarms, networks, or self-sustained turbulence [3–5]. This intriguing dynamical behavior is a consequence of the complex interplay of self-propulsion, internal or external noise, and many-body interactions. The understanding of the collective behavior requires the characterization of the underlying physical interaction mechanisms. Experiments and simulations indicate that alignment induced by particle interactions, e.g., inelastic collisions between elongated objects [5–7] or hydrodynamic interactions [8], lead to clustering and collective motion. Studies of rodlike self-propelled particles in two dimensions (2D) revealed mobile clusters and a variety of other dynamical phases [5–7]. In contrast, systems of disclike particles in 2D, which lack an alignment mechanism, do not form any ordered moving states. Yet, they exhibit an activity-induced phase transition. At lower densities small, transient clusters appear [9–12]. Above a critical density, the system separates into a dense and dilute phase [9, 12, 13]. Thereby, the cluster are immobile with an internal crystalline order [11,13]. Far less attention has been paid to three-dimensional (3D) suspensions of spherical (colloid-like) active particles. In such systems, the question naturally arises, whether a collective behavior emerges despite the particles lack any aligning interactions. In this letter, we present simulation results of the emergent structure and dynamics of motile spherical particles in 3D—as a generic model of nonaligning self-driven particles. We find that an isotropic system phase separates into a dilute, gas-like phase, and a dense, fluid-like phase at sufficiently large activity. Inside the dense phase, the particles exhibit collective motion— in the form of jets and swirls—even at densities very close to random close packing (RCP). Although a global polar order is absent in the system, long-lived cooperative motion with nearly scale-free correlations emerge. Model. – We model an active particle as a hardsphere-like particle which is propelled with constant velocity V0 along its orientation vector e in 3D [9, 11–14]. Its translational motion is described by ṙ = V0e + F/γt + η, (1) where ṙ is the velocity, F the total interparticle force, and η a Gaussian white-noise random velocity, with 〈η〉 = 0 and 〈ηi(t)ηj(t)〉 = 2Dt1δijδ(t − t′). The transp-1 ar X iv :1 30 8. 64 23 v3 [ co nd -m at .s of t] 2 6 N ov 2 01 3