Active Nematics Are Intrinsically Phase Separated

Abstract

Two-dimensional nonequilibrium nematic steady states, as found in agitated granular-rod monolayers or films of orientable amoeboid cells, were predicted [Europhys. Lett. 62 (2003) 196] to have giant number fluctuations, with standard deviation proportional to the mean. We show numerically that the steady state of such systems is macroscopically phase-separated, yet dominated by fluctuations, as in the Das-Barma model [PRL 85 (2000) 1602]. We suggest experimental tests of our findings in granular and living-cell systems. The ordering or "flocking" [1, 2, 3] of self-propelled particles obeys laws strikingly different from those governing thermal equilibrium systems of the same spatial symmetry. Even in two dimensions, the velocities of particles in such flocks show true longrange order [1,2], despite the spontaneous breaking of continuous rotational invariance. Density fluctuations in the ordered phase are anomalously large [2], and the onset of the ordered phase is discontinuous [4]. The ultimate origin of these nonequilibrium phenomena is that the order parameter is not simply an orientation but a macroscopic velocity. It is thus intriguing that even the nematic phase of a collection of self-driven particles, which is apolar and hence has zero macroscopic velocity, shows [5,6] giant number fluctuations [7], as a result of the manner in which orientational fluctuations drive mass currents. This Letter takes a closer look at these fluctuations and shows that they offer a physical realisation of the remarkable nonequilibrium phenomenon known as fluctuation-dominated phase separation [8], hitherto a theoretical curiosity.Before presenting our results, we make precise the term active nematic. An active particle extracts energy from sources in the ambient medium or an internal fuel tank, dissipates it by the cyclical motion of an internal "motor" coordinate, and moves as a consequence. For the anisotropic particles that concern us here, the direction of motion is determined predominantly by the orientation. Our definition encompasses self-propelled organisms, living cells, molecular motors, and macroscopic rods on a vertically vibrated substrate (where the tilt of the rod * Also with CMTU, JNCASR, Bangalore 560064, India † Electronic address: sriram@physics.iisc.ernet.in serves as the motor coordinate). An active nematic is a collection of such particles with axes on average spontaneously aligned in a directionn, with invariance undern → −n. We know of two realisations of active nematics: collections of living amoeboid cells [10] and granular-rod monolayers [11,12]. We study active nematics in a simple numerical model described in detail below. Our results confirm (see Fig. 1) the giant number fluctuations (standard deviation ∝ mean) [6] predicted by the linearised analysis of [5], but are far richer: (i) A statistically uniform initial distribution of particles, on a well-ordered nematic background, undergoes a delicate "fluctuation-dominated" [8] phase separation, where the system explores many statistically simila...

Collective motion of self-propelled particles interacting without cohesion

“…16a). This is reminiscent of the recent discovery of "giant density fluctuations" in active nematics [14,51,52]. However, the theoretical argument which initially predicted such fluctuations [53] cannot be invoked directly in the present case.…”

“…Again, these phenomena, reported also in the context of "active" nematics [14,51,53], deserve further investigation.…”

Correlation lengths in hydrodynamic models of active nematics

“…Much interest has recently focused on active nematics -systems composed of active units with head-tail symmetry that can order into states with nematic liquid crystalline order, with the activity giving rise to a rich variety of collective phenomena. These include spontaneous laminar flow [2][3][4] , large density fluctuations [5][6][7] , pattern formation 8,9 , spontaneous unbinding of topological defects [10][11][12][13] , and active turbulence [14][15][16][17][18] .…”

Role of interfacial friction for flow instabilities in a thin polar-ordered active fluid layer

“…Notice that for a finite Γ, boundary conditions (20) implies partial slip between v β (x, y) and v ′ β (x, y, z = ±ǫ), β = x, y. While the no-slip boundary condition is more conventionally used, on mesoscopic scales, however, instances of violation of the no-slip boundary conditions are known.…”

“…These are known as dry active matter in the classification used in Ref. [16] and have been studied extensively, see, e.g., [6,7,10,20]. The properties of active matter systems are often considered in the form of thin, quasi two-dimensional (2D) layer.…”