Long-range nematic order and anomalous fluctuations in suspensions of swimming filamentous bacteria

Abstract

We study the collective dynamics of elongated swimmers in a very thin fluid layer by devising long, filamentous, non-tumbling bacteria. The strong confinement induces weak nematic alignment upon collision, which, for large enough density of cells, gives rise to global nematic order. This homogeneous but fluctuating phase, observed on the largest experimentally-accessible scale of millimeters, exhibits the properties predicted by standard models for flocking such as the Vicsek-style model of polar particles with nematic alignment: true long-range nematic order and non-trivial giant number fluctuations.PACS numbers: 47.63. Gd, 05.65.+b 87.18.Gh 87.18.Hf Collective motion of self-propelled elements, as seen in bird flocks, fish schools, bacterial swarms, etc., is so ubiquitous that it has driven physicists to search for its possibly universal properties [1][2][3]. If generic and robust features of such active matter systems exist, they should also be present in the emergent phenomena observed in simple models. Evidence for such universality has been provided by many theoretical and numerical studies of dry active matter systems where local alignment competes with noise, following the seminal works by Vicsek et al.[4], Toner, Tu , and Ramaswamy et al. [5][6][7][8][9]. It was notably understood that the transition to orientational order/collective motion, in this context, is best described as a phase-separation between a disordered gas and an ordered 'liquid' separated by a coexistence phase whose nature depends on the symmetries of the system [3,[10][11][12][13][14][15][16]. The homogeneous but highly fluctuating liquid phase is characterized by unique properties often different from those of equilibrium orientationally-ordered phases. In particular, the crucial coupling between the order and the density fields generates anomalously-large number fluctuations from the algebraic correlations of orientation and density [5][6][7][8][9].Such 'giant' number fluctuations (GNF), being relatively easy to measure experimentally, have become the landmark signature of orientationally-ordered active matter. Several experimental studies have indeed searched for GNF using controllable systems simpler than bird flocks and fish schools such as biofilaments driven by molecular motors [17], colloids consuming electric energy [18], shaken granular materials [19][20][21], monolayers of fibroblast cells [22], and common bacteria [23,24]. However, none of these experiments has been fully convincing in demonstrating the presence of bona fide GNF * nishiguchi@daisy.phys.s.u-tokyo.ac.jp as predicted from the works of Toner, Tu, Ramaswamy et al. [3, 7, 8], and observed in Vicsek-style models [10, 11, 13, 14]. These GNF have to be discussed in a fluctuating phase with global long-range orientational order and are distinct from the trivial, non-asymptotic ones present in the case of phase-separation into dense clusters sitting in a disordered sparse gas. In some experiments, only normal number fluctuations were found [17,18]. In others, GNF ...

Low-noise phase of a two-dimensional active nematic system

“…We also argue that the ordered nematic phase in both 2d active nematic and self-propelled rod systems must have the same universal description, and hence one cannot have long-ranged nematic order in any locally driven 2d nematic (in the absence of long ranged interactions or hydrodynamics). Reconciling this result with previous numerical and experimental findings of long-ranged nematic order in self-propelled rod systems [12,61] remains a theoretical challenge. By conventional expectations of universality and hydrodynamics, a simple resolution to this question, other than a long crossover, seems to be ruled out at least at the perturbative level.…”

“…As the ordered nematic phase of a self-propelled rod system also has only two slow modes (δρ and θ), with the velocity always decaying on a finite time scale, the long distance hydrodynamic description of such a phase is identical to the one discussed here. One would have to verify if the long-ranged order claimed in such systems [12,61] is actually a finite size effect in the sense of Eq. 47, as the phase fluctuations though not finite, grow slower than a logarithm below the crossover scale ξ * , with only much larger systems eventually recovering true QLRO.…”

“…Unlike its polar counterpart, where the appearance of macroscopic polar order results in collective directed motion or flocking [3,4], the active nematic involves driven apolar constituents, which means on average the system goes nowhere [5] making its properties far more subtle. Examples of active nematics include monolayers of melanocytes [6,7], fibroblasts [8], neural progenitors [9], myxobacteria [10,11], swimming filamentous bacteria [12][13][14], vibrated rods [15] and microtubule-kinesin suspensions [16].…”

“…As emphasized in Ref. [12], it is important to distinguish GNFs from regular phase separation, generically present close to the transition, as well as from the inhomogeneous structures that occur in fluctuationdominated transitions [35]. A study of the ideal phenomenology of these anomalous fluctuations requires a well developed ordered phase in a large enough system which has a mean homogeneous density and is not phase separated in the thermodynamic limit.…”

Onset of meso-scale turbulence in active nematics

“…Low-Reynolds-number turbulence is established through continuous energy injection from the constituent elements of an active fluid in many biological systems, including bacterial suspensions123456, cellular monolayers789 or sub-cellular filament/motor protein mixtures1011. Although the inertia is negligible (Reynolds number ≫1) in such systems, active turbulence is characterized by a highly disordered distribution of vortices1213.…”