Active nematic materials with substrate friction

Abstract

Active turbulence in dense active systems is characterised by high vorticity on a length scale large compared to that of individual entities. We describe the properties of active turbulence as momentum propagation is screened by frictional damping. As friction is increased, the spacing between the walls in the nematic director field decreases as a consequence of the more rapid velocity decays. This leads to, firstly, a regime with more walls and an increased number of topological defects, and then to a jammed state in which the walls deliminate bands of opposing flow, analogous to the shear bands observed in passive complex fluids.Active materials intrinsically exist out of equilibrium driven by a continuous input of energy. Many such systems are of biological origin, including suspensions of cytoskeletal elements, cells and bacteria. Vibrated granular rods and active colloids provide examples of inanimate active materials [1,2]. Dense active systems often exhibit collective behaviour producing long range spatial and temporal correlations that are much larger than the typical length and time scales associated with individual particles [3][4][5][6]. Active turbulence, observed in active nematics, is a canonical example of this behaviour, which is characterised by rapidly varying flow fields with a high degree of vorticity. Recently it has been proposed that there are links between active turbulence and the appearance of lines of kinks, or walls, in the director field and the formation of topological defects also appears to be relevant in defining the active turbulent state [4,[7][8][9][10][11].Active turbulence has been observed in experiments on systems as diverse as dense suspensions of bacteria [3], microtubules and molecular motors [4], cells [5], mixtures of bacteria and liquid crystals [10], and vertically vibrated rods [6]. Diverse simulations from those considering discrete particles [11,12], eg driven, self-avoiding rods of high aspect ratio, to those based on differing continuum theories, eg active nematohydrodynamics, [7,8,13] all see the hallmarks of active turbulence. However we still lack a predictive theory of this dynamical state, or an understanding of which of the properties of active turbulence are universal and which are system specific.A classification often applied to active nematics is the relevance of momentum conservation in determining their dynamics [2]. Systems that conserve momentum (eg a free-standing fluid layer) are termed 'wet', those with no momentum conservation (eg vibrated granular rods) 'dry'. In reality completely wet or dry systems are two ends of a continuum. We are not aware of any analysis investigating connections between these limits, a question important in establishing the extent to which active turbulence is universal. Therefore, the aim of this paper is to study active turbulence in the crossover regime between wet and dry nematics when momentum propagation is increasingly being damped.We stress that understanding the crossover between wet and dry systems is not ju...

Topological Defects in a Living Nematic Ensnare Swimming Bacteria

“…nematics [27][28][29][30][31]46]. However, for the conditions of our experiment [32], this reduction is nonphysical.…”

“…The viscous friction term −ζv originates from depth averaging of the flow profile, ζ ¼ 12η=h 2 , where η is the isotropic viscosity (compare Refs. [14,29]). A self-propelled particle, such as a motile bacterium, exerts a pair of forces on the suspending fluid (force dipole or stresslet); see Fig.…”

“…Additionally, in the living nematic, the energy input is provided by swimming bacteria, whereas in the motor-microtubules system, it is due to relative sliding of nonmotile microtubules. Moreover, it is not clear to what extent the generic models of an active nematic [27][28][29][30][31] are applied to suspensions of self-propelled particles in a nematic fluid [32].…”

“…A theoretical understanding of active nematics was achieved by particle simulations [20], phenomenological hydrodynamic models [21,22], or by asymptotic reduction of the probabilistic Boltzmann equation for interacting particles to the Ginzburg-Landau-type model [23,24]. An equilibrium nematic liquid crystal (LC) model [25,26] supplemented by a phenomenological active stress was used in a number of works [27][28][29][30][31]. These studies provided important insights into the annihilation dynamics of defects, velocity correlations, and the onset of "active turbulence."…”

New class of turbulence in active fluids

“…Nevertheless, the correlation functions of the velocity and vorticity fields display some essential differences compared with their counterparts in classical fluid turbulence (8,9). Moreover, the collective motion of bacteria in such suspensions exhibits long-range correlations (10), appears to be driven by internal instabilities (11), and depends strongly also on physical parameters like large-scale friction (12). Such results challenge the orthodox understanding of turbulent motion and call for a detailed theoretical investigation.…”