Efficient nutrient mixing is crucial for the survival of bacterial colonies and other living systems. This raises the question of whether the optimization of mixing through the emergence of active turbulent motion in bacterial swarms played a role in the evolution of bacterial shapes. Here, to address this question, we solve the hydrodynamic equation for active nematics coupled with an advection-diffusion equation for the nutrients. The latter models a conserved activity field and mimics the conservation of nutrients in bacterial swarms. At the interface between active and passive nematic phases, in addition to diffusion, the activity is transported by interfacial flows and in turn modifies them through active stresses. We find that the interfacial dispersion of the conserved activity is subdiffusive due to the emergence of a barrier of negative defects at the active-passive interface, which hinders the propagation of the motile positive defects. Furthermore, we observe a non-monotonic dependence of the generalized diffusion coefficient on the aligning parameter, which is related to the shape of the particles. Our simulations suggest that there is an optimal shape that maximizes the dispersion of conserved activity at the active-passive nematic interface.
We investigate similarities in the micro-structural dynamics between externally driven and actively driven nematics. Walls, lines of strong deformations in the director field, and topological defects are characteristic features of an active nematic. Similar structures form in driven passive nematics when there are inhomogeneities in imposed velocity gradients due to non-linear flow fields or geometrical constraints. Specifically, pressure driven flow of a tumbling passive nematic in an expanding-contracting channel produces walls and defects similar to those seen in active nematics. We also st…
We investigate the emergence of orientational order among +1/2 disclinations in active nematic liquid crystals. Using a combination of theoretical and experimental methods, we show that +1/2 disclinations have short-range antiferromagnetic alignment, as a consequence of the elastic torques originating from their polar structure. The presence of intermediate -1/2 disclinations, however, turns this interaction from anti-aligning to aligning at scales that are smaller than the typical distance between like-sign defects. No long-range orientational order is observed. Strikingly, these effects are …
We use linear stability analysis to show that an isotropic phase of elongated particles with dipolar flow fields can develop nematic order as a result of their activity. We argue that ordering is favoured if the particles are flow-aligning and is strongest if the wavevector of the order perturbation is neither parallel nor perpendicular to the nematic director. Numerical solutions of the hydrodynamic equations of motion of an active nematic confirm the results. The instability is contrasted to the well-known hydrodynamic instability of an ordered active nematic.
The motion of topological defects is an important feature of the dynamics of all liquid crystals, and is especially conspicuous in active liquid crystals. Understanding defect motion is a challenging theoretical problem, because the dynamics of orientational order is coupled with backflow of the fluid, and because a liquid crystal has several distinct viscosity coefficients. Here, we suggest a coarse-grained, variational approach, which describes the motion of defects as effective `particles.' For passive liquid crystals, the theory shows how the drag depends on defect orientation, and shows t…
We analyze a model of mutually-propelled filaments suspended in a two-dimensional solvent. The system undergoes a mean-field isotropic-nematic transition for large enough filament concentrations and the nematic order parameter is allowed to vary in space and time. We show that the interplay between non-uniform nematic order, activity and flow results in spatially modulated relaxation oscillations, similar to those seen in excitable media. In this regime the dynamics consists of nearly stationary periods separated by "bursts" of activity in which the system is elastically distorted and solvent …
Defect dynamics in a thin active nematic layer is studied by asymptotic matching of solutions in the defect core and the far field. The analysis is facilitated by the correspondence between the 2D nematic and complex scalar field models. Self-propulsion and topological interactions are identified as the primary drivers of the defect motion, surpassing the influence of both passive backflow and active flow induced by other defects.
Motivated by results for the propagation of active-passive interfaces of bacterial Serratia marcescens swarms [Nat. Comm., 9, 5373 (2018)] we use a hydrodynamic multiphase model to investigate the propagation of interfaces of active nematics on substrates. We characterize the active nematic phase of the model and discuss its description of the statistical dynamics of the swarms. We show that the velocicity correlation functions and the energy spectrum of the active turbulent phase of the model scale with the active length, for a range of activities. In addition, the energy spectrum exhibits tw…
The flow properties of a continuum model for an active nematic is studied and compared with recent experiments on suspensions of microtubule bundles and molecular motors. The velocity correlation length is found to be independent of the strength of the activity while the characteristic velocity scale increases monotonically as the activity is increased, both in agreement with the experimental observations. We interpret our results in terms of the creation and annihilation dynamics of a gas of topological defects.
Active nematics are microscopically driven liquid crystals that exhibit dynamical steady states characterized by the creation and annihilation of topological defects. Motivated by experimental realizations of such systems made of biopolymer filaments and motor proteins, we describe a large-scale simulation study of a particle-based computational model that explicitly incorporates the semiflexibility of the biopolymers. We find that energy injected into the system at the particle scale preferentially excites bend deformations, renormalizing the filament bend modulus to smaller values. The emerg…
We numerically investigate how spatial variations of extensile or contractile active stress affect bulk active nematic systems in two and three dimensions. In the absence of defects, activity gradients drive flows which re-orient the nematic director field and thus act as an effective anchoring force. At high activity, defects are created and the system transitions into active turbulence, a chaotic flow state characterized by strong vorticity. We find that in two-dimensional (2D) systems active torques robustly align $+1/2$ defects parallel to activity gradients, with defect heads pointing tow…
Basing our arguments on the theory of active liquid crystals, we demonstrate both analytically and numerically, that the activity can induce an effective free energy which enhances ordering in extensile systems of active rods and in contractile suspensions of active discs. We argue that this occurs because any ordering fluctuation is enhanced by the flow field it produces. A phase-diagram in the temperature-activity plane compares ordering due to a thermodynamic free energy to that resulting from the activity. We also demonstrate that activity can drive variations in concentration, but for a d…
Specific features of two-dimensional nematodynamics give rise to shortfalls of the tensor representation of the nematic order parameter commonly used in computations, especially in theory of active matter. The alternative representation in terms of the vector order parameter follows with small adjustments the classical director-based theory, but is applicable to 2D problems where both nematic alignment and deviation from the isotropic state are variable. Stability analysis of nematic alignment and flow is used as a testing ground. A director-based analysis demonstrates a shortfall of the stand…
We report numerical results for the hydrodynamics of inhomogeneous lyotropic and extensile active nematic gels. By simulating the coupled Cahn-Hilliard, Navier-Stokes, and Beris-Edwards equation for the evolution of the composition, flow and orientational order of an active nematic, we ask whether composition variations are important to determine its emergent physics. As in active gels of uniform composition, we find that increasing either activity or nematic tendency (e.g., overall active matter concentration) triggers a transition between an isotropic passive phase and an active nematic one.…
I put forward a continuum theory for active nematic gels, defined as fluids or suspensions of orientable rodlike objects endowed with active dynamics, that is based on symmetry arguments and compatibility with thermodynamics. The starting point is our recent theory that models (passive) nematic liquid crystals as relaxing nematic elastomers. The interplay between viscoelastic response and active dynamics of the microscopic constituents is naturally taken into account. By contrast with standard theories, activity is not introduced as an additional term of the stress tensor, but it is added as a…
Activity in nematics drives interfacial flows that lead to preferential alignment that is tangential or planar for extensile systems (pushers) and perpendicular or homeotropic for contractile ones (pullers). This alignment is known as active anchoring and has been reported for a number of systems and described using active nematic hydrodynamic theories. The latter are based on the one-elastic constant approximation, i.e., they assume elastic isotropy of the underlying passive nematic. Real nematics, however, have different elastic constants, which lead to interfacial anchoring. In this paper, …
Recent theoretical studies found that mixtures of active and passive colloidal particles phase separate but only at very high activity ratio. The high value poses serious obstacles for experimental exploration of this phenomenon. Here we show using simulations that when the active and passive particles are polymers, the critical activity ratio decreases with the polymer length. This not only facilitates the experiments but also has implications on the DNA organization in living cell nuclei. Entropy production can be used as an accurate indicator of this non-equilibrium phase transition.
We formulate the statistical dynamics of topological defects in the active nematic phase, formed in two dimensions by a collection of self-driven particles on a substrate. An important consequence of the non-equilibrium drive is the spontaneous motility of strength +1/2 disclinations. Starting from the hydrodynamic equations of active nematics, we derive an interacting particle description of defects that includes active torques. We show that activity, within perturbation theory, lowers the defect-unbinding transition temperature, determining a critical line in the temperature-activity plane t…
We investigate the effect of an anisotropic substrate on the turbulent dynamics of a simulated two dimensional active nematic. This is introduced as an anisotropic friction and an effective anisotropic viscosity, with the orientation of the anisotropy being defined by the substrate. In this system we observe the emergence of global nematic order of topological defects that is controlled by the degree of anisotropy in the viscosity and the magnitude of the active stress. No global defect alignment is seen in passive liquid crystals with anisotropic viscosity or friction confirming that ordering…
We derive a fully covariant theory of the hydrodynamics of nematic and polar active surfaces, subjected to internal and external forces and torques. We study the symmetries of polar and nematic surfaces and find that in addition to 5 different types of in-plane isotropic surfaces, polar and nematic surfaces can be classified into 5 polar, 2 pseudopolar, 5 nematic and 2 pseudonematic types of surfaces. We give examples of physical realisations of the different types of surfaces we have identified. We obtain expressions for the equilibrium tensions, moments, and external forces and torques actin…
Active turbulence in dense active systems is characterized by high vorticity on a length scale that is 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, first, 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 sh…
We examine the dynamics of a compressible active nematic liquid crystal on a frictional substrate. When frictional damping dominates over viscous dissipation, we eliminate flow in favor of active stresses to obtain a minimal dynamical model for the nematic order parameter, with elastic constants renormalized by activity. The renormalized elastic constants can become negative at large activity, leading to the selection of spatially inhomogeneous patterns via a mechanism analogous to that responsible for modulated phases arising at an equilibrium Lifshitz point. Tuning activity and the degree of…
From the mitotic spindle up to tissues and biofilms, many biological systems behave as active droplets, which often break symmetry and change shape spontaneously. Here, I show that active nematic droplets can experience a fingering instability. I consider an active fluid that acquires nematic order through anchoring at the droplet interface, and I predict its morphological stability in terms of three dimensionless parameters: the anchoring angle, the penetration length of nematic order compared to droplet size, and an active capillary number. Droplets with extensile (contractile) stresses and …
We study the dynamics of topological defects in active nematic films with spatially-varying activity and consider two setups: i) a constant activity gradient, and ii) a sharp jump in activity. A constant gradient of extensile (contractile) activity endows the comet-like $+1/2$ defect with a finite vorticity that drives the defect to align its nose in the direction of decreasing (increasing) gradient. A constant gradient does not, however, affect the known self-propulsion of the $+1/2$ defect and has no effect on the $-1/2$ that remains a non-motile particle. A sharp jump in activity acts like …
Recent experiments and numerical studies have drawn attention to the dynamics of active nematics. Two-dimensional active nematics flow spontaneously and exhibit spatiotemporal chaotic flows with proliferation of topological defects in the nematic texture. It has been proposed that the dynamics of active nematics can be understood in terms of the dynamics of interacting defects, propelled by active stress. Previous work has derived effective equations of motion for individual defects as quasi-particles moving in the mean field generated by other defects, but an effective theory governing multi-…
Topological delocalisation of confined 3D active nematics
Johns Hopkins University（约翰斯·霍普金斯大学）；Università degli Studi di Bari Aldo Moro（巴里阿尔多·莫罗大学）；INFN（意大利国家核物理研究所）；University of Edinburgh（爱丁堡大学）；Universitat de Barcelona（巴塞罗那大学）
We examine the scaling with activity of the emergent length scales that control the nonequilibrium dynamics of an active nematic liquid crystal, using two popular hydrodynamic models that have been employed in previous studies. In both models we find that the chaotic spatio-temporal dynamics in the regime of fully developed active turbulence is controlled by a single active scale determined by the balance of active and elastic stresses, regardless of whether the active stress is extensile or contractile in nature. The observed scaling of the kinetic energy and enstropy with activity is consist…
Suspensions of actively driven anisotropic objects exhibit distinctively nonequilibrium behaviors, and current theories predict that they are incapable of sustaining orientational order at high activity. By contrast, here we show that nematic suspensions on a substrate can display order at arbitrarily high activity due to a previously unreported, potentially stabilizing active force. The resulting nonequilibrium ordered phase displays robust giant number fluctuations that cannot be suppressed even by an incompressible solvent. Our results apply to virtually all experimental assays used to inve…
We numerically investigate the morphology and disclination line dynamics of active nematic droplets in three dimensions. Although our model only incorporates the simplest possible form of achiral active stress, active nematic droplets display an unprecedented range of complex morphologies. For extensile activity finger-like protrusions grow at points where disclination lines intersect the droplet surface. For contractile activity, however, the activity field drives cup-shaped droplet invagination, run-and-tumble motion or the formation of surface wrinkles. This diversity of behaviour is explai…
