Correlation lengths in hydrodynamic models of active nematics

Topological defects play a prominent role in the physics of two-dimensional materials. When driven out of equilibrium in active nematics, disclinations can acquire spontaneous self-propulsion and drive self-sustained flows upon proliferation. Here we construct a general hydrodynamic theory for a two-dimensional active nematic interrupted by a large number of such defects. Our equations describe the flows and spatio-temporal defect chaos characterizing active turbulence, even close to the defect unbinding transition. At high activity, nonequilibrium torques combined with manybody screening cause the active disclinations to spontaneously break rotational symmetry forming a collectively moving defect ordered polar liquid. By recognizing defects as the relevant quasiparticle excitations, we construct a comprehensive phase diagram for two-dimensional active nematics. Using our hydrodynamic approach, we additionally show that activity gradients can act like "electric fields", driving the sorting of topological charge. This demonstrates the versatility of our continuum model and its relevance for quantifying the use of spatially inhomogeneous activity for controlling active flows and for the fabrication of active devices with targeted transport capabilities.

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“…or velocity are all controlled mainly by the mean defect spacing ξ ∼ 1/ √ n, in agreement with previous numerical results [26,27].…”

Section: B Results and Outlinesupporting

confidence: 92%

Hydrodynamics of Active Defects: From Order to Chaos to Defect Ordering

Shankar

2019

Phys. Rev. X

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121

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“…2a). This parameter characterizes the ratio of the channel height h , which here is equivalent to the hydrodynamic screening length, to the characteristic activity-induced length scale , which represents the relative importance of the intrinsic activity ζ and the orientational elasticity K of the nematic fluid3334.…”

Section: Resultsmentioning

confidence: 99%

Onset of meso-scale turbulence in active nematics

et al. 2017

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Meso-scale turbulence is an innate phenomenon, distinct from inertial turbulence, that spontaneously occurs at low Reynolds number in fluidized biological systems. This spatiotemporal disordered flow radically changes nutrient and molecular transport in living fluids and can strongly affect the collective behaviour in prominent biological processes, including biofilm formation, morphogenesis and cancer invasion. Despite its crucial role in such physiological processes, understanding meso-scale turbulence and any relation to classical inertial turbulence remains obscure. Here we show how the motion of active matter along a micro-channel transitions to meso-scale turbulence through the evolution of locally disordered patches (active puffs) from an ordered vortex-lattice flow state. We demonstrate that the stationary critical exponents of this transition to meso-scale turbulence in a channel coincide with the directed percolation universality class. This finding bridges our understanding of the onset of low-Reynolds-number meso-scale turbulence and traditional scale-invariant turbulence in confinement.

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“…By varying these factors it is possible to observe diverse spatiotemporal patterns including vortices [14,16], oscillating textures [8,18] and travelling bands [8,16]. When the driving force is sufficiently high, active nematics can spontaneously nucleate many topological defects, generating flows and interacting chaotically in a regime referred to as low reynolds number, active turbulence [1,4,10,11]. These defects have been shown to exert an elastic torque on each other [19] and experiments have indicated that long range nematic order of defects is possible in a state of active turbulence [20] though this hasn't been reproduced theoretically.…”

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confidence: 99%

Activity Driven Orientational Order in Active Nematic Liquid Crystals on an Anisotropic Substrate

Pearce

2019

Phys. Rev. Lett.

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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 is driven by the active stress. We then closely examine the active flow generated by a single defect to show that the kinetic energy of the flow is orientation dependent, resulting in a torque on the defect to align them with the anisotropy in the substrate.Active nematic liquid crystals are fluids consisting of self (or mutually) propelling rod shaped particles resulting in an anisotropic fluid with broken rotational symmetry that drives itself at the microscopic scale [1,2]. This interesting combination of broken rotational symmetry and out of equilibrium, active behaviour has lead to an explosion of interest from both experimental and theoretical physics [1][2][3][4][5][6]. There have been many successful experiments reproducing active nematics often utilising biological components, including microtubule kinesin suspensions [1, 2, 7], acto-myosin gels [8,9] and elongated cells [10,[12][13][14], but also from inert components such as vibrated monolayers of granular rods [15].These systems have been shown to display a rich phenomenology depending on many factors such as the degree to which the system is driven [4], the confining geometry [16], the density [13] and the boundary conditions [17]. By varying these factors it is possible to observe diverse spatiotemporal patterns including vortices [14,16], oscillating textures [8,18] and travelling bands [8,16]. When the driving force is sufficiently high, active nematics can spontaneously nucleate many topological defects, generating flows and interacting chaotically in a regime referred to as low reynolds number, active turbulence [1,4,10,11]. These defects have been shown to exert an elastic torque on each other [19] and experiments have indicated that long range nematic order of defects is possible in a state of active turbulence [20] though this hasn't been reproduced theoretically. It has been shown that the position and orientation of these defects can be influenced by the substrate on which the active nematic is placed. By changing the geometry of the substrate it is possible to reorient defects and sort them by charge [21], by changing the topology of the substrate it is possible to control the total number of defects and their trajectories [18]. A defect ordered active nematic has been recreated by placing a 2D active nematic on top of a passive liquid crystal that can be controlled by an external magnetic field [22]. When the passive liquid crystal layer is ordered ...

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Correlation lengths in hydrodynamic models of active nematics

Cited by 96 publications

References 39 publications

Hydrodynamics of Active Defects: From Order to Chaos to Defect Ordering

Hydrodynamics of Active Defects: From Order to Chaos to Defect Ordering

Onset of meso-scale turbulence in active nematics

Activity Driven Orientational Order in Active Nematic Liquid Crystals on an Anisotropic Substrate

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