Flow States and Transitions of an Active Nematic in a Three-Dimensional Channel

Periodic orbits, pair nucleation, and unbinding of active nematic defects on cones

Geometric confinement and topological constraints present promising means of controlling active materials. By combining analytical arguments derived from the Born-Oppenheimer approximation with numerical simulations, we investigate the simultaneous impact of confinement together with curvature singularity by characterizing the dynamics of an active nematic on a cone. Here, the Born-Oppenheimer approximation means that textures can follow defect positions rapidly on the timescales of interest. Upon imposing strong anchoring boundary conditions at the base of a cone, we find a rich phase diagram of multidefect dynamics, including exotic periodic orbits of one or two +1/2 flank defects, depending on activity and nonquantized geometric charge at the cone apex. By characterizing the transitions between these ordered dynamical states, we present detailed understanding of (i) defect unbinding, (ii) defect absorption, and (iii) defect pair nucleation at the apex. Numerical simulations confirm theoretical predictions of not only the nature of the circular orbits but also defect unbinding from the apex.

Flow states of two dimensional active gels driven by external shear

Using a minimal hydrodynamic model, we theoretically and computationally study the Couette flow of active gels in straight and annular two-dimensional channels subject to an externally imposed shear. The gels are isotropic in the absence of externally- or activity-driven shear, but have nematic order that increases with shear rate. Using the finite element method, we determine the possible flow states for a range of activities and shear rates. Linear stability analysis of an unconfined gel in a straight channel shows that an externally imposed shear flow can stabilize an extensile fluid that would be unstable to spontaneous flow in the absence of the shear flow, and destabilize a contractile fluid that would be stable against spontaneous flow in the absence of shear flow. These results are in rough agreement with the stability boundaries between the base shear flow state and the nonlinear flow states that we find numerically for a confined active gel. For extensile fluids, we find three kinds of nonlinear flow states in the range of parameters we study: unidirectional flows, oscillatory flows, and dancing flows. To highlight the activity-driven spontaneous component of the nonlinear flows, we characterize these states by the average volumetric flow rate and the wall stress. For contractile fluids, we only find the linear shear flow and a nonlinear unidirectional flow in the range of parameters that we studied. For large magnitudes of the activity, the unidirectional contractile flow develops a boundary layer. Our analysis of annular channels shows how curvature of the streamlines in the base flow affects the transitions among flow states.

Symmetry Breaking of Self-Propelled Topological Defects in Thin-Film Active Chiral Nematics

Active nematics represent a range of dense active matter systems which can engender spontaneous flows and self-propelled topological defects. Two-dimensional (2D) active nematic theory and simulation have been successful in explaining many quasi-2D experiments in which self-propelled +1/2 defects are observed to move along their symmetry axis. However, many active liquid crystals are essentially chiral nematic, but their twist mode becomes irrelevant under the 2D assumption. Here, we use theory and simulation to examine a three-dimensional active chiral nematic confined to a thin film, thus forming a quasi-2D system. We predict that the self-propelled +1/2 disclination in a curved thin film can break its mirror symmetry by moving circularly. Our prediction is confirmed by hydrodynamic simulations of thin spherical-shell and thin cylindrical-shell systems. In the spherical-shell confinement, the four emerged +1/2 disclinations exhibit rich dynamics as a function of activity and chirality. As such, we have proposed a new symmetry-breaking scenario in which self-propelled defects in quasi-2D active nematics can acquire an active angular velocity, greatly enriching their dynamics for finer control and emerging applications.

Vortex Lattices in Active Nematics with Periodic Obstacle Arrays

We numerically model a two-dimensional active nematic confined by a periodic array of fixed obstacles. Even in the passive nematic, the appearance of topological defects is unavoidable due to planar anchoring by the obstacle surfaces. We show that a vortex lattice state emerges as activity is increased, and that this lattice may be tuned from "ferromagnetic" to "antiferromagnetic" by varying the gap size between obstacles. We map the rich variety of states exhibited by the system as a function of distance between obstacles and activity, including a pinned defect state, motile defects, the vortex lattice, and active turbulence. We demonstrate that the flows in the active turbulent phase can be tuned by the presence of obstacles, and explore the effects of a frustrated lattice geometry on the vortex lattice phase.

Elasticity tunes mechanical stress localization around active topological defects

Mechanical stresses are increasingly found to be associated with various biological functionalities. At the same time, topological defects are being identified across a diverse range of biological systems and are points of localized mechanical stress. It is therefore important to ask how mechanical stress localization around topological defects is controlled. Here, we use continuum simulations of nonequilibrium, fluctuating and active nematics to explore the patterns of stress localization, as well as their extent and intensity around topological defects. We find that by increasing the orientational elasticity of the material, the isotropic stress pattern around topological defects is changed substantially, from a stress dipole characterized by symmetric compression-tension regions around the core of the defect, to a localized stress monopole at the defect position. Moreover, we show that elastic anisotropy alters the extent and intensity of the stresses, and can result in the dominance of tension or compression around defects. Finally, including both nonequilibrium fluctuations and active stress generation, we find that the elastic constant tunes the relative effect of each, leading to the flipping of tension and compression regions around topological defects. This flipping of the tension-compression regions only by changing the elastic constant presents an interesting, simple, way of switching the dynamic behavior in active matter by changing a passive material property. We expect these findings to motivate further exploration tuning stresses in active biological materials by varying material properties of the constituent units.

Vorticity phase separation and defect lattices in the isotropic phase of active liquid crystals

We use numerical simulations and linear stability analysis to study the dynamics of an active liquid crystal film on a substrate in the regime where the passive system would be isotropic. Extensile activity builds up local orientational order and destabilizes the quiescent isotropic state above a critical activity, eventually resulting in spatiotemporal chaotic dynamics akin to the one observed ubiquitously in the nematic state. Here we show that tuning substrate friction yields a variety of emergent structures at intermediate activity, including lattices of flow vortices with associated regular arrangements of topological defects and a new state where flow vortices trap pairs of +1/2 defect that chase each other's tail. These chiral units spontaneously pick the sense of rotation and organize in a hexagonal lattice, surrounded by a diffuse flow of opposite rotation to maintain zero net vorticity. The length scale of these emergent structures is set by the screening length of the flow, controlled by the shear viscosity η and the substrate friction Γ, and can be captured by simple mode selection of the vortical flows. We demonstrate that the emergence of coherent structures can be interpreted as a phase separation of vorticity, where friction plays a role akin to that of birth/death processes in breaking conservation of the phase separating species and selecting a characteristic scale for the patterns. Our work shows that friction provides an experimentally accessible tuning parameter for designing controlled active flows.

Spontaneous flows and dynamics of full-integer topological defects in polar active matter

Polar active matter of self-propelled particles sustain spontaneous flows through the full-integer topological defects. We study theoretically the incompressible flow profiles around ±1 defects induced by polar and dipolar active forces. We show that dipolar forces induce vortical flows around the +1 defect, while the flow around the -1 defect has an 8-fold rotational symmetry. The vortical flow changes its chirality near the +1 defect core in the absence of the friction with a substrate. We show analytically that the flow induced by polar active forces is vortical near the +1 defect and is 4-fold symmetric near the -1 defect, while it becomes uniform in the far-field. For a pair of oppositely charged defects, this polar flow contributes to a mutual interaction force that depends only on the orientation of the defect pair relative to the background polarization, and that enhances defect pair annihilation. This is in contradiction with the effect of dipolar active forces which decay inversely proportional with the defect separation distance. As such, our analyses reveals a long-ranged mechanism for the pairwise interaction between topological defects in polar active matter.

Friction-mediated phase transition in confined active nematics

Using a minimal continuum model, we investigate the interplay between circular confinement and substrate friction in active nematics. Upon increasing the friction from low to high, we observe a dynamical phase transition from a circulating flow phase to an anisotropic flow phase in which the flow tends to align perpendicular to the nematic director at the boundary. We demonstrate that both the flow structure and dynamic correlations in the latter phase differ from those of an unconfined, active turbulent system and may be controlled by the prescribed nematic boundary conditions. Our results show that substrate friction and geometric confinement act as valuable control parameters in active nematics.

Nematronics: Reciprocal Coupling between Ionic Currents and Nematic Dynamics

Adopting a spintronics-inspired approach, we study the reciprocal coupling between ionic charge currents and nematic texture dynamics in a uniaxial nematic electrolyte. Assuming quenched fluid dynamics, we develop equations of motion analogously to spin torque and spin pumping. Based on the principle of least dissipation of energy, we derive the adiabatic "nematic torque" exerted by ionic currents on the nematic director field as well as the reciprocal motive force on ions due to the orientational dynamics of the director. We discuss several simple examples that illustrate the potential functionality of this coupling. Furthermore, using our phenomenological framework, we propose a practical means to extract the coupling strength through impedance measurements on a nematic cell. Exploring further applications based on this physics could foster the development of nematronics-nematic iontronics.

Fluid interfaces laden by force dipoles: towards active matter-driven microfluidic flows

In recent years, nonlinear microfluidics in combination with lab-on-a-chip devices has opened a new avenue for chemical and biomedical applications such as droplet formation and cell sorting. In this article, we integrate ideas from active matter into a microfluidic setting, where two fluid layers with identical densities but different viscosities flow through a microfluidic channel. Most importantly, the fluid interface is laden with active particles that act with dipolar forces on the adjacent fluids and thereby generate flows. We perform lattice-Boltzmann simulations and combine them with phase field dynamics of the interface and an advection-diffusion equation for the density of active particles. We show that only contractile force dipoles can destabilize the flat fluid interface. It develops a viscous finger from which droplets break up. For interfaces with non-zero surface tension, a critical value of activity equal to the surface tension is necessary to trigger the instability. Since activity depends on the density of force dipoles, the interface can develop steady deformation. Lastly, we demonstrate how to control droplet formation using switchable activity.

Emergence of macroscopic directional motion of deformable active cells in confined structures

There is now growing evidence of collective turbulentlike motion of cells in dense tissues. However, how to control and harness this collective motion is an open question. We investigate the transport of deformable active cells in a periodically asymmetric channel by using a phase-field model. We demonstrate that collective turbulent-like motion of cells can power and steer the macroscopic directional motion through the ratchet channel. The active intercellular forces proportional to the deformation of cells can break thermodynamical equilibrium and induce the directional motion. This directional motion is caused by the ratchet effect rather than the spontaneous symmetry breaking. The motion direction is determined by the asymmetry of the channel. Remarkably, there exits an optimal nonequilibrium driving (depending on the active strength, the elasticity, and the packing fraction) at which the average velocity reaches the maximum. In addition, the optimized packing fraction and the optimized minimum width of the channel can facilitate the directional motion of cells. Our findings are relevant to understanding how macroscopic directional motion relates to the local force transmission mediated by cell-cell contacts in cellular monolayers.

Data-Driven Discovery of Active Nematic Hydrodynamics

Active nematics can be modeled using phenomenological continuum theories that account for the dynamics of the nematic director and fluid velocity through partial differential equations (PDEs). While these models provide a statistical description of the experiments, the relevant terms in the PDEs and their parameters are usually identified indirectly. We adapt a recently developed method to automatically identify optimal continuum models for active nematics directly from spatiotemporal data, via sparse regression of the coarse-grained fields onto generic low order PDEs. After extensive benchmarking, we apply the method to experiments with microtubule-based active nematics, finding a surprisingly minimal description of the system. Our approach can be generalized to gain insights into active gels, microswimmers, and diverse other experimental active matter systems.

Helical flow states in active nematics

We show that confining extensile nematics in three-dimensional (3D) channels leads to the emergence of two self-organized flow states with nonzero helicity. The first is a pair of braided antiparallel streams-this double helix occurs when the activity is moderate, anchoring negligible, and reduced temperature high. The second consists of axially aligned counter-rotating vortices-this grinder train arises between spontaneous axial streaming and the vortex lattice. These two unanticipated helical flow states illustrate the potential of active fluids to break symmetries and form complex but organized spatiotemporal structures in 3D fluidic devices.

Defect loops in three-dimensional active nematics as active multipoles

We develop a description of defect loops in three-dimensional active nematics based on a multipole expansion of the far-field director and show how this leads to a self-dynamics dependent on the loop's geometric type. The dipole term leads to active stresses that generate a global self-propulsion for splay and bend loops. The quadrupole moment is nonzero only for nonplanar loops and generates a net "active torque," such that defect loops are both self-motile and self-orienting. Our analysis identifies right- and left-handed twist loops as the only force- and torque-free geometries, suggesting a mechanism for generating an excess of twist loops. Finally, we determine the Stokesian flows created by defect loops and describe qualitatively their hydrodynamics.

Flow transitions and length scales of a channel-confined active nematic

We perform lattice Boltzmann simulations of an active nematic fluid confined in a two-dimensional channel to study the range of flow states that are stabilised by the confinement: unidirectional flow, oscillatory flow, the dancing state, localised active turbulence and fully-developed active turbulence. We analyse the flows in Fourier space, and measure a range of different length scales which describe the flows. We argue that the different states occur as a result of flow instabilities inherent to the system. As a consequence the characteristic length scale for oscillatory flow, the dancing state and localised active turbulence is set by the channel width. Fully-developed active turbulence occurs only when the channel width is larger than the intrinsic, active length scale of the bulk fluid. The results clarify why the activity number is a control parameter for the flow transitions.

Flow coupling between active and passive fluids across water-oil interfaces

Active fluid droplets surrounded by oil can spontaneously develop circulatory flows. However, the dynamics of the surrounding oil and their influence on the active fluid remain poorly understood. To investigate interactions between the active fluid and the passive oil across their interface, kinesin-driven microtubule-based active fluid droplets were immersed in oil and compressed into a cylinder-like shape. The droplet geometry supported intradroplet circulatory flows, but the circulation was suppressed when the thickness of the oil layer surrounding the droplet decreased. Experiments with tracers and network structure analyses and continuum models based on the dynamics of self-elongating rods demonstrated that the flow transition resulted from flow coupling across the interface between active fluid and oil, with a millimeter-scale coupling length. In addition, two novel millifluidic devices were developed that could trigger and suppress intradroplet circulatory flows in real time: one by changing the thickness of the surrounding oil layer and the other by locally deforming the droplet. This work highlights the role of interfacial dynamics in the active fluid droplet system and shows that circulatory flows within droplets can be affected by millimeter-scale flow coupling across the interface between the active fluid and the oil.

Spontaneous directional flow of active magnetic particles

We predict the emergence of large-scale polar order and spontaneous directional flows in a class of self-propelled autonomous particles that interact via passive repulsion between off-center sites. The coupling of active motion with the passive torque acting about the particle centers results in hybrid active-passive interactions responsible for a macroscopic phase transition from an isotropic state to a polar-aligned state in systems of particles with front interaction sites. We employ a continuum kinetic theory to explain that the emergence of long-ranged orientational order, which occurs in unbounded domains at finite densities, can be externally activated independently of the self-propulsion mechanism and drives a macroscopic particle flow in a direction selected by symmetry breaking.

Confinement-Induced Self-Pumping in 3D Active Fluids

Two dimensional active fluids display a transition from turbulent to coherent flow upon decreasing the size of the confining geometry. A recent experiment suggests that the behavior in three dimensions is remarkably different; emergent flows transition from turbulence to coherence upon increasing the confinement height to match the width. Using a simple hydrodynamic model of a suspension of extensile rodlike units, we provide the theoretical explanation for this puzzling behavior. Furthermore, using extensive numerical simulations supported by theoretical arguments, we map out the conditions that lead to coherent flows and elucidate the critical role played by the aspect ratio of the confining channel. The mechanism that we identify applies to a large class of symmetries and propulsion mechanisms, leading to a unified set of design principles for self-pumping 3D active fluids.

Confinement Controls the Bend Instability of Three-Dimensional Active Liquid Crystals

Spontaneous growth of long-wavelength deformations is a defining feature of active liquid crystals. We investigate the effect of confinement on the instability of 3D active liquid crystals in the isotropic phase composed of extensile microtubule bundles and kinesin molecular motors. When shear aligned, such fluids exhibit finite-wavelength self-amplifying bend deformations. By systematically changing the channel size we elucidate how the instability wavelength and its growth rate depend on the channel dimensions. Experimental findings are qualitatively consistent with a minimal hydrodynamic model, where the fastest growing deformation is set by a balance of active driving and elastic relaxation. Our results demonstrate that confinement determines the structure and dynamics of active fluids on all experimentally accessible length scales.