We propose and study a local map capable of describing the full variety of dynamical states, ranging from regular to chaotic, obtained when a nematic liquid crystal is subjected to a steady shear flow. The map is formulated in terms of a quaternion parametrization of rotations of the local frame described by the axes of the nematic director, subdirector and the joint normal to these, with two additional scalars describing the strength of ordering. Our model yields kayaking, wagging, tumbling, aligned and coexistence states, in agreement with previous formulations based on coupled ordinary differential equations. Such a map can serve as a building block for the construction of lattice models of the complex spatio-temporal states predicted for sheared nematics.
We study the flow behaviour of a twist-bend nematic $(N_{TB})$ liquid crystal. It shows three distinct shear stress ($σ$) responses in a certain range of temperatures and shear rates ($\dotγ$). In Region-I, $σ\sim\sqrt{\dotγ}$, in region-II, the stress shows a plateau, characterised by a power law $σ\sim{\dotγ}^α$, where $α\sim0.1-0.4$ and in region-III, $σ\sim\dotγ$. With increasing shear rate, $σ$ changes continuously from region-I to II, whereas it changes discontinuously with a hysteresis from region-II to III. In the plateau (region-II), we observe a dynamic stress fluctuations, exhibitin…
We study the role of the control parameter triggering nematic order (temperature or concentration) on the dynamical behavior of a system of nanorods under shear. Our study is based on a set of mesoscopic equations of motion for the components of the tensorial orientational order parameter. We investigating these equations via a systematic bifurcation analysis based on a numerical continuation technique, focusing on spatially homogeneous states. Exploring a wide range of parameters we find, unexpectedly, that states with oscillatory motion can exist even under conditions where the equilibrium s…
Motivated by the observation of rheochaos in sheared wormlike micelles [Bandyopadhyay et al., Phys. Rev. Lett, 84 2022, (2000); Europhys. Lett. 56, 447 (2001); Pramana 53, 223 (1999)] we study the coupled nonlinear partial differential equations for the hydrodynamic velocity and order parameter fields in a sheared nematogenic fluid. In a suitable parameter range, we find irregular, dynamic shear-banding and establish by decisive numerical tests that the chaos we observe in the model is spatiotemporal in nature.
We demonstrate how to construct dynamic phase diagrams for complex fluids that undergo transitions under flow, in which the conserved composition variable and the broken-symmetry order parameter (nematic, smectic, crystalline, etc.) are coupled to shear rate. Our construction relies on a selection criterion, the existence of a steady interface connecting two stable homogeneous states. We use the (generalized) Doi model of lyotropic nematic liquid crystals as a model system, but the method can be easily applied to other systems, provided non-local effects are included.
A variety of complex fluids under shear exhibit complex spatio-temporal behaviour, including what is now termed rheological chaos, at moderate values of the shear rate. Such chaos associated with rheological response occurs in regimes where the Reynolds number is very small. It must thus arise as a consequence of the coupling of the flow to internal structural variables describing the local state of the fluid. We propose a coupled map lattice (CML) model for such complex spatio-temporal behaviour in a passively sheared nematic liquid crystal, using local maps constructed so as to accurately de…
The nonlinear flow behaviour of a viscoelastic gel formed due to entangled, cylindrical micelles in aqueous solutions of the surfactant CTAT has been studied. On subjecting the system to a step shear rate lying above a certain value, the shear and normal stresses show interesting time dependent behaviour. The analysis of the measured time series shows the existence of a finite correlation dimension and a positive Lyapunov exponent, unambiguously implying that the dynamics can be described by that of a dynamical system with a strange attractor whose dimension increases with the increase in shea…
We introduce a new mesoscopic model for nematic liquid crystals (LCs). We extend the particle-based stochastic rotation dynamics method, which reproduces the Navier-Stokes equation, to anisotropic fluids by including a simplified Ericksen-Leslie formulation of nematodynamics. We verify the applicability of this hybrid model by studying the equilibrium isotropic-nematic phase transition and nonequilibrium problems, such as the dynamics of topological defects, and the rheology of sheared LCs. Our simulation results show that this hybrid model captures many essential aspects of LC physics at the …
Based on a continuum theory, we investigate the manipulation of the non-equilibrium behavior of a sheared liquid crystal via closed-loop feedback control. Our goal is to stabilize a specific dynamical state, that is, the stationary "flow-alignment", under conditions where the uncontrolled system displays oscillatory director dynamics with in-plane symmetry. To this end we employ time-delayed feedback control (TDFC), where the equation of motion for the ith component, q_i(t), of the order parameter tensor is supplemented by a control term involving the difference q_i(t)-q_i(t-τ). In this diagon…
While studies of active nematics in two dimensions have shed light on various aspects of the flow regimes and topology of active matter, three-dimensional properties of topological defects and chaotic flows remain unexplored. By confining a film of active nematics between two parallel plates, we use continuum simulations and analytical arguments to demonstrate that the crossover from quasi-2D to 3D chaotic flows is controlled by the morphology of the disclination lines. For small plate separations, the active nematic behaves as a quasi-2D material, with straight topological disclination lines …
Dense, active systems show active turbulence, a state characterised by flow fields that are chaotic, with continually changing velocity jets and swirls. Here we review our current understanding of active turbulence. The development is primarily based on the theory and simulations of active liquid crystals, but with accompanying summaries of related literature.
Recent studies have shown that packings of cells, both eukaryotic cellular tissues and growing or swarming bacterial colonies, can often be understood as active nematic fluids. A key property of volume-conserving active nematic model systems is chaotic self-mixing characterized by motile topological defects. However, for active nematics driven by growth rather than motility, less is understood about mixing and defect motion. Mixing could affect evolutionary outcomes in bacterial colonies by counteracting the tendency to spatially segregate into monoclonal sectors, which reduces the local genet…
Discontinuous transition to active nematic turbulence
Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）；University of Cape Town（开普敦大学）；Cluster of Excellence Physics of Life, TU Dresden（德累斯顿工业大学生命物理卓越集群）；Universitat de Barcelona（巴塞罗那大学）；Universitat de Barcelona Institute of Complex Systems (UBICS)（巴塞罗那大学复杂系统研究所）；Institució Catalana de Recerca i Estudis Avançats (ICREA)（加泰罗尼亚研究高级学院）
Flatiron Institute（平顿研究所）；Center for Computational Biology, Flatiron Institute（平顿研究所计算生物学中心）；Departament de Física de la Matèria Condensada, Universitat de Barcelona（巴塞罗那大学凝聚态物理系）；Max Planck Institute for the Physics of Complex Systems（马克斯·普朗克复杂系统物理研究所）；Center for Systems Biology Dresden（德累斯顿系统生物学中心）；Cluster of Excellence Physics of Life, TU Dresden（德累斯顿工业大学生命物理学卓越集群）；Collège de France（法兰西公学院）；Laboratoire PhysicoChimie Curie, Institut Curie, Université Paris Sciences & Lettres (PSL), Sorbonne Universités, Université Pierre et Marie Curie (UPMC)（居里研究所物理化学实验室，巴黎文理研究大学，索邦大学，皮埃尔和玛丽·居里大学）；Universitat de Barcelona Institute of Complex Systems (UBICS)（巴塞罗那大学复杂系统研究所）
Here we study theoretically the dynamics of a 2D and a 3D isotropic droplet in a nematic liquid crystal under a shear flow. We find a large repertoire of possible nonequilibrium steady states as a function of the shear rate and of the anchoring of the nematic director field at the droplet surface. We first discuss homeotropic anchoring. For weak anchoring, we recover the typical behaviour of a sheared isotropic droplet in a binary fluid, which rotates, stretches and can be broken by the applied flow. For intermediate anchoring, new possibilities arise due to elastic effects in the nematic flui…
The study of liquid crystals at equilibrium has led to fundamental insights into the nature of ordered materials, as well as to practical applications such as display technologies. Active nematics are a fundamentally different class of liquid crystals, driven away from equilibrium by the autonomous motion of their constituent rod-like particles. This internally generated activity powers the continuous creation and annihilation of topological defects, which leads to complex streaming flows whose chaotic dynamics appear to destroy long-range order. Here, we study these dynamics in experimental a…
Utilizing molecular dynamics simulations, we report a non-monotonic dependence of the shear stress on the strength of an external magnetic field ($H$) in a liquid-crystalline mixture of magnetic and non-magnetic anisotropic particles. This non-monotonic behavior is in sharp contrast with the well-studied monotonic $H$-dependency of the shear stress in conventional ferrofluids, where the shear stress increases with $H$ until it reaches a saturation value. We relate the origin of this non-monotonicity to the competing effects of particle alignment along the shear-induced direction, on the one ha…
In periodically sheared suspensions there is a dynamical phase transition characterized by a critical strain amplitude $γ_c$ between an absorbing state where particle trajectories are reversible and an active state where trajectories are chaotic and diffusive. Repulsive non-hydrodynamic interactions between "colliding" particles' surfaces have been proposed as a source of this broken time reversal symmetry. A simple toy model called Random Organization qualitatively reproduces the dynamical features of this transition. Random Organization and other absorbing state models exhibit hyperuniformit…
Stabilizing defects in liquid-crystal systems is crucial for many physical processes and applications ranging from functionalizing liquid-crystal textures to recently reported command of chaotic behaviors of active matters. In this work, we perform analytical calculations to study the curvature driven stability mechanism of defects based on the isotropic nematic disk model that is free of any topological constraint. We show that in a growing spherical disk covering a sphere the accumulation of curvature effect can prevent typical +1 and +1/2 defects from forming boojum textures where the defec…
Using non-equilibrium molecular dynamics simulations, we study the rheology of a model hybrid mixture of liquid crystals (LCs) and dipolar soft spheres (DSS) representing magnetic nanoparticles. The bulk isotropic LC-DSS mixture is sheared with different shear rates using Lees-Edwards periodic boundary conditions. The steady-state rheological properties and the effect of the shear on the microstructure of the mixture are studied for different strengths of the dipolar coupling, $λ$, among the DSS. We find that at large shear rates, the mixture shows a shear-thinning behavior for all considered …
Through experiments, we studied defect turbulence, a type of spatiotemporal chaos in planar systems of nematic liquid crystals, to clarify the chaotic advection of weak turbulence. In planar systems of large aspect ratio, structural relaxation which is characterized by the dynamic structure factor exhibits a long-period oscillation that is described well by a combination of a simple exponential relaxation and underdamped oscillation. The simple relaxation arises as a result of the roll modulation while the damped oscillation is manifest in the repetitive gliding of defect pairs in a local area…
Dynamics of small particles, both living such as swimming bacteria and inanimate, such as colloidal spheres, has fascinated scientists for centuries. If one could learn how to control and streamline their chaotic motion, that would open technological opportunities in areas such as the transformation of stored or environmental energy into systematic motion, micro-robotics, and transport of matter at the microscale. This overview presents an approach to command microscale dynamics by replacing an isotropic medium such as water with an anisotropic fluid, a nematic liquid crystal. Orientational or…
In vitro epithelial monolayers exhibit a rich repertoire of collective dynamical behaviours according to microenvironment mechanical features. We investigate the statistical and dynamical properties of human bronchial epithelial cell (HBEC) flows in bulk, by analysing their large length-scale and long time-scale spatiotemporal dynamics. Activity-driven spontaneous collective flows consist of an ensemble of vortices randomly positioned in space. By analysing a large population of vortices, we show that their area follows an exponential law with a constant mean value and their rotational frequen…
Active matter exhibits remarkable collective behavior in which flows, continuously generated by active particles, are intertwined with the orientational order of these particles. The relationship remains poorly understood as the activity and order are difficult to control independently. Here we demonstrate important facets of this interplay by exploring dynamics of swimming bacteria in a liquid crystalline environment with pre-designed periodic splay and bend in molecular orientation. The bacteria are expelled from the bend regions and condense into polar jets that propagate and transport carg…
We numerically study the dynamics of quasi-two dimensional cholesteric liquid crystal droplets in the presence of a time-dependent electric field, rotating at constant angular velocity. A surfactant sitting at droplet interface is also introduced to prevent droplet coalescence. The dynamics is modeled following a hybrid numerical approach, where a standard lattice Boltzmann technique solves the Navier-Stokes equation and a finite difference scheme integrates the evolution equations of liquid crystal and surfactant. Our results show that, once the field is turned on, the liquid crystal rotates …
