Statistical mechanics provides the foundation for describing complex materials using only a few thermodynamic variables. No such framework currently exists far from equilibrium. In this Letter, we demonstrate how thermodynamics emerges far from equilibrium, using fluids composed of active spinners as a case study. Activity gives rise to a single effective temperature that parameterizes both the equation of state and the emergent Boltzmann statistics. The same effective temperature, renormalized by velocity correlations, controls the linear response through canonical Green-Kubo relations for both the familiar shear viscosity and the odd (or Hall) viscosity observed in chiral fluids. The full frequency dependence of these viscosities can be derived analytically by modeling the active-spinner fluid as a random walker undergoing cyclotron motion in shear-stress space. More generally, we provide a first-principles derivation of the Green-Kubo relations valid for a broader class of fluids far from equilibrium. Besides advancing non-equilibrium thermodynamics, our work demonstrates in silico a non-invasive microrheology of active fluids.
Diffusion is a fundamental aspect of transport processes in biological systems, and thus, in the development of life itself. And yet, the diffusive dynamics of active fluids with directed rotation, known as chiral fluids, has not been analyzed in detail so far. Here, we describe the diffusive regimes of a two-dimensional chiral fluid, composed in this case of a set of identical disk-shaped rotors. We found strong experimental evidence of odd diffusion. This odd diffusion emerges in the form of a two-dimensional tensor with an antisymmetric part. In particular, we show that chiral diffusion is …
We examine the motion of a probe particle driven through a chiral fluid composed of circularly swimming disks. We find that the probe particle travels in both the longitudinal direction, parallel to the driving force, and in the transverse direction, perpendicular to the driving force, giving rise to a Hall angle. Under constant driving force, we show that the probe particle velocity in both the longitudinal and transverse directions exhibits nonmonotonic behavior as a function of the activity of the circle swimmers. The Hall angle is maximized when a resonance occurs between the frequency of …
Phase separation in a chiral active fluid of inertial self-spinning disks
Dipartimento di Fisica, Università degli studi di Bari（巴里大学物理系）；INFN, Sezione di Bari（意大利国家核物理研究所巴里分部）；Universitat de Barcelona Institute of Complex Systems (UBICS)（巴塞罗那大学复杂系统研究所）；Departament de Física de la Matèria Condensada, Universitat de Barcelona（巴塞罗那大学凝聚态物理系）；Universidad de Extremadura（埃斯特雷马杜拉大学）
Equation of state for the edge flow of chiral colloidal fluids
Massachusetts Institute of Technology（麻省理工学院）；Université Paris Cité & CNRS (UMR 7057)（巴黎西岱大学及法国国家科学研究中心）；Entalpic（恩塔尔皮克公司）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）
Reversal of tracer advection and Hall drift in an interacting chiral fluid
University of Potsdam（波茨坦大学）；Leibniz-Institute for Polymer Research（莱布尼茨聚合物研究所）；Technical University of Dresden（德累斯顿工业大学）；Asia Pacific Centre for Theoretical Physics（亚太理论物理中心）；University of Augsburg（奥格斯堡大学）
Chiral active fluids are materials composed of self-spinning rotors that continuously inject energy and angular momentum at the microscale. Out-of-equilibrium fluids with active-rotor constituents have been experimentally realized using nanoscale biomolecular motors, microscale active colloids, or macroscale driven chiral grains. Here, we show how such chiral active fluids break both parity and time-reversal symmetries in their steady states, giving rise to a dissipationless linear-response coefficient called odd viscosity in their constitutive relations. Odd viscosity couples pressure and vor…
We conceived a model experiment for a continuous separation strategy of chiral molecules (enantiomers) without the need of any chiral selector structure or derivatization agents: Micro-particles that only differ by their chirality are shown to migrate along different directions when driven by a steady fluid flow through a square lattice of cylindrical posts. In accordance with our numerical predictions, the transport directions of the enantiomers depend very sensitively on the orientation of the lattice relatively to the fluid flow.
The equations of hydrodynamics including mass, linear momentum, angular momentum, and energy are derived by coarse-graining the microscopic equations of motion for systems consisting of rotary dumbbells driven by internal torques.
Active hydrodynamic theories are a powerful tool to study the emergent ordered phases of internally driven particles such as bird flocks, bacterial suspension and their artificial analogues. While theories of orientationally ordered phases are by now well established, the effect of chirality on these phases is much less studied. In this paper, we present the first complete dynamical theory of orientationally ordered chiral particles in two-dimensional incompressible systems. We show that phase-coherent states of rotating chiral particles are remarkably stable in both momentum-conserved and non…
In this article, we review the progress made on the statistical mechanics of liquids and fluids embedded in curved space. Our main focus will be on two-dimensional manifolds of constant nonzero curvature and on the influence of the latter on the phase behavior, thermodynamics and structure of simple liquids. Reference will also be made to existing work on three-dimensional curved space and two-dimensional manifolds with varying curvature.
Chiral active matter is enjoying a rapid increase of interest, spurred by the rich variety of asymmetries that can be attained in e.g. the shape or self-propulsion mechanism of active particles. Though this has already led to the observance of so-called chiral crystals, active chiral glasses remain largely unexplored. A possible reason for this could be the naive expectation that interactions dominate the glassy dynamics and the details of the active motion become increasingly less relevant. Here we show that quite the opposite is true by studying the glassy dynamics of interacting chiral acti…
Large density fluctuations observed in active systems and hyperuniformity are two seemingly incompatible phenomena. However, the formation of hyperuniform states has been recently predicted in non-equilibrium fluids formed by chiral particles performing circular motion with the same handedness. Here we report evidence of hyperuniformity realized in a chiral active fluid comprised of pear-shaped Quincke rollers of arbitrary handedness. We show that hyperuniformity and large density fluctuations, triggered by dynamic clustering, coexist in this system at different length scales. The system loses…
An active colloidal fluid comprised of self-propelled spinning particles injecting energy and angular momentum at the microscale demonstrates spontaneous collective states that range from flocks to coherent vortices. Despite their seeming simplicity, the emergent far-from-equilibrium behavior of these fluids remains poorly understood, presenting a challenge to the design and control of next-generation active materials. When confined in a ring, such so-called polar active fluids acquire chirality once the spontaneous flow chooses a direction. In a perfect ring, this chirality is indefinitely lo…
The success of spectroscopy to characterise equilibrium fluids, for example the heat capacity ratio, suggests a parallel approach for active fluids. Here, we start from a hydrodynamic description of chiral active fluids composed of spinning constituents and derive their low-frequency, long-wavelength response functions using the Kadanoff-Martin formalism. We find that the presence of odd (equivalently, Hall) viscosity leads to mixed density-vorticity response even at linear order. Such response, prohibited in time-reversal-invariant fluids, is a large-scale manifestation of the microscopic bre…
Thinning-by-spinning: shear rheology of dense chiral fluids
Università degli Studi di Bari（巴里大学）；INFN, Sezione di Bari（意大利国家核物理研究所巴里分部）；Universitat de Barcelona（巴塞罗那大学）；University of Barcelona Institute of Complex Systems（巴塞罗那复杂系统研究所）；University of Edinburgh（爱丁堡大学）
In simple fluids, such as water, invariance under parity and time-reversal symmetry imposes that the rotation of constituent 'atoms' are determined by the flow and that viscous stresses damp motion. Activation of the rotational degrees of freedom of a fluid by spinning its atomic building blocks breaks these constraints and has thus been the subject of fundamental theoretical interest across classical and quantum fluids. However, the creation of a model liquid which isolates chiral hydrodynamic phenomena has remained experimentally elusive. Here we report the creation of a cohesive two-dimensi…
We perform experiments on an active chiral fluid system of self-spinning rotors in confining boundary. Along the boundary, actively rotating rotors collectively drives a unidirectional material flow. We systematically vary rotor density and boundary shape; boundary flow robustly emerges under all conditions. Flow strength initially increases then decreases with rotor density (quantified by area fraction $ϕ$); peak strength appears around a density $ϕ=0.65$. Boundary curvature plays an important role: flow near a concave boundary is stronger than that near a flat or convex boundary in the same …
City College of the City University of New York（纽约市立大学城市学院）；The Pennsylvania State University（宾夕法尼亚州立大学）；Western Washington University（西华盛顿大学）；Graduate Center of City University of New York（纽约市立大学研究生中心）
Elasticity-Driven Periodic Polarization Patterns in Confined Chiral Ferroelectric Nematic Fluid
Jožef Stefan Institute（约瑟夫·斯特凡研究所）；Faculty of Mathematics and Physics, University of Ljubljana（卢布尔雅那大学数学与物理学院）；CENN Nanocenter（CENN纳米中心）；Department of Physics, Faculty of Science and Technology, University of the Basque Country UPV/EHU（巴斯克国立大学理学院物理系）；School of Chemistry, University of Leeds（利兹大学化学学院）；School of Physics and Astronomy, University of Leeds（利兹大学物理与天文学院）
Prior studies have revealed that nonzero odd viscosity is an essential property for chiral active fluids. Here we report that such an odd viscosity also exists in suspensions of non-active or non-externally-driven but chirally-shaped particles. Computational simulations are carried out for monolayers of dense ratchets in simple shear and planar extensional flows. The contact between two ratchets can be either frictionless or infinitely-frictional, depending on their teeth and sliding directions at the contact point. Our results show that the ratchet suspension has the intermediate shear/extens…
We carry out Monte Carlo simulations of a colloidal fluid membrane composed of chiral rod-like viruses. The membrane is modeled by a triangular mesh of beads connected by bonds in which the bonds and beads are free to move at each Monte Carlo step. Since the constituent viruses are experimentally observed to twist only near the membrane edge, we use an effective energy that favors a particular sign of the geodesic torsion of the edge. The effective energy also includes membrane bending stiffness, edge bending stiffness, and edge tension. We find three classes of membrane shapes resulting from …
Colloidal particles trapped at an interface between two fluids can form a wide range of different structures. Replacing one of the fluid with a liquid crystal increases the complexity of interactions and results in a greater range of possible structures. New behaviour emerges when colloidal particles interact with defects in the liquid crystal phases. Here we discuss the templating of colloids at a cholesteric isotropic interface.
Active fluids are a class of non-equilibrium systems where energy is injected into the system continuously by the constituent particles themselves. Many examples, such as bacterial suspensions and actomyosin networks, are intrinsically chiral at a local scale, so that their activity involves torque dipoles alongside the force dipoles usually considered. Although many aspects of active fluids have been studied, the effects of chirality on them are much less known. Here we study by computer simulation the dynamics of an unstructured droplet of chiral active fluid in three dimensions. Our model o…
Arnold showed that the Euler equations of an ideal fluid describe geodesics in the Lie algebra of incompressible vector fields. We will show that helicity induces a splitting of the Lie algebra into two isotropic subspaces, forming a Manin triple. Viewed another way, this shows that there is an infinitesimal quantum group (a.k.a. Lie bi-algebra) underlying classical fluid mechanics.
Plants live in constantly moving fluid, whether air or water. In response to the loads associated with fluid motion, plants bend and twist, often with great amplitude. These large deformations are not found in traditional engineering application and thus necessitate new specialised scientific developments. Studying Fluid-Structure Interactions (FSI) in botany, forestry and agricultural science is crucial to the optimisation of biomass production for food, energy, and construction materials. FSI are also central in the study of the ecological adaptation of plants to their environment. This revi…
We study the equilibrium conformations of a lipid domain on a planar fluid membrane where the domain is decorated by a vector field representing the tilt of the stiff fatty acid chains of the lipid molecules, while the surrounding membrane is fluid and structureless. The inclusion of chirality in the bulk of the domain induces a novel budding of the membrane, which preempts the budding induced by a decrease in interfacial tension.
Analytical response functions for a compressible thin fluid layer with odd viscosity
The Open University（开放大学）；Max Planck Institute for Dynamics and Self-Organization (MPI–DS)（马克斯·普朗克动力学与自组织研究所）；Kyoto University（京都大学）；Wenzhou Institute, University of Chinese Academy of Sciences（中国科学院大学温州研究院）
