1
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Yu H, Jack RL. Competition between lanes and transient jammed clusters in driven binary mixtures. Phys Rev E 2024; 109:024123. [PMID: 38491710 DOI: 10.1103/physreve.109.024123] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/31/2023] [Accepted: 01/23/2024] [Indexed: 03/18/2024]
Abstract
We consider mixtures of oppositely driven particles, showing that their nonequilibrium steady states form lanes parallel to the drive, which coexist with transient jammed clusters where particles are temporarily immobilized. We analyze the interplay between these two types of nonequilibrium pattern formation, including their implications for macroscopic demixing perpendicular to the drive. Finite-size scaling analysis indicates that there is no critical driving force associated with demixing, which appears as a crossover in finite systems. We attribute this effect to the disruption of long-ranged order by the transient jammed clusters.
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Affiliation(s)
- Honghao Yu
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Robert L Jack
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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2
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Qian D, Olvera de la Cruz M. Field-driven cluster formation in two-dimensional colloidal binary mixtures. Phys Rev E 2023; 107:044605. [PMID: 37198853 DOI: 10.1103/physreve.107.044605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2022] [Accepted: 03/22/2023] [Indexed: 05/19/2023]
Abstract
We study size- and charge-asymmetric oppositely charged colloids driven by an external electric field. The large particles are connected by harmonic springs, forming a hexagonal-lattice network, while the small particles are free of bonds and exhibit fluidlike motion. We show that this model exhibits a cluster formation pattern when the external driving force exceeds a critical value. The clustering is accompanied with stable wave packets in vibrational motions of the large particles.
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Affiliation(s)
- Dingwen Qian
- Applied Physics Program, Northwestern University, Evanston, Illinois 60208, USA
| | - Monica Olvera de la Cruz
- Applied Physics Program, Department of Materials Science and Engineering, Department of Chemistry, and Department of Physic and Astronomy, Northwestern University, Evanston, Illinois 60208, USA
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3
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Yu H, Thijssen K, Jack RL. Perpendicular and parallel phase separation in two-species driven diffusive lattice gases. Phys Rev E 2022; 106:024129. [PMID: 36110007 DOI: 10.1103/physreve.106.024129] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2022] [Accepted: 08/01/2022] [Indexed: 06/15/2023]
Abstract
We study three different lattice models in which two species of diffusing particles are driven in opposite directions by an electric field. We focus on dynamical phase transitions that involve phase separation into domains that may be parallel or perpendicular to a driving field. In all cases, the perpendicular state appears for weak driving, consistent with previous work. For strong driving, we introduce two models that support the parallel state. In one model, this state occurs because of the inclusion of dynamical rules that enhance lateral diffusion during collisions; in the other, it is a result of a nearest-neighbor attractive or repulsive interaction between particles of the same or opposite species. We discuss the connections between these results and the behavior found in off-lattice systems, including laning and freezing by heating.
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Affiliation(s)
- Honghao Yu
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Kristian Thijssen
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Robert L Jack
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
- Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom
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4
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Vater T, Isele M, Siems U, Nielaba P. Lane and band formation of oppositely driven colloidal particles in two-dimensional ring geometries. Phys Rev E 2022; 106:024606. [PMID: 36109916 DOI: 10.1103/physreve.106.024606] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/08/2022] [Accepted: 07/18/2022] [Indexed: 06/15/2023]
Abstract
We study the segregation phenomena for oppositely driven colloidal particles in two-dimensional ring geometries by means of Brownian dynamics simulations without hydrodynamic interactions. The particles interact via a repulsive Yukawa potential and are confined to a two-dimensional circular channel by hard walls, in which half of the particles are driven clockwise and the other half are driven counterclockwise. In addition to lane formation, which is commonly found in oppositely driven systems, we found band formation along the angular direction in channels with a very large radius. This indicates that a formation of lanes is prevented in the limit of channels with an infinitely large inner radius. The dependency of this segregation has been examined for the two control parameters, the interaction strength between the particles and the width of the circular channel.
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Affiliation(s)
- Tobias Vater
- Physics Department, University of Konstanz, 78467 Konstanz, Germany
| | - Marc Isele
- Physics Department, University of Konstanz, 78467 Konstanz, Germany
| | - Ullrich Siems
- Physics Department, University of Konstanz, 78467 Konstanz, Germany
| | - Peter Nielaba
- Physics Department, University of Konstanz, 78467 Konstanz, Germany
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5
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Stochastic Density Functional Theory on Lane Formation in Electric-Field-Driven Ionic Mixtures: Flow-Kernel-Based Formulation. ENTROPY 2022; 24:e24040500. [PMID: 35455163 PMCID: PMC9028018 DOI: 10.3390/e24040500] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 01/21/2022] [Revised: 03/28/2022] [Accepted: 03/28/2022] [Indexed: 12/04/2022]
Abstract
Simulation and experimental studies have demonstrated non-equilibrium ordering in driven colloidal suspensions: with increasing driving force, a uniform colloidal mixture transforms into a locally demixed state characterized by the lane formation or the emergence of strongly anisotropic stripe-like domains. Theoretically, we have found that a linear stability analysis of density dynamics can explain the non-equilibrium ordering by adding a non-trivial advection term. This advection arises from fluctuating flows due to non-Coulombic interactions associated with oppositely driven migrations. Recent studies based on the dynamical density functional theory (DFT) without multiplicative noise have introduced the flow kernel for providing a general description of the fluctuating velocity. Here, we assess and extend the above deterministic DFT by treating electric-field-driven binary ionic mixtures as the primitive model. First, we develop the stochastic DFT with multiplicative noise for the laning phenomena. The stochastic DFT considering the fluctuating flows allows us to determine correlation functions in a steady state. In particular, asymptotic analysis on the stationary charge-charge correlation function reveals that the above dispersion relation for linear stability analysis is equivalent to the pole equation for determining the oscillatory wavelength of charge–charge correlations. Next, the appearance of stripe-like domains is demonstrated not only by using the pole equation but also by performing the 2D inverse Fourier transform of the charge–charge correlation function without the premise of anisotropic homogeneity in the electric field direction.
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6
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Samsuzzaman M, Sayeed A, Saha A. Reentrant melting of lanes of rough circular disks. Phys Rev E 2022; 105:024608. [PMID: 35291112 DOI: 10.1103/physreve.105.024608] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2021] [Accepted: 02/04/2022] [Indexed: 06/14/2023]
Abstract
We consider binary suspension of rough, circular particles in two dimensions under athermal conditions. The suspension is subject to a time-independent external drive in response to which half of the particles are pulled along the field direction, whereas the other half is pushed in the opposite direction. Simulating the system with different magnitude of external drive in steady state, we obtain oppositely moving macroscopic lanes only for a moderate range of external drive. Below as well as above the range we obtain states with no lane. Hence we find that the no-lane state reenters along the axis of the external drive in the nonequilibrium phase diagram corresponding to the laning transition, with varying roughness of individual particles and external drive. Interparticle friction (contact dissipation) due to the roughness of the individual particle is the main player behind the reentrance of the no-lane state at high external drives.
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Affiliation(s)
- Md Samsuzzaman
- Department of Physics, Savitribai Phule Pune University, Pune 411007, India
| | - Ahmed Sayeed
- Department of Physics, Savitribai Phule Pune University, Pune 411007, India
| | - Arnab Saha
- Department of Physics, University Of Calcutta, 92 Acharya Prafulla Chandra Road, Kolkata-700009, India
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7
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Li B, Wang YL, Shi G, Gao Y, Shi X, Woodward CE, Forsman J. Phase Transitions of Oppositely Charged Colloidal Particles Driven by Alternating Current Electric Field. ACS NANO 2021; 15:2363-2373. [PMID: 33576616 PMCID: PMC8023798 DOI: 10.1021/acsnano.0c04095] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/02/2023]
Abstract
We study systems containing oppositely charged colloidal particles under applied alternating current electric fields (AC fields) using overdamped Langevin dynamics simulations in three dimensions. We obtain jammed bands perpendicular to the field direction under intermediate frequencies and lanes parallel with the field under low frequencies. These structures also depend upon the particle charges. The pathway for generating jammed bands follows a stepwise mechanism, and intermediate bands are observed during lane formation in some systems. We investigate the component of the pressure tensors in the direction parallel to the field and observe that the jammed to lane transition occurs at a critical value for this pressure. We also find that the stable steady states appear to satisfy the principle of maximum entropy production. Our results may help to improve the understand of the underlying mechanisms for these types of dynamic phase transitions and the subsequent cooperative assemblies of colloidal particles under such non-equilibrium conditions.
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Affiliation(s)
- Bin Li
- Laboratory
of Theoretical and Computational Nanoscience, CAS Key Laboratory for
Nanosystem and Hierarchy Fabrication, CAS Center for Excellence in
Nanoscience, National Center for Nanoscience and Technology, Chinese Academy of Sciences, Beijing 100190, China
- Theoretical
Chemistry, Chemical Center, Lund University, P.O. Box 124, S-221 00 Lund, Sweden
- School
of Chemical Engineering and Technology, Sun Yat-sen University, Zhuhai 519082, China
| | - Yong-Lei Wang
- Department
of Materials and Environmental Chemistry, Arrhenius Laboratory, Stockholm University, SE-106 91 Stockholm, Sweden
| | - Guang Shi
- Department
of Chemistry, University of Texas at Austin, Austin, Texas 78712, United States
| | - Yangyang Gao
- Key
Laboratory of Beijing City on Preparation and Processing of Novel
Polymer Materials, Beijing University of
Chemical Technology, Beijing 10029, China
- State Key
Laboratory of Organic−Inorganic Composites, Beijing University of Chemical Technology, Beijing 10029, China
| | - Xinghua Shi
- Laboratory
of Theoretical and Computational Nanoscience, CAS Key Laboratory for
Nanosystem and Hierarchy Fabrication, CAS Center for Excellence in
Nanoscience, National Center for Nanoscience and Technology, Chinese Academy of Sciences, Beijing 100190, China
| | - Clifford E. Woodward
- School
of Physical, Environmental and Mathematical Sciences, University College,
ADFA, University of New South Wales, Canberra, ACT 2600, Australia
| | - Jan Forsman
- Theoretical
Chemistry, Chemical Center, Lund University, P.O. Box 124, S-221 00 Lund, Sweden
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8
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Krinninger P, Schmidt M. Power functional theory for active Brownian particles: General formulation and power sum rules. J Chem Phys 2019; 150:074112. [DOI: 10.1063/1.5061764] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Philip Krinninger
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
| | - Matthias Schmidt
- Theoretische Physik II, Physikalisches Institut, Universität Bayreuth, D-95440 Bayreuth, Germany
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9
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Lüders A, Siems U, Nielaba P. Dynamic ordering of driven spherocylinders in a nonequilibrium suspension of small colloidal spheres. Phys Rev E 2019; 99:022601. [PMID: 30934328 DOI: 10.1103/physreve.99.022601] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/01/2018] [Indexed: 06/09/2023]
Abstract
The ordering effects of driven spherocylinder-shaped rods in a colloidal suspension of small spheres confined to a two-dimensional channel geometry are observed via Brownian dynamics simulations without hydrodynamics. To describe the ordering, an order parameter and an expression for a potential of mean force of an equivalent equilibrium system are defined and analyzed. By varying the application point of the external force along the rods and thus the resulting lever, a transition from a preferred orientation parallel to the direction of the force to a preferred orientation perpendicular to the direction of the force was observed. It is shown that this effect can only be found if the spheres and multiple rods are present. Furthermore, a dependency of the order parameter on the absolute value of the force was discovered. The analysis of the potential of mean force further indicates a transition between two different phases of mean orientation. An observation of the flow equilibrium mean velocity in channel direction led to a s-shaped progression regarding the lever dependency, also marking a transition between two states linked to the mean orientation of the rods. A finite size analysis was conducted. Its results indicate that the transition between the two orientation states is a general phenomenon of the observed rod-sphere mixture.
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Affiliation(s)
- Anton Lüders
- Department of Physics, University of Konstanz, 78457 Konstanz, Germany
| | - Ullrich Siems
- Department of Physics, University of Konstanz, 78457 Konstanz, Germany
| | - Peter Nielaba
- Department of Physics, University of Konstanz, 78457 Konstanz, Germany
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10
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Bénichou O, Illien P, Oshanin G, Sarracino A, Voituriez R. Tracer diffusion in crowded narrow channels. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:443001. [PMID: 30211693 DOI: 10.1088/1361-648x/aae13a] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/08/2023]
Abstract
We summarise different results on the diffusion of a tracer particle in lattice gases of hard-core particles with stochastic dynamics, which are confined to narrow channels-single-files, comb-like structures and quasi-one-dimensional channels with the width equal to several particle diameters. We show that in such geometries a surprisingly rich, sometimes even counter-intuitive, behaviour emerges, which is absent in unbounded systems. This is well-documented for the anomalous diffusion in single-files. Less known is the anomalous dynamics of a tracer particle in crowded branching single-files-comb-like structures, where several kinds of anomalous regimes take place. In narrow channels, which are broader than single-files, one encounters a wealth of anomalous behaviours in the case where the tracer particle is subject to a regular external bias: here, one observes an anomaly in the temporal evolution of the tracer particle velocity, super-diffusive at transient stages, and ultimately a giant diffusive broadening of fluctuations in the position of the tracer particle, as well as spectacular multi-tracer effects of self-clogging of narrow channels. Interactions between a biased tracer particle and a confined crowded environment also produce peculiar patterns in the out-of-equilibrium distribution of the environment particles, very different from the ones appearing in unbounded systems. For moderately dense systems, a surprising effect of a negative differential mobility takes place, such that the velocity of a biased tracer particle can be a non-monotonic function of the force. In some parameter ranges, both the velocity and the diffusion coefficient of a biased tracer particle can be non-monotonic functions of the density. We also survey different results obtained for a tracer particle diffusion in unbounded systems, which will permit a reader to have an exhaustively broad picture of the tracer diffusion in crowded environments.
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Affiliation(s)
- O Bénichou
- Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (UMR 7600), 4 Place Jussieu, 75252 Paris Cedex 05, France
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11
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Reichhardt C, Thibault J, Papanikolaou S, Reichhardt CJO. Laning and clustering transitions in driven binary active matter systems. Phys Rev E 2018; 98:022603. [PMID: 30253470 DOI: 10.1103/physreve.98.022603] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/17/2018] [Indexed: 06/08/2023]
Abstract
It is well known that a binary system of nonactive disks that experience driving in opposite directions exhibits jammed, phase separated, disordered, and laning states. In active matter systems, such as a crowd of pedestrians, driving in opposite directions is common and relevant, especially in conditions which are characterized by high pedestrian density and emergency. In such cases, the transition from laning to disordered states may be associated with the onset of a panic state. We simulate a laning system containing active disks that obey run-and-tumble dynamics, and we measure the drift mobility and structure as a function of run length, disk density, and drift force. The activity of each disk can be quantified based on the correlation timescale of the velocity vector. We find that in some cases, increasing the activity can increase the system mobility by breaking up jammed configurations; however, an activity level that is too high can reduce the mobility by increasing the probability of disk-disk collisions. In the laning state, the increase of activity induces a sharp transition to a disordered strongly fluctuating state with reduced mobility. We identify a novel drive-induced clustered laning state that remains stable even at densities below the activity-induced clustering transition of the undriven system. We map out the dynamic phase diagrams highlighting transitions between the different phases as a function of activity, drive, and density.
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Affiliation(s)
- C Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - J Thibault
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
- Department of Mechanical and Aerospace Engineering, Western Virginia University, Morgantown, West Virginia 26506, USA
| | - S Papanikolaou
- Department of Mechanical and Aerospace Engineering, Western Virginia University, Morgantown, West Virginia 26506, USA
- Department of Physics, Western Virginia University, Morgantown, West Virginia 26506, USA
| | - C J O Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
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12
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Whitelam S, Klymko K, Mandal D. Phase separation and large deviations of lattice active matter. J Chem Phys 2018; 148:154902. [PMID: 29679965 DOI: 10.1063/1.5023403] [Citation(s) in RCA: 32] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Off-lattice active Brownian particles form clusters and undergo phase separation even in the absence of attractions or velocity-alignment mechanisms. Arguments that explain this phenomenon appeal only to the ability of particles to move persistently in a direction that fluctuates, but existing lattice models of hard particles that account for this behavior do not exhibit phase separation. Here we present a lattice model of active matter that exhibits motility-induced phase separation in the absence of velocity alignment. Using direct and rare-event sampling of dynamical trajectories, we show that clustering and phase separation are accompanied by pronounced fluctuations of static and dynamic order parameters. This model provides a complement to off-lattice models for the study of motility-induced phase separation.
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Affiliation(s)
- Stephen Whitelam
- Molecular Foundry, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA
| | - Katherine Klymko
- Department of Chemistry, University of California at Berkeley, Berkeley, California 94720, USA
| | - Dibyendu Mandal
- Department of Physics, University of California at Berkeley, Berkeley, California 94720, USA
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13
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Critical mingling and universal correlations in model binary active liquids. Nat Commun 2017; 8:15969. [PMID: 28656963 PMCID: PMC5493750 DOI: 10.1038/ncomms15969] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2017] [Accepted: 05/15/2017] [Indexed: 11/12/2022] Open
Abstract
Ensembles of driven or motile bodies moving along opposite directions are generically reported to self-organize into strongly anisotropic lanes. Here, building on a minimal model of self-propelled bodies targeting opposite directions, we first evidence a critical phase transition between a mingled state and a phase-separated lane state specific to active particles. We then demonstrate that the mingled state displays algebraic structural correlations also found in driven binary mixtures. Finally, constructing a hydrodynamic theory, we single out the physical mechanisms responsible for these universal long-range correlations typical of ensembles of oppositely moving bodies. Self-driven particles can drive the system out of equilibrium without the help of external forces. Here Bain et al. develop a model for two groups of motile bodies targeting opposite directions and show that the system exhibits critical behaviour as a function of particle density.
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14
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Poncet A, Bénichou O, Démery V, Oshanin G. Universal Long Ranged Correlations in Driven Binary Mixtures. PHYSICAL REVIEW LETTERS 2017; 118:118002. [PMID: 28368633 DOI: 10.1103/physrevlett.118.118002] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/06/2016] [Indexed: 06/07/2023]
Abstract
When two populations of "particles" move in opposite directions, like oppositely charged colloids under an electric field or intersecting flows of pedestrians, they can move collectively, forming lanes along their direction of motion. The nature of this "laning transition" is still being debated and, in particular, the pair correlation functions, which are the key observables to quantify this phenomenon, have not been characterized yet. Here, we determine the correlations using an analytical approach based on a linearization of the stochastic equations for the density fields, which is valid for dense systems of soft particles. We find that the correlations decay algebraically along the direction of motion, and have a self-similar exponential profile in the transverse direction. Brownian dynamics simulations confirm our theoretical predictions and show that they also hold beyond the validity range of our analytical approach, pointing to a universal behavior.
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Affiliation(s)
- Alexis Poncet
- Gulliver, CNRS, ESPCI Paris, PSL Research University, 10 rue Vauquelin, 75005 Paris, France
- Département de Physique, ENS, PSL Research University, 24 Rue Lhomond, 75005 Paris, France
| | - Olivier Bénichou
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS/UPMC, 4 Place Jussieu, F-75005 Paris, France
| | - Vincent Démery
- Gulliver, CNRS, ESPCI Paris, PSL Research University, 10 rue Vauquelin, 75005 Paris, France
| | - Gleb Oshanin
- Laboratoire de Physique Théorique de la Matière Condensée, CNRS/UPMC, 4 Place Jussieu, F-75005 Paris, France
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15
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Wächtler CW, Kogler F, Klapp SHL. Lane formation in a driven attractive fluid. Phys Rev E 2016; 94:052603. [PMID: 27967106 DOI: 10.1103/physreve.94.052603] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/15/2016] [Indexed: 05/18/2023]
Abstract
We investigate nonequilibrium lane formation in a generic model of a fluid with attractive interactions, that is, a two-dimensional Lennard-Jones fluid composed of two particle species driven in opposite directions. Performing Brownian dynamics simulations for a wide range of parameters, supplemented by a stability analysis based on dynamical density functional theory, we identify generic features of lane formation in the presence of attraction, including structural properties. In fact, we find a variety of states (as compared to purely repulsive systems), as well as a close relation between laning and long-wavelength instabilities of the homogeneous phase such as demixing and condensation.
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Affiliation(s)
- C W Wächtler
- Institute of Theoretical Physics, Secr. EW 7-1, Technical University Berlin, Hardenbergstraße 36, D-10623 Berlin, Germany
| | - F Kogler
- Institute of Theoretical Physics, Secr. EW 7-1, Technical University Berlin, Hardenbergstraße 36, D-10623 Berlin, Germany
| | - S H L Klapp
- Institute of Theoretical Physics, Secr. EW 7-1, Technical University Berlin, Hardenbergstraße 36, D-10623 Berlin, Germany
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16
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Klymko K, Geissler PL, Whitelam S. Microscopic origin and macroscopic implications of lane formation in mixtures of oppositely driven particles. Phys Rev E 2016; 94:022608. [PMID: 27627361 DOI: 10.1103/physreve.94.022608] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/17/2016] [Indexed: 11/07/2022]
Abstract
Colloidal particles of two types, driven in opposite directions, can segregate into lanes [Vissers et al., Soft Matter 7, 2352 (2011)1744-683X10.1039/c0sm01343a]. This phenomenon can be reproduced by two-dimensional Brownian dynamics simulations of model particles [Dzubiella et al., Phys. Rev. E 65, 021402 (2002)1063-651X10.1103/PhysRevE.65.021402]. Here we use computer simulation to assess the generality of lane formation with respect to variation of particle type and dynamical protocol. We find that laning results from rectification of diffusion on the scale of a particle diameter: oppositely driven particles must, in the time taken to encounter each other in the direction of the drive, diffuse in the perpendicular direction by about one particle diameter. This geometric constraint implies that the diffusion constant of a particle, in the presence of those of the opposite type, grows approximately linearly with the Péclet number, a prediction confirmed by our numerics over a range of model parameters. Such environment-dependent diffusion is statistically similar to an effective interparticle attraction; consistent with this observation, we find that oppositely driven nonattractive colloids display features characteristic of the simplest model system possessing both interparticle attractions and persistent motion, the driven Ising lattice gas [Katz, Leibowitz, and Spohn, J. Stat. Phys. 34, 497 (1984)JSTPBS0022-471510.1007/BF01018556]. These features include long-ranged correlations in the disordered regime, a critical regime characterized by a change in slope of the particle current with the Péclet number, and fluctuations that grow with system size. By analogy, we suggest that lane formation in the driven colloid system is a phase transition in the macroscopic limit, but that macroscopic phase separation would not occur in finite time upon starting from disordered initial conditions.
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Affiliation(s)
- Katherine Klymko
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Phillip L Geissler
- Department of Chemistry, University of California, Berkeley, California 94720, USA.,Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Stephen Whitelam
- Molecular Foundry, Lawrence Berkeley National Laboratory, 1 Cyclotron Road, Berkeley, California 94720, USA
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17
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Kuan HS, Blackwell R, Hough LE, Glaser MA, Betterton MD. Hysteresis, reentrance, and glassy dynamics in systems of self-propelled rods. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:060501. [PMID: 26764616 PMCID: PMC5064941 DOI: 10.1103/physreve.92.060501] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/17/2014] [Indexed: 05/25/2023]
Abstract
Nonequilibrium active matter made up of self-driven particles with short-range repulsive interactions is a useful minimal system to study active matter as the system exhibits collective motion and nonequilibrium order-disorder transitions. We studied high-aspect-ratio self-propelled rods over a wide range of packing fractions and driving to determine the nonequilibrium state diagram and dynamic properties. Flocking and nematic-laning states occupy much of the parameter space. In the flocking state, the average internal pressure is high and structural and mechanical relaxation times are long, suggesting that rods in flocks are in a translating glassy state despite overall flock motion. In contrast, the nematic-laning state shows fluidlike behavior. The flocking state occupies regions of the state diagram at both low and high packing fraction separated by nematic-laning at low driving and a history-dependent region at higher driving; the nematic-laning state transitions to the flocking state for both compression and expansion. We propose that the laning-flocking transitions are a type of glass transition that, in contrast to other glass-forming systems, can show fluidization as density increases. The fluid internal dynamics and ballistic transport of the nematic-laning state may promote collective dynamics of rod-shaped micro-organisms.
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Affiliation(s)
- Hui-Shun Kuan
- Department of Chemistry and Biochemistry, University of Colorado at Boulder, Boulder, Colorado 80302, USA
| | - Robert Blackwell
- Department of Physics, University of Colorado at Boulder, Boulder, Colorado 80302, USA
| | - Loren E Hough
- Department of Physics, University of Colorado at Boulder, Boulder, Colorado 80302, USA
| | - Matthew A Glaser
- Department of Physics, University of Colorado at Boulder, Boulder, Colorado 80302, USA
| | - M D Betterton
- Department of Physics, University of Colorado at Boulder, Boulder, Colorado 80302, USA
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Heinze B, Siems U, Nielaba P. Segregation of oppositely driven colloidal particles in hard-walled channels: A finite-size study. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:012323. [PMID: 26274177 DOI: 10.1103/physreve.92.012323] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/23/2014] [Indexed: 05/18/2023]
Abstract
We investigate segregation phenomena of particles driven in opposite directions with Brownian dynamics simulations. The particles interact via a repulsive potential and are confined in three-dimensional hard-walled pipes with quadratic cross sections. In a systematic finite-size study, the pipe length is varied. Ordering on finite length scales can be observed, but global segregation seems to vanish for infinite channel length, as it was recently found for lane formation in two dimensions. As an additional effect of the finite hard-walled boundary conditions, interface vibrations and longitudinal demixing are found.
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Affiliation(s)
- Birte Heinze
- Physics Department, University of Konstanz, 78467 Konstanz, Germany
| | - Ullrich Siems
- Physics Department, University of Konstanz, 78467 Konstanz, Germany
| | - Peter Nielaba
- Physics Department, University of Konstanz, 78467 Konstanz, Germany
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19
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Vezirov TA, Klapp SHL. Nonequilibrium dynamics of a confined colloidal bilayer in a planar shear flow. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:052307. [PMID: 24329264 DOI: 10.1103/physreve.88.052307] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/27/2013] [Revised: 09/19/2013] [Indexed: 06/03/2023]
Abstract
Using Brownian dynamics (BD) simulations we investigate the impact of shear flow on structural and dynamical properties of a system of charged colloids confined to a narrow slit pore. Our model consists of spherical microions interacting through a Derjaguin-Landau-Verwey-Overbeek (DLVO) and a soft-sphere potential. The DLVO parameters were chosen according to a system of moderately charged silica particles (with valence Z~35) in a solvent of low ionic strength. At the confinement conditions considered, the colloids form two well-pronounced layers. In the present study we investigate shear-induced transitions of the translational order and dynamics in the layers, including a discussion of the translational diffusion. In particular, we show that diffusion in the shear-melted state can be described by an analytical model involving a single shear-driven particle in a harmonic trap. We also explore the emergence of zigzag motion characterized by spatiotemporal oscillations of the particles in the layers in the vorticity direction. Similar behavior has been recently observed in experiments of much thicker colloidal films.
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Affiliation(s)
- Tarlan A Vezirov
- Institut für Theoretische Physik, Hardenbergstr. 36, Technische Universität Berlin, D-10623 Berlin, Germany
| | - Sabine H L Klapp
- Institut für Theoretische Physik, Hardenbergstr. 36, Technische Universität Berlin, D-10623 Berlin, Germany
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20
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Kohl M, Ivlev AV, Brandt P, Morfill GE, Löwen H. Microscopic theory for anisotropic pair correlations in driven binary mixtures. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2012; 24:464115. [PMID: 23114114 DOI: 10.1088/0953-8984/24/46/464115] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/01/2023]
Abstract
A self-consistent microscopic approach to calculate non-equilibrium pair correlations in strongly interacting driven binary mixtures is presented. The theory is derived from the many-body Smoluchowski equation for interacting Brownian particles by employing Kirkwood's superposition approximation as a closure relation. It is shown that the pair correlations can exhibit notable anisotropy and a strong tendency to laning in the driving direction. Furthermore, there are strong indications that pair correlations are characterized by a long-range decay along the drive. The theoretical results are in good quantitative agreement with the complementary Brownian dynamics computer simulations.
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Affiliation(s)
- Matthias Kohl
- Institut für Theoretische Physik II: Weiche Materie, Heinrich-Heine-Universität Düsseldorf, D-40225 Düsseldorf, Germany.
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