1
|
Čopar S, Kos Ž. Many-defect solutions in planar nematics: interactions, spiral textures and boundary conditions. SOFT MATTER 2024; 20:6894-6906. [PMID: 39150404 DOI: 10.1039/d4sm00586d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 08/17/2024]
Abstract
From incompressible flows to electrostatics, harmonic functions can provide solutions to many two-dimensional problems and, similarly, the director field of a planar nematic can be determined using complex analysis. We derive a closed-form solution for a quasi-steady state director field induced by an arbitrarily large set of point defects and circular inclusions with or without fixed rotational degrees of freedom, and compute the forces and torques acting on each defect or inclusion. We show that a complete solution must include two types of singularities, generating a defect winding number and its spiral texture, which have a direct effect on defect equilibrium textures and their dynamics. The solution accounts for discrete degeneracy of topologically distinct free energy minima which can be obtained by defect braiding. The derived formalism can be readily applied to equilibrium and slowly evolving nematic textures for active or passive fluids with multiple defects present within the orientational order.
Collapse
Affiliation(s)
- Simon Čopar
- Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia.
| | - Žiga Kos
- Faculty of Mathematics and Physics, University of Ljubljana, Ljubljana, Slovenia.
- Department of Condensed Matter Physics, Jožef Stefan Institute, Ljubljana, Slovenia
- International Institute for Sustainability with Knotted Chiral Meta Matter (WPI-SKCM2), Hiroshima University, Higashi-Hiroshima, Japan
| |
Collapse
|
2
|
Schimming CD, Reichhardt CJO, Reichhardt C. Active nematic ratchet in asymmetric obstacle arrays. Phys Rev E 2024; 109:064602. [PMID: 39021011 DOI: 10.1103/physreve.109.064602] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2024] [Accepted: 05/03/2024] [Indexed: 07/20/2024]
Abstract
We numerically investigate the effect of an asymmetric periodic obstacle array in a two-dimensional active nematic. We find that activity in conjunction with the asymmetry leads to a ratchet effect or unidirectional flow of the fluid along the asymmetry direction. The directional flow is still present even in the active turbulent phase when the gap between obstacles is sufficiently small. We demonstrate that the dynamics of the topological defects transition from flow mirroring to smectic-like as the gap between obstacles is made smaller, and explain this transition in terms of the pinning of negative winding number defects between obstacles. This also leads to a nonmonotonic ratchet effect magnitude as a function of obstacle size, so that there is an optimal obstacle size for ratcheting at fixed activity.
Collapse
|
3
|
Caballero F, You Z, Marchetti MC. Vorticity phase separation and defect lattices in the isotropic phase of active liquid crystals. SOFT MATTER 2023; 19:7828-7835. [PMID: 37796173 DOI: 10.1039/d3sm00744h] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/06/2023]
Abstract
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.
Collapse
Affiliation(s)
- Fernando Caballero
- Department of Physics, University of California Santa Barbara, Santa Barbara, CA 93106, USA.
| | - Zhihong You
- Fujian Provincial Key Laboratory for Soft Functional Materials Research, Research Institute for Biomimetics and Soft Matter, Department of Physics, Xiamen University, Xiamen, Fujian 361005, China
| | - M Cristina Marchetti
- Department of Physics, University of California Santa Barbara, Santa Barbara, CA 93106, USA.
| |
Collapse
|
4
|
Schimming CD, Reichhardt CJO, Reichhardt C. Friction-mediated phase transition in confined active nematics. Phys Rev E 2023; 108:L012602. [PMID: 37583137 DOI: 10.1103/physreve.108.l012602] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/28/2023] [Accepted: 06/28/2023] [Indexed: 08/17/2023]
Abstract
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.
Collapse
Affiliation(s)
- Cody D Schimming
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C J O Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - C Reichhardt
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| |
Collapse
|
5
|
Zhu X, Luo Y, Liu Y, Wang X, Zhang H, Zhao X. Understanding the Effect of Oil-Based Lubricants on the Tribological Behavior of Fe-Cr Alloys from Reactive Molecular Dynamics. LANGMUIR : THE ACS JOURNAL OF SURFACES AND COLLOIDS 2023; 39:5145-5155. [PMID: 37010490 DOI: 10.1021/acs.langmuir.3c00217] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/19/2023]
Abstract
In this paper, the frictional behaviors of Fe-Cr alloys in the lubricating effect of oil-based lubricant are investigated through reactive molecular dynamics. It is shown that the oil-based lubricant achieves ultralow friction through hydrodynamic lubrication by linear alpha olefin (C8H16) and passivation of the friction pairs by hydrogen gas (H2) and free H atoms generated by the friction chemistry. Moreover, there is a critical value for the transition of the crystal structure of Fe-Cr alloy from body-centered cubic (Bcc) to amorphous structure (Other), leading to a dramatic change in friction. Meanwhile, a sliding interface consisting of a large number of amorphous structures is formed near the rigid layer, which keeps the friction force stable.
Collapse
Affiliation(s)
- Xiaohua Zhu
- School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, China
| | - Yiyao Luo
- School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, China
| | - Yunhai Liu
- School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, China
| | - Xiaowen Wang
- School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, China
| | - Hu Zhang
- School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, China
| | - Xiao Zhao
- Pipechina Guizhou Pipeline Co., Ltd., Guiyang 550081, China
| |
Collapse
|
6
|
Chattopadhyay J, Ramaswamy S, Dasgupta C, Maiti PK. Two-temperature activity induces liquid-crystal phases inaccessible in equilibrium. Phys Rev E 2023; 107:024701. [PMID: 36932588 DOI: 10.1103/physreve.107.024701] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/29/2022] [Accepted: 01/17/2023] [Indexed: 02/08/2023]
Abstract
In equilibrium hard-rod fluids, and in effective hard-rod descriptions of anisotropic soft-particle systems, the transition from the isotropic (I) phase to the nematic phase (N) is observed above the rod aspect ratio L/D=3.70 as predicted by Onsager. We examine the fate of this criterion in a molecular dynamics study of a system of soft repulsive spherocylinders rendered active by coupling half the particles to a heat bath at a higher temperature than that imposed on the other half. We show that the system phase-separates and self-organizes into various liquid-crystalline phases that are not observed in equilibrium for the respective aspect ratios. In particular, we find a nematic phase for L/D=3 and a smectic phase for L/D=2 above a critical activity.
Collapse
Affiliation(s)
- Jayeeta Chattopadhyay
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Sriram Ramaswamy
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Chandan Dasgupta
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| | - Prabal K Maiti
- Centre for Condensed Matter Theory, Department of Physics, Indian Institute of Science, Bangalore 560012, India
| |
Collapse
|
7
|
Ascione F, Caserta S, Esposito S, Villella VR, Maiuri L, Nejad MR, Doostmohammadi A, Yeomans JM, Guido S. Collective rotational motion of freely expanding T84 epithelial cell colonies. J R Soc Interface 2023; 20:20220719. [PMID: 36872917 PMCID: PMC9943890 DOI: 10.1098/rsif.2022.0719] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/30/2022] [Accepted: 01/23/2023] [Indexed: 02/25/2023] Open
Abstract
Coordinated rotational motion is an intriguing, yet still elusive mode of collective cell migration, which is relevant in pathological and morphogenetic processes. Most of the studies on this topic have been carried out on epithelial cells plated on micropatterned substrates, where cell motion is confined in regions of well-defined shapes coated with extracellular matrix adhesive proteins. The driver of collective rotation in such conditions has not been clearly elucidated, although it has been speculated that spatial confinement can play an essential role in triggering cell rotation. Here, we study the growth of epithelial cell colonies freely expanding (i.e. with no physical constraints) on the surface of cell culture plates and focus on collective cell rotation in such conditions, a case which has received scarce attention in the literature. One of the main findings of our work is that coordinated cell rotation spontaneously occurs in cell clusters in the free growth regime, thus implying that cell confinement is not necessary to elicit collective rotation as previously suggested. The extent of collective rotation was size and shape dependent: a highly coordinated disc-like rotation was found in small cell clusters with a round shape, while collective rotation was suppressed in large irregular cell clusters generated by merging of different clusters in the course of their growth. The angular motion was persistent in the same direction, although clockwise and anticlockwise rotations were equally likely to occur among different cell clusters. Radial cell velocity was quite low as compared to the angular velocity, in agreement with the free expansion regime where cluster growth is essentially governed by cell proliferation. A clear difference in morphology was observed between cells at the periphery and the ones in the core of the clusters, the former being more elongated and spread out as compared to the latter. Overall, our results, to our knowledge, provide the first quantitative and systematic evidence that coordinated cell rotation does not require a spatial confinement and occurs spontaneously in freely expanding epithelial cell colonies, possibly as a mechanism for the system.
Collapse
Affiliation(s)
- Flora Ascione
- Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale (DICMAPI), Università di Napoli Federico II, P.le Tecchio 80, 80125 Napoli, Italy
| | - Sergio Caserta
- Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale (DICMAPI), Università di Napoli Federico II, P.le Tecchio 80, 80125 Napoli, Italy
- CEINGE Biotecnologie Avanzate, Via Sergio Pansini 5, 80131 Naples, Italy
| | - Speranza Esposito
- Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale (DICMAPI), Università di Napoli Federico II, P.le Tecchio 80, 80125 Napoli, Italy
- European Institute for Research in Cystic Fibrosis, San Raffaele Scientific Institute, Milan, Italy
| | - Valeria Rachela Villella
- Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale (DICMAPI), Università di Napoli Federico II, P.le Tecchio 80, 80125 Napoli, Italy
- European Institute for Research in Cystic Fibrosis, San Raffaele Scientific Institute, Milan, Italy
| | - Luigi Maiuri
- European Institute for Research in Cystic Fibrosis, San Raffaele Scientific Institute, Milan, Italy
| | - Mehrana R. Nejad
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
| | | | - Julia M. Yeomans
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, UK
| | - Stefano Guido
- Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale (DICMAPI), Università di Napoli Federico II, P.le Tecchio 80, 80125 Napoli, Italy
- CEINGE Biotecnologie Avanzate, Via Sergio Pansini 5, 80131 Naples, Italy
| |
Collapse
|
8
|
Vafa F. Defect dynamics in active polar fluids vs. active nematics. SOFT MATTER 2022; 18:8087-8097. [PMID: 36239265 DOI: 10.1039/d2sm00830k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/16/2023]
Abstract
Topological defects play a key role in two-dimensional active nematics, and a transient role in two-dimensional active polar fluids. Using a variational method, we study both the transient and long-time behavior of defects in two-dimensional active polar fluids in the limit of strong order and overdamped, compressible flow, and compare the defect dynamics with the corresponding active nematics model studied recently. One result is non-central interactions between defect pairs for active polar fluids, and by extending our analysis to allow orientation dynamics of defects, we find that the orientation of +1 defects, unlike that of ±1/2 defects in active nematics, is not locked to defect positions and relaxes to asters. Moreover, using a scaling argument, we explain the transient feature of active polar defects and show that in the steady state, active polar fluids are either devoid of defects or consist of a single aster. We argue that for contractile (extensile) active nematic systems, +1 vortices (asters) should emerge as bound states of a pair of +1/2 defects, which has been recently observed. Moreover, unlike the polar case, we show that for active nematics, a linear chain of equally spaced bound states of pairs of +1/2 defects can screen the activity term. A common feature in both models is the appearance of +1 defects (elementary in polar and composite in nematic) in the steady state.
Collapse
Affiliation(s)
- Farzan Vafa
- Center of Mathematical Sciences and Applications, Harvard University, Cambridge, MA 02138, USA.
| |
Collapse
|
9
|
Li ZY, Zhang DQ, Lin SZ, Góźdź WT, Li B. Spontaneous organization and phase separation of skyrmions in chiral active matter. SOFT MATTER 2022; 18:7348-7359. [PMID: 36124977 DOI: 10.1039/d2sm00819j] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
Skyrmions are topologically protected vortex-like excitations that hold promise for applications such as information processing and electron manipulation. Here we combine theoretical analysis and numerical simulations to show that skyrmions can spontaneously emerge in chiral active matter without external confinements or regulation. Strikingly, these activity-driven skyrmions can either self-organize into a periodic, stable square lattice consisting of half Néel skyrmions and antiskyrmions, where the in-plane flows display an antiferromagnetic vortex array, or undergo phase separation between skyrmions with different topological numbers. We identify that the emerging skyrmion dynamics stems from the competition between the chiral and polar coherence length scales dictated by the interplay of intrinsic chirality, polarity, and elasticity in the system. Our results reveal unanticipated topological excitations, self-organization, and phase separation in non-equilibrium systems and also suggest a potential way towards engineering complicated bespoke skyrmionic structures through manipulating active matter.
Collapse
Affiliation(s)
- Zhong-Yi Li
- Institute of Biomechanics and Medical Engineering, Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China.
| | - De-Qing Zhang
- Institute of Biomechanics and Medical Engineering, Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China.
| | - Shao-Zhen Lin
- Aix Marseille Université, CNRS, Centre de Physique Théorique, Turing Center for Living Systems, 13009 Marseille, France
| | - Wojciech T Góźdź
- Institute of Physical Chemistry, Polish Academy of Sciences, Kasprzaka 44/52, 01-224 Warsaw, Poland
| | - Bo Li
- Institute of Biomechanics and Medical Engineering, Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China.
| |
Collapse
|
10
|
Bonn L, Ardaševa A, Mueller R, Shendruk TN, Doostmohammadi A. Fluctuation-induced dynamics of nematic topological defects. Phys Rev E 2022; 106:044706. [PMID: 36397561 DOI: 10.1103/physreve.106.044706] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2022] [Accepted: 09/29/2022] [Indexed: 06/16/2023]
Abstract
Topological defects are increasingly being identified in various biological systems, where their characteristic flow fields and stress patterns are associated with continuous active stress generation by biological entities. Here, using numerical simulations of continuum fluctuating nematohydrodynamics, we show that even in the absence of any specific form of active stresses associated with self-propulsion, mesoscopic fluctuations in either orientational alignment or hydrodynamics can independently result in flow patterns around topological defects that resemble the ones observed in active systems. Our simulations further show the possibility of extensile- and contractile-like motion of fluctuation-induced positive half-integer topological defects. Remarkably, isotropic stress fields also reproduce the experimentally measured stress patterns around topological defects in epithelia. Our findings further reveal that extensile- or contractile-like flow and stress patterns around fluctuation-induced defects are governed by passive elastic stresses and flow-aligning behavior of the nematics.
Collapse
Affiliation(s)
- Lasse Bonn
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen 2100, Denmark
| | - Aleksandra Ardaševa
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen 2100, Denmark
| | - Romain Mueller
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Tyler N Shendruk
- School of Physics and Astronomy, University of Edinburgh, Peter Guthrie Tait Road, Edinburgh EH9 3FD, United Kingdom
| | - Amin Doostmohammadi
- Niels Bohr Institute, University of Copenhagen, Blegdamsvej 17, Copenhagen 2100, Denmark
| |
Collapse
|
11
|
Sultan SA, R Nejad M, Doostmohammadi A. Quadrupolar active stress induces exotic patterns of defect motion in compressible active nematics. SOFT MATTER 2022; 18:4118-4126. [PMID: 35579323 DOI: 10.1039/d1sm01683k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/15/2023]
Abstract
A wide range of living and artificial active matter exists in close contact with substrates and under strong confinement, where in addition to dipolar active stresses, quadrupolar active stresses can become important. Here, we numerically investigate the impact of quadrupolar non-equilibrium stresses on the emergent patterns of self-organisation in non-momentum conserving active nematics. Our results reveal that beyond having stabilising effects, the quadrupolar active forces can induce various modes of topological defect motion in active nematics. In particular, we find the emergence of both polar and nematic ordering of the defects, as well as new patterns of self-organisation that comprise topological defect chains and transient topological defect asters. The results contribute to further understanding of emergent patterns of collective motion and non-equilibrium self-organisation in active matter.
Collapse
Affiliation(s)
- Salik A Sultan
- The Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark.
| | - Mehrana R Nejad
- Rudolf Peierls Centre for Theoretical Physics, University of Oxford, UK
| | | |
Collapse
|
12
|
Zhang DQ, Li ZY, Li B. Self-rotation regulates interface evolution in biphasic active matter through taming defect dynamics. Phys Rev E 2022; 105:064607. [PMID: 35854599 DOI: 10.1103/physreve.105.064607] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2022] [Accepted: 05/27/2022] [Indexed: 06/15/2023]
Abstract
Chirality can endow nonequilibrium active matter with unique features and functions. Here, we explore the chiral dynamics in biphasic active nematics composed of self-rotating units that continuously inject energy and angular momentum at the microscale. We show that the self-rotation of units can regularize the boundaries between two phases, rendering sinusoidal-like interfaces, which allow lateral wave propagation and are characterized by chains of ordered antiferromagnetic cross-interface flow vortices. Through the spontaneous coordination of counter-rotating units across the interfaces, topological defects excited by activity are sorted spatiotemporally, where positive defects are locally trapped at the interfaces but, unexpectedly, are transported laterally in a unidirectional rather than wavy mode, whereas inertial negative defects remain spinning in the bulks. Our findings reveal that individual chirality could be harnessed to modulate interfacial morphodynamics in active systems and suggest a potential approach toward controlling topological defects for programmable microfluidics and logic operations.
Collapse
Affiliation(s)
- De-Qing Zhang
- Institute of Biomechanics and Medical Engineering, Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
| | - Zhong-Yi Li
- Institute of Biomechanics and Medical Engineering, Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
| | - Bo Li
- Institute of Biomechanics and Medical Engineering, Applied Mechanics Laboratory, Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China
| |
Collapse
|
13
|
Brézin L, Risler T, Joanny JF. Spontaneous flow created by active topological defects. THE EUROPEAN PHYSICAL JOURNAL. E, SOFT MATTER 2022; 45:30. [PMID: 35389081 DOI: 10.1140/epje/s10189-022-00186-2] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/04/2022] [Accepted: 03/18/2022] [Indexed: 06/14/2023]
Abstract
Topological defects are at the root of the large-scale organization of liquid crystals. In two-dimensional active nematics, two classes of topological defects of charges [Formula: see text] are known to play a major role due to active stresses. Despite this importance, few analytical results have been obtained on the flow-field and active-stress patterns around active topological defects. Using the generic hydrodynamic theory of active systems, we investigate the flow and stress patterns around these topological defects in unbounded, two-dimensional active nematics. Under generic assumptions, we derive analytically the spontaneous velocity and stall force of self-advected defects in the presence of both shear and rotational viscosities. Applying our formalism to the dynamics of monolayers of elongated cells at confluence, we show that the non-conservation of cell number generically increases the self-advection velocity and could provide an explanation for their observed role in cellular extrusion and multilayering. We finally investigate numerically the influence of the Ericksen stress. Our work paves the way to a generic study of the role of topological defects in active nematics, and in particular in monolayers of elongated cells.
Collapse
Affiliation(s)
- Louis Brézin
- Laboratoire Physico-Chimie Curie, CNRS UMR168, Institut Curie, Université PSL, Sorbonne Université, 75005, Paris, France
- Collège de France, 75005, Paris, France
| | - Thomas Risler
- Laboratoire Physico-Chimie Curie, CNRS UMR168, Institut Curie, Université PSL, Sorbonne Université, 75005, Paris, France.
| | - Jean-Francois Joanny
- Laboratoire Physico-Chimie Curie, CNRS UMR168, Institut Curie, Université PSL, Sorbonne Université, 75005, Paris, France
- Collège de France, 75005, Paris, France
| |
Collapse
|
14
|
Nejad MR, Yeomans JM. Active Extensile Stress Promotes 3D Director Orientations and Flows. PHYSICAL REVIEW LETTERS 2022; 128:048001. [PMID: 35148135 DOI: 10.1103/physrevlett.128.048001] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/23/2021] [Revised: 08/21/2021] [Accepted: 12/24/2021] [Indexed: 06/14/2023]
Abstract
We use numerical simulations and linear stability analysis to study an active nematic layer where the director is allowed to point out of the plane. Our results highlight the difference between extensile and contractile systems. Contractile stress suppresses the flows perpendicular to the layer and favors in-plane orientations of the director. By contrast extensile stress promotes instabilities that can turn the director out of the plane, leaving behind a population of distinct, in-plane regions that continually elongate and divide. This supports extensile forces as a mechanism for the initial stages of layer formation in living systems, and we show that a planar drop with extensile (contractile) activity grows into three dimensions (remains in two dimensions). The results also explain the propensity of disclination lines in three dimensional active nematics to be of twist type in extensile or wedge type in contractile materials.
Collapse
Affiliation(s)
- Mehrana R Nejad
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| | - Julia M Yeomans
- The Rudolf Peierls Centre for Theoretical Physics, Department of Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom
| |
Collapse
|
15
|
Rønning J, Marchetti CM, Bowick MJ, Angheluta L. Flow around topological defects in active nematic films. Proc Math Phys Eng Sci 2022; 478:20210879. [PMID: 35153617 PMCID: PMC8791053 DOI: 10.1098/rspa.2021.0879] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/16/2021] [Accepted: 12/22/2021] [Indexed: 11/14/2022] Open
Abstract
We study the active flow around isolated defects and the self-propulsion velocity of +1/2 defects in an active nematic film with both viscous dissipation (with viscosity η) and frictional damping Γ with a substrate. The interplay between these two dissipation mechanisms is controlled by the hydrodynamic dissipation length ℓd=η/Γ that screens the flows. For an isolated defect, in the absence of screening from other defects, the size of the shear vorticity around the defect is controlled by the system size R. In the presence of friction that leads to a finite value of ℓd, the vorticity field decays to zero on the lengthscales larger than ℓd. We show that the self-propulsion velocity of +1/2 defects grows with R in small systems where R<ℓd, while in the infinite system limit or when R≫ℓd, it approaches a constant value determined by ℓd.
Collapse
Affiliation(s)
- Jonas Rønning
- Njord Centre, Department of Physics, University of Oslo, PO Box 1048, Oslo 0316, Norway
| | - Cristina M Marchetti
- Department of Physics, University of California Santa Barbara, Santa Barbara, CA 93106, USA
| | - Mark J Bowick
- Kavli Institute for Theoretical Physics, University of California Santa Barbara, Santa Barbara, CA 93106, USA
| | - Luiza Angheluta
- Njord Centre, Department of Physics, University of Oslo, PO Box 1048, Oslo 0316, Norway
| |
Collapse
|
16
|
Pearce DJG, Nambisan J, Ellis PW, Fernandez-Nieves A, Giomi L. Orientational Correlations in Active and Passive Nematic Defects. PHYSICAL REVIEW LETTERS 2021; 127:197801. [PMID: 34797140 DOI: 10.1103/physrevlett.127.197801] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/10/2021] [Accepted: 09/10/2021] [Indexed: 06/13/2023]
Abstract
We investigate the emergence of orientational order among +1/2 disclinations in active nematic liquid crystals. Using a combination of theoretical and experimental methods, we show that +1/2 disclinations have short-range antiferromagnetic alignment, as a consequence of the elastic torques originating from their polar structure. The presence of intermediate -1/2 disclinations, however, turns this interaction from antialigning to aligning at scales that are smaller than the typical distance between like-sign defects. No long-range orientational order is observed. Strikingly, these effects are insensitive to material properties and qualitatively similar to what is found for defects in passive nematic liquid crystals.
Collapse
Affiliation(s)
- D J G Pearce
- Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02142, USA
- Departments of Biochemistry and Theoretical Physics, Université de Genéve, 1205 Genéve, Switzerland
| | - J Nambisan
- Department of Condensed Matter Physics, University of Barcelona, 08028 Barcelona, Spain
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
| | - P W Ellis
- John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
| | - A Fernandez-Nieves
- Department of Condensed Matter Physics, University of Barcelona, 08028 Barcelona, Spain
- School of Physics, Georgia Institute of Technology, Atlanta, Georgia 30332, USA
- ICREA-Institucio Catalana de Recerca i Estudis Avancats, 08010 Barcelona, Spain
| | - L Giomi
- Instituut-Lorentz, Universiteit Leiden, P.O. Box 9506, 2300 RA Leiden, Netherlands
| |
Collapse
|
17
|
Submersed micropatterned structures control active nematic flow, topology, and concentration. Proc Natl Acad Sci U S A 2021; 118:2106038118. [PMID: 34535551 DOI: 10.1073/pnas.2106038118] [Citation(s) in RCA: 27] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 07/24/2021] [Indexed: 01/10/2023] Open
Abstract
Coupling between flows and material properties imbues rheological matter with its wide-ranging applicability, hence the excitement for harnessing the rheology of active fluids for which internal structure and continuous energy injection lead to spontaneous flows and complex, out-of-equilibrium dynamics. We propose and demonstrate a convenient, highly tunable method for controlling flow, topology, and composition within active films. Our approach establishes rheological coupling via the indirect presence of fully submersed micropatterned structures within a thin, underlying oil layer. Simulations reveal that micropatterned structures produce effective virtual boundaries within the superjacent active nematic film due to differences in viscous dissipation as a function of depth. This accessible method of applying position-dependent, effective dissipation to the active films presents a nonintrusive pathway for engineering active microfluidic systems.
Collapse
|