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Bahr C. Lattice Boltzmann and Jones matrix calculations for the determination of the director field structure in self-propelling nematic droplets. Phys Rev E 2021; 104:044703. [PMID: 34781516 DOI: 10.1103/physreve.104.044703] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/28/2021] [Accepted: 09/24/2021] [Indexed: 11/07/2022]
Abstract
Nematic droplets immersed in aqueous surfactant solutions can show a self-propelled motion induced by a Marangoni flow in the droplet surface. In addition to the self-propulsion, the Marangoni flow induces within the droplet a convective flow which considerably influences the nematic director field of the droplet. We report numerical simulations aiming at the determination of the director field in the self-propelling droplet. The convective flow and the resulting structure of director field are described by a lattice Boltzmann model. The reliability of the obtained structures is proved by subsequent Jones matrix calculations which enable the direct comparison of experimental polarizing microscopy images of self-propelling droplets with calculated images based on the simulated structures.
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Affiliation(s)
- Christian Bahr
- Max Planck Institute for Dynamics and Self-Organization, Am Faßberg 17, D-37077 Göttingen, Germany
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2
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Qiu M, Feng JJ, Loudet JC. Phase-field model for elastocapillary flows of liquid crystals. Phys Rev E 2021; 103:022706. [PMID: 33736098 DOI: 10.1103/physreve.103.022706] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/23/2020] [Accepted: 01/19/2021] [Indexed: 11/07/2022]
Abstract
We propose a phase-field model to study interfacial flows of nematic liquid crystals that couple the capillary forces on the interface with the elastic stresses in the nematic phase. The theoretical model has two key ingredients: A tensor order parameter that provides a consistent description of the molecular and distortional elasticity, and a phase-field formalism that accurately represents the interfacial tension and the nematic anchoring stress by approximating a sharp-interface limit. Using this model, we carry out finite-element simulations of drop retraction in a surrounding fluid, with either component being nematic. The results are summarized by eight representative steady-state solutions in planar and axisymmetric geometries, each featuring a distinct configuration for the drop and the defects. The dynamics is dominated by the competition between the interfacial tension and the distortional elasticity in the nematic phase, mediated by the anchoring condition on the drop surface. As consequences of this competition, the steady-state drop deformation and the clearance between the defects and the drop surface both depend linearly on the elastocapillary number.
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Affiliation(s)
- Mingfeng Qiu
- Department of Mathematics, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
| | - James J Feng
- Department of Mathematics and Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, British Columbia V6T 1Z2, Canada
| | - Jean-Christophe Loudet
- Université de Bordeaux, CNRS, Centre de Recherche Paul Pascal (UMR 5031), F-33600 Pessac, France
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Mandal S, Mazza MG. Multiparticle collision dynamics for tensorial nematodynamics. Phys Rev E 2019; 99:063319. [PMID: 31330733 DOI: 10.1103/physreve.99.063319] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/26/2019] [Indexed: 02/02/2023]
Abstract
Liquid crystals establish a nearly unique combination of thermodynamic, hydrodynamic, and topological behavior. This poses a challenge to their theoretical understanding and modeling. The arena where these effects come together is the mesoscopic (micron) scale. It is then important to develop models aimed at capturing this variety of dynamics. We have generalized the particle-based multiparticle collision dynamics (MPCD) method to model the dynamics of nematic liquid crystals. Following the Qian-Sheng theory [Phys. Rev. E 58, 7475 (1998)1063-651X10.1103/PhysRevE.58.7475] of nematics, the spatial and temporal variations of the nematic director field and order parameter are described by a tensor order parameter. The key idea is to assign tensorial degrees of freedom to each MPCD particle, whose mesoscopic average is the tensor order parameter. This nematic MPCD method includes backflow effect, velocity-orientation coupling, and thermal fluctuations. We validate the applicability of this method by testing (i) the nematic-isotropic phase transition, (ii) the flow alignment of the director in shear and Poiseuille flows, and (iii) the annihilation dynamics of a pair of line defects. We find excellent agreement with existing literature. We also investigate the flow field around a force dipole in a nematic liquid crystal, which represents the leading-order flow field around a force-free microswimmer. The anisotropy of the medium not only affects the magnitude of velocity field around the force dipole, but can also induce hydrodynamic torques depending on the orientation of dipole axis relative to director field. A force dipole experiences a hydrodynamic torque when the dipole axis is tilted with respect to the far-field director. The direction of hydrodynamic torque is such that the pusher- (or puller-) type force dipole tends to orient along (or perpendicular to) the director field. Our nematic MPCD method can have far-reaching implications not only in modeling of nematic flows, but also to study the motion of colloids and microswimmers immersed in an anisotropic medium.
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Affiliation(s)
- Shubhadeep Mandal
- Max-Planck-Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany
| | - Marco G Mazza
- Max-Planck-Institute for Dynamics and Self-Organization, Am Faßberg 17, 37077 Göttingen, Germany.,Interdisciplinary Centre for Mathematical Modelling and Department of Mathematical Sciences, Loughborough University, Loughborough, Leicestershire LE11 3TU, United Kingdom
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Tiribocchi A, Da Re M, Marenduzzo D, Orlandini E. Shear dynamics of an inverted nematic emulsion. SOFT MATTER 2016; 12:8195-8213. [PMID: 27714315 DOI: 10.1039/c6sm01275b] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
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 fluid. We find that in this regime the 2D droplet can tilt and move in the flow, or tumble incessantly at the centre of the channel. For sufficiently strong anchoring, finally, one or both of the topological defects which form close to the surface of the isotropic droplet in equilibrium detach from it and get dragged deep into the nematic state by the flow. In 3D, instead, the Saturn ring associated with the normal anchoring disclination line can be deformed and shifted downstream by the flow, but remains always localized in the proximity of the droplet, at least for the parameter range we explored. Tangential anchoring in 2D leads to a different dynamic response, as the boojum defects characteristic of this situation can unbind from the droplet under a weaker shear with respect to the normal anchoring case. Our results should stimulate further experiments with inverted liquid crystal emulsions under shear, as most of the predictions can be testable in principle by monitoring the evolution of liquid crystalline orientation patterns or by tracking the position and shape of the droplet over time.
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Affiliation(s)
- A Tiribocchi
- Dipartimento di Fisica e Astronomia and Sezione INFN di Padova, Universitá di Padova, Via Marzolo 8, 35131 Padova, Italy.
| | - M Da Re
- Dipartimento di Fisica e Astronomia and Sezione INFN di Padova, Universitá di Padova, Via Marzolo 8, 35131 Padova, Italy.
| | - D Marenduzzo
- SUPA and The School of Physics and Astronomy, University of Edinburgh, Edinburgh EH9 3FD, UK
| | - E Orlandini
- Dipartimento di Fisica e Astronomia and Sezione INFN di Padova, Universitá di Padova, Via Marzolo 8, 35131 Padova, Italy.
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Lee KW, Mazza MG. Stochastic rotation dynamics for nematic liquid crystals. J Chem Phys 2015; 142:164110. [DOI: 10.1063/1.4919310] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Turk J, Svenšek D. Backflow-mediated domain switching in nematic liquid crystals. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 89:032508. [PMID: 24730865 DOI: 10.1103/physreve.89.032508] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/21/2013] [Indexed: 06/03/2023]
Abstract
We study the dynamics of the nematic liquid crystal kickback effect upon removal of a primary electric field and its amplification by a perpendicular secondary electric field resulting in the formation of domains with a reverse director orientation. Using computational fluid dynamics, we show that the domain formation is a robust phenomenon that takes place also in the complex case of multiple irregular random Freedericksz domains in three dimension as they appear in a realistic experimental situation. We propose domain switching by kickback amplification as a tool for self-insertion of shell-like inhomogeneities into an otherwise perfectly uniform director field configuration.
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Affiliation(s)
- Janez Turk
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
| | - Daniel Svenšek
- Department of Physics, Faculty of Mathematics and Physics, University of Ljubljana, Jadranska 19, SI-1000 Ljubljana, Slovenia
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Blow ML, Telo da Gama MM. Interfacial motion in flexo- and order-electric switching between nematic filled states. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2013; 25:245103. [PMID: 23709473 DOI: 10.1088/0953-8984/25/24/245103] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/02/2023]
Abstract
We consider a nematic liquid crystal, in coexistence with its isotropic phase, in contact with a substrate patterned with rectangular grooves. In such a system the nematic phase may fill the grooves without the occurrence of complete wetting. There may exist multiple (meta)stable filled states, each characterized by the type of distortion (bend or splay) in each corner of the groove and by the shape of the nematic-isotropic interface, and additionally the plateaux that separate the grooves may be either dry or wet with a thin layer of nematic. Using numerical simulations, we analyse the dynamical response of the system to an externally-applied electric field, with the aim of identifying switching transitions between these filled states. We find that order-electric coupling between the fluid and the field provides a means of switching between states where the plateaux between grooves are dry and states where they are wetted by a nematic layer, without affecting the configuration of the nematic within the groove. We find that flexoelectric coupling may change the nematic texture in the groove, provided that the flexoelectric coupling differentiates between the types of distortion at the corners of the substrate. We identify intermediate stages of the transitions, and the role played by the motion of the nematic-isotropic interface. We determine quantitatively the field magnitudes and orientations required to effect each type of transition.
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Affiliation(s)
- M L Blow
- Centro de Física Teórica e Computacional, Lisboa, Portugal.
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Araki T. Dynamic coupling between a multistable defect pattern and flow in nematic liquid crystals confined in a porous medium. PHYSICAL REVIEW LETTERS 2012; 109:257801. [PMID: 23368501 DOI: 10.1103/physrevlett.109.257801] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/18/2012] [Revised: 10/27/2012] [Indexed: 06/01/2023]
Abstract
When a nematic liquid crystal is confined in a porous medium with strong anchoring conditions, topological defects, called disclinations, are stably formed with numerous possible configurations. Since the energy barriers between them are large enough, the system shows multistability. Our lattice Boltzmann simulations demonstrate dynamic couplings between the multistable defect pattern and the flow in a regular porous matrix. At sufficiently low flow speed, the topological defects are pinned at the quiescent positions. As the flow speed is increased, the defects show cyclic motions and nonlinear rheological properties, which depend on whether or not they are topologically constrained in the porous networks. In addition, we discover that the defect pattern can be controlled by controlling the flow. Thus, the flow path is recorded in the porous channels owing to the multistability of the defect patterns.
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Affiliation(s)
- Takeaki Araki
- Department of Physics, Kyoto University, Kyoto 606-8502, Japan
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Dolganov PV, Kats EI, Cluzeau P. Stepwise transition of a topological defect from the smectic film to the boundary of a dipolar inclusion. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 81:031709. [PMID: 20365753 DOI: 10.1103/physreve.81.031709] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/14/2010] [Indexed: 05/29/2023]
Abstract
Cholesteric droplets accompanied by a topological defect are studied in free standing smectic C;{ *} films. We observed a transition between two droplet-defect configurations with the defect in the film and on the droplet boundary. We found that the distance between the droplet surface and the topological defect decreases continuously with increasing temperature and above a certain critical temperature the defect jumps to the droplet boundary. We relate this stepwise change in the defect position to the change in the anchoring on the droplet boundary. This transformation leads to a decrease in the interparticle distances in self-organized chains from droplets. Our simple theory allows us to estimate the value of the anchoring energy.
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Affiliation(s)
- P V Dolganov
- Institute of Solid State Physics, Russian Academy of Sciences, 142432 Chernogolovka, Moscow District, Russia
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Rotenberg B, Pagonabarraga I, Frenkel D. Coarse-grained simulations of charge, current and flow in heterogeneous media. Faraday Discuss 2010; 144:223-43; discussion 323-45, 467-81. [DOI: 10.1039/b901553a] [Citation(s) in RCA: 45] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Spencer TJ, Care CM. Lattice Boltzmann scheme for modeling liquid-crystal dynamics: Zenithal bistable device in the presence of defect motion. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:061708. [PMID: 17280085 DOI: 10.1103/physreve.74.061708] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/10/2006] [Indexed: 05/13/2023]
Abstract
A lattice Boltzmann scheme is presented which recovers the dynamics of nematic and chiral liquid crystals; the method essentially gives solutions to the Qian-Sheng [Phys. Rev. E 58, 7475 (1998)] equations for the evolution of the velocity and tensor order-parameter fields. The resulting algorithm is able to include five independent Leslie viscosities, a Landau-deGennes free energy which introduces three or more elastic constants, a temperature dependent order parameter, surface anchoring and viscosity coefficients, flexoelectric and order electricity, and chirality. When combined with a solver for the Maxwell equations associated with the electric field, the algorithm is able to provide a full "device solver" for a liquid crystal display. Coupled lattice Boltzmann schemes are used to capture the evolution of the fast momentum and slow director motions in a computationally efficient way. The method is shown to give results in close agreement with analytical results for a number of validating examples. The use of the method is illustrated through the simulation of the motion of defects in a zenithal bistable liquid crystal device.
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Affiliation(s)
- T J Spencer
- Materials and Engineering Research Institute, Sheffield Hallam University, Howard Street, Sheffield, S1 1WB, United Kingdom
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Sulaiman N, Marenduzzo D, Yeomans JM. Lattice Boltzmann algorithm to simulate isotropic-nematic emulsions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:041708. [PMID: 17155079 DOI: 10.1103/physreve.74.041708] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/01/2006] [Revised: 07/26/2006] [Indexed: 05/12/2023]
Abstract
We present lattice Boltzmann simulations of the dynamical equations of motion of a drop of isotropic fluid in a nematic liquid crystal solvent, both in the absence and in the presence of an electric field. The coupled equations we solve are the Beris-Edward equations for the dynamics of the tensor order parameter describing the nematic solvent, the Cahn-Hilliard equation for the concentration evolution, and the Navier-Stokes equations for the determination of the instantaneous velocity field. We implement the lattice Boltzmann algorithm to ensure that spurious velocities are close to zero in equilibrium. We first study the effects of the liquid crystal elastic constant, K, anchoring strength, W, and surface tension, sigma, on the shape of the droplet and on the director field texture in equilibrium. We then consider how the drop behaves as the director field is switched by an applied electric field. We also show that the algorithm allows us to follow the motion of a drop of isotropic fluid placed in a liquid crystal cell with a tilted director field at the boundaries.
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Affiliation(s)
- N Sulaiman
- Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford, OX1 3NP, United Kingdom
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Lishchuk SV, Care CM. Shape of an isotropic droplet in a nematic liquid crystal: the role of surfactant. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:011702. [PMID: 15324067 DOI: 10.1103/physreve.70.011702] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2004] [Indexed: 05/24/2023]
Abstract
We investigate theoretically, and numerically, the shape of a droplet of an isotropic fluid immersed in a nematic liquid crystal in the presence of an interfacial layer of surfactant; the droplet size is assumed to be small compared to the extrapolation length of the nematic and homeotropic alignment is favored by the anchoring energy at the nematic-isotropic interface. In a certain range of droplet sizes, the droplets are found to be lens shaped with the rotation axis aligned along the imposed director field and the aspect ratio dependent upon the ratio of anchoring strength and surface tension coefficients. For anchoring strengths large compared to the surface tension, the curvature of the edge of lens is controlled by the bending rigidity of surfactant.
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Affiliation(s)
- S V Lishchuk
- Materials Research Institute, Sheffield Hallam University, Howard Street, Sheffield S1 1WB, United Kingdom
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