Stokes drag of spherical particles in a nematic environment at low Ericksen numbers

Stark, Holger; Ventzki, Dieter

doi:10.1103/physreve.64.031711

Cited by 113 publications

(172 citation statements)

References 48 publications

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“…The defect-mediated pair-interaction force F int is balanced by the viscous drag that can be estimated using Stokes' law, yielding F int ¼ F viscous ¼ 6πηRν, where R is the particle radius. We use a value of viscosity coefficient that is the average of the measured values for directions parallel and perpendicular to the uniform nðrÞ, obtaining η ¼ 56.3 mPa · s for 5CB-based cholesteric (36). Interactions due to defect lines of zero Burgers vector may involve multiple mobile or stationary particles interconnected by defects.…”

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confidence: 99%

Reconfigurable interactions and three-dimensional patterning of colloidal particles and defects in lamellar soft media

Trivedi

Klevets

Senyuk

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

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Colloidal systems find important applications ranging from fabrication of photonic crystals to direct probing of phenomena typically encountered in atomic crystals and glasses. New applicationssuch as nanoantennas, plasmonic sensors, and nanocircuits-pose a challenge of achieving sparse colloidal assemblies with tunable interparticle separations that can be controlled at will. We demonstrate reconfigurable multiscale interactions and assembly of colloids mediated by defects in cholesteric liquid crystals that are probed by means of laser manipulation and three-dimensional imaging. We find that colloids attract via distance-independent elastic interactions when pinned to the ends of cholesteric oily streaks, line defects at which one or more layers are interrupted. However, dislocations and oily streaks can also be optically manipulated to induce kinks, allowing one to lock them into the desired configurations that are stabilized by elastic energy barriers for structural transformation of the particle-connecting defects. Under the influence of elastic energy landscape due to these defects, sublamellarsized colloids self-assemble into structures mimicking the cores of dislocations and oily streaks. Interactions between these defectembedded colloids can be varied from attractive to repulsive by optically introducing dislocation kinks. The reconfigurable nature of defect-particle interactions allows for patterning of defects by manipulation of colloids and, in turn, patterning of particles by these defects, thus achieving desired colloidal configurations on scales ranging from the size of defect core to the sample size. This defect-colloidal sculpturing may be extended to other lamellar media, providing the means for optically guided self-assembly of mesoscopic composites with predesigned properties.

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mentioning

confidence: 99%

Reconfigurable interactions and three-dimensional patterning of colloidal particles and defects in lamellar soft media

Trivedi

Klevets

Senyuk

et al. 2012

Proc. Natl. Acad. Sci. U.S.A.

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“…Nevertheless, a comparison is interesting. In the limit of vanishing Er, Stark & Ventzki (2001) fixed the n(r) field to the equilibrium solution with a point defect, and computed the drag in terms of an effective viscosity η eff defined from the Stokes formula. In our case, a similar η eff can be estimated from the Hadamard-Rybczynski formula.…”

Section: Rising Velocity Drag Force and The Flow Fieldmentioning

confidence: 99%

“…Owing to the rheological complexity, only a handful of theoretical studies have appeared on the moving particle problem, most of which sought to decouple the flow field and the director field (Stark 2001). For instance, the director field may be fixed at the static solution, and the resulting flow field and drag are calculated Stark & Ventzki 2001). This corresponds to the low Ericksen number (Er) limit, where the viscous forces are too weak to modify the orientational field maintained by elasticity.…”

Section: Introductionmentioning

confidence: 99%

The rise of Newtonian drops in a nematic liquid crystal

2007

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We simulate the rise of Newtonian drops in a nematic liquid crystal parallel to the far-field molecular orientation. The moving interface is computed in a diffuseinterface framework, and the anisotropic rheology of the liquid crystal is represented by the Leslie-Ericksen theory, regularized to permit topological defects. Results reveal interesting coupling between the flow field and the orientational field surrounding the drop, especially the defect configuration. The flow generally sweeps the point and ring defects downstream, and may transform a ring defect into a point defect. The stability of these defects and their transformation are depicted in a phase diagram in terms of the Ericksen number and the ratio between surface anchoring and bulk elastic energies. The nematic orientation affects the flow field in return. Drops with planar anchoring on the surface rise faster than those with homeotropic anchoring, and the former features a vortex ring in the wake. These are attributed to the viscous anisotropy of the nematic. With homeotropic anchoring, the drop rising velocity experiences an overshoot, owing to the transformation of the initial surface ring defect to a satellite point defect. With both types of anchoring, the drag coefficient of the drop decreases with increasing Ericksen number as the flow-alignment of the nematic orientation reduces the effective viscosity of the liquid crystal.

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“…More recently, the flow of a nematic liquid crystal (NLC) through a homeotropic porous network has shown reconfigurable deformation of defects around the solid portions of the network [193]. The Stokes drag on spherical particles with accompanying topological defects at low Ericksen numbers Er [76] was investigated by Stark et al [237]. Subsequently, the time evolution of flow-induced orientational profiles of defects around colloids [27], and around drops and bubbles rising through a nematic bulk [28,29] were investigated.…”

Section: Nematic Flow Past a Cylindrical Micro-pillarmentioning

confidence: 99%

Nematic Liquid Crystals and Nematic Colloids in Microfluidic Environment

Sengupta

Herminghaus

Bahr

2011

Molecular Crystals and Liquid Crystals

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Where the mind is without fear and the head is held high;Where knowledge is free;Where the world has not been broken up into fragments by narrow domestic walls;Where words come out from the depth of truth;Where tireless striving stretches its arms towards perfection;Where the clear stream of reason has not lost its way into the dreary desert sand of dead habit;Where the mind is led forward by thee into ever-widening thought and actionInto that heaven of freedom, my Father, let my country awake.Rabindranath Tagore (1861Tagore ( -1941 To my parents, my brother, and all the sacrifices they made for me AbstractThe doctoral thesis presented here is one of the first systematic attempts to unravel the wonderful world of liquid crystals within microfluidic confinements, typically channels with dimensions of tens of micrometers. The present work is based on experiments with a roomtemperature nematic liquid crystal, 5CB, and its colloidal dispersions within microfluidic devices of rectangular cross-section, fabricated using standard techniques of soft lithography. To begin with, a combination of physical and chemical methods was employed to create well defined boundary conditions for investigating the flow experiments. The walls of the microchannels were functionalized to induce different kinds of surface anchoring of the 5CB molecules: degenerate planar, uniform planar, and homeotropic surface anchoring. Channels possessing composite anchoring conditions (hybrid) were additionally fabricated, e. g. homeotropic and uniform planar anchoring within the same channel. On filling the microchannels with 5CB in the isotropic phase, different equilibrium configurations of the nematic director resulted, as the sample cooled down to nematic phase. For a given surface anchoring, the equilibrium director configuration varied also with the channel aspect ratio. The static director field within the channel registered the initial conditions for the flow experiments. The static and i ii dynamic experiments have been analyzed using a combination of polarization, and confocal fluorescence microscopy techniques, along with particle tracking method for measuring the flow speeds. Additionally, dual-focus fluorescence correlation spectroscopy is introduced as a generic velocimetry tool for liquid crystal flows.The flow of nematic liquid crystals is inherently complex due to the coupling between the flow and the nematic director. The presence of the four confining walls and the nature of surface anchoring on them complicate the flow-director interactions further. In microchannels possessing degenerate planar anchoring, four different flow-induced defect textures were identified with increasing Ericksen number: π-walls, disclination lines pinned to the channel walls, disclination lines with one pinned and one freely suspended end, and disclination loops freely flowing in a chaotic manner. However, such textures and sequence of defects were not observed for flows within channels with homogeneous anchoring.Using experiments and numerical modeling...

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Stokes drag of spherical particles in a nematic environment at low Ericksen numbers

Cited by 113 publications

References 48 publications

Reconfigurable interactions and three-dimensional patterning of colloidal particles and defects in lamellar soft media

Reconfigurable interactions and three-dimensional patterning of colloidal particles and defects in lamellar soft media

The rise of Newtonian drops in a nematic liquid crystal

Nematic Liquid Crystals and Nematic Colloids in Microfluidic Environment

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