Constitutive Equation for Nematic Liquid Crystals under Weak Velocity Gradient Derived from a Molecular Kinetic Equation. II. –Leslie Coefficients for Rodlike Polymers–

Kuzuu, Nobu; Doi, Masao

doi:10.1143/jpsj.53.1031

Cited by 104 publications

(41 citation statements)

References 15 publications

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“…Here to decrease the number of parameters we have taken the coefficients of the advective and vorticity coupling to be 1 and have introduced a single flow coupling parameter λ as appropriate for passive 2d nematics. Note that with this choice λ is known to be finite in the limit where the strength S of nematic order vanishes [34][35][36] .…”

Section: Active Nematics On a Substratementioning

confidence: 99%

Negative stiffness and modulated states in active nematics

2016

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We examine the dynamics of an active nematic liquid crystal on a frictional substrate. When frictional damping dominates over viscous dissipation, we eliminate flow in favor of active stresses to obtain a minimal dynamical model for the nematic order parameter, with elastic constants renormalized by activity. The renormalized elastic constants can become negative at large activity, leading to the selection of spatially inhomogeneous patterns via a mechanism analogous to that responsible for modulated phases arising at an equilibrium Lifshitz point. Tuning activity and the degree of nematic order in the passive system, we obtain a linear stability phase diagram that exhibits a nonequilibrium tricritical point where ordered, modulated and disordered phases meet. Numerical solution of the nonlinear equations yields a succession of spatial structures of increasing complexity with increasing activity, including kink walls and active turbulence, as observed in experiments on microtubule bundles confined at an oil-water interface. Our work provides a minimal model for an overdamped active nematic that reproduces all the nonequilibrium structures seen in simulations of the full active nematic hydrodynamics and provides a framework for understanding some of the mechanisms for selection of the nonequilibrium patterns in the language of equilibrium critical phenomena.Active systems are continuously driven out of equilibrium by energy injected at the local scale and generate collective motion at the large scale. Examples include bacterial colonies, in vitro extracts of cytoskeletal filaments and motor proteins, and living cells 1 . Elongated active particles can order in states with liquid crystalline order. The emergent behavior of such 'living' liquid crystals has been described using liquid crystal hydrodynamics, modified to include the local energy input from active processes 2,3 . This work has highlighted a rich variety of collective phenomena, including spontaneous laminar flow, pattern formation, spontaneous unbinding of topological defects, and active turbulence 4-13 . Previous studies have established that bulk active nematics are generically unstable 1,3,14,15 . Confinement, on the other hand, has profound effects on active fluids. It damps the flow 16,17 and suppresses the generic instability of unbound systems, resulting in a finite activity threshold for the onset of spontaneously flowing states 8,18 . Frictional damping due to confinement plays a key role in experimental realizations of active systems. In bacterial suspensions channel confinement was shown to stabilize vortex In confined nematics the energy input from active stresses is dissipated both via viscous flows that mediate hydrodynamic interactions between the active units and via friction with a substrate. Systems where viscous dissipation dominates so that frictional damping is negligible and momentum is conserved are referred to as 'wet', while those where dissipation is mainly controlled by friction are referred to as 'dry'. Previous work has ex...

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Section: Active Nematics On a Substratementioning

confidence: 99%

Negative stiffness and modulated states in active nematics

2016

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“…Furthermore, for weak orientational order, our approximation of isotropic viscosity becomes asymptotically exact. Indeed, Kuzuu and Doi [32] showed that the anisotropic parts of the viscosities vanish as the amplitude of the nematic order parameter goes to zero (the isotropic viscosity does not vanish in the same limit since a completely isotropic liquid has a nonvanishing isotropic viscosity). To sum up, the hydrodynamic theory we employ is exact for low-activity, weakly ordered nematics.…”

Section: Hydrodynamics Of Active Nematicsmentioning

confidence: 99%

“…We now justify the isotropic viscosity approximation. In the limit of weak order, which in the notation of Kuzuu and Doi [32] is the limit S 2 ,S 4 1, our isotropic viscosity approximation becomes valid because α 4 (our activity parameter α should not be confused with Kuzuu and Doi's anisotropic viscosities), which is just the isotropic piece of the viscosity, is much greater than the anisotropic pieces α 1,5,6 of the viscosity, since the latter all vanish when S 2,4 → 0, with (again in the notation of Kuzuu and Doi) η = α 4 /2 ≈ η * C 3 r 2 . Furthermore, the coefficient γ 1 = α 3 − α 2 = 10η * C 3 r 2 S 2 /λ.…”

Section: Appendix B: Justification Of the Frozen Director And Isotropmentioning

confidence: 99%

Geometry of thresholdless active flow in nematic microfluidics

2017

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Active nematics are orientationally ordered but apolar fluids composed of interacting constituents individually powered by an internal source of energy. When activity exceeds a system-size-dependent threshold, spatially uniform active apolar fluids undergo a hydrodynamic instability leading to spontaneous macroscopic fluid flow. Here we show that a special class of spatially nonuniform configurations of such active apolar fluids display laminar (i.e., time-independent) flow even for arbitrarily small activity. We also show that two-dimensional active nematics confined on a surface of nonvanishing Gaussian curvature must necessarily experience a nonvanishing active force. This general conclusion follows from a key result of differential geometry: Geodesics must converge or diverge on surfaces with nonzero Gaussian curvature. We derive the conditions under which such curvatureinduced active forces generate thresholdless flow for two-dimensional curved shells. We then extend our analysis to bulk systems and show how to induce thresholdless active flow by controlling the curvature of confining surfaces, external fields, or both. The resulting laminar flow fields are determined analytically in three experimentally realizable configurations that exemplify this general phenomenon: (i) toroidal shells with planar alignment, (ii) a cylinder with nonplanar boundary conditions, and (iii) a Frederiks cell that functions like a pump without moving parts. Our work suggests a robust design strategy for active microfluidic chips and could be tested with the recently discovered living liquid crystals.

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“…To put this in context, Table D give α ≈ 0.01. The theory of Kuzuu and Doi [36] for rodlike molecules predicts a value of α < 0.004 over the entire nematic range. An affine transformation theory [37,38] predicts values α < 0.1 for molecules of elongation κ ≥ 3 at modest nematic order parameters, and α ≡ 0 in the perfectly aligned limit.…”

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confidence: 93%

Propagating Director Bend Fluctuations in Nematic Liquid Crystals

Humpert

Allen

2015

Phys. Rev. Lett.

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We show, by molecular simulation, that for a range of standard, coarse-grained, nematic liquid crystal models, the director bend fluctuation is a propagating mode. This is in contrast to the generally-accepted picture of nematic hydrodynamics, in which all the director modes (splay, twist, bend, and combinations thereof) are overdamped. By considering the various physical parameters that enter the equations of nematodynamics, we propose an explanation of this effect, and conclude that propagating bend fluctuations may be observable in some experimental systems.

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Constitutive Equation for Nematic Liquid Crystals under Weak Velocity Gradient Derived from a Molecular Kinetic Equation. II. –Leslie Coefficients for Rodlike Polymers–

Cited by 104 publications

References 15 publications

Negative stiffness and modulated states in active nematics

Negative stiffness and modulated states in active nematics

Geometry of thresholdless active flow in nematic microfluidics

Propagating Director Bend Fluctuations in Nematic Liquid Crystals

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