Stability and Instability of an Uniaxial Alignment Against Biaxial Distortions in the Isotropic and Nematic Phases of Liquid Crystals

Kaiser, P.; Wiese, Wolfgang L.; Hess, Siegfried

doi:10.1515/jnet.1992.17.2.153

Cited by 100 publications

(56 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In these units, the clearing point T c and the pseudo critical temperature T * correspond to ϑ = 1 and ϑ = 0, respectively [12]. Note that, for convenience, the tildes are dropped in all subsequent formulae.…”

Section: Solution Strategymentioning

confidence: 99%

“…The shading of the box shows its degree of biaxiality: a white box corresponds to uniaxial alignment, where two eigenvalues are equal (such as in the initial configuration), and a black box corresponds to perfectly biaxial alignment, where one eigenvalue is zero. In general, the level of darkness of a particular box is proportional to the biaxiality measure β 2 = 1 − 6(tr Q 3 ) 2 /(tr Q 2 ) 3 used in [12]. Note that the number of boxes plotted has been chosen for clear representation of the solutions, and does not correspond to the number of degrees of freedom used in the calculations.…”

Section: In-plane Orientationmentioning

confidence: 99%

See 1 more Smart Citation

Computational fluid dynamics for nematic liquid crystals

Ramage

Sonnet

2015

Bit Numer Math

View full text Add to dashboard Cite

Due to recent advances in fast iterative solvers in the field of computational fluid dynamics, more complex problems which were previously beyond the scope of standard techniques can be tackled. In this paper, we describe one such situation, namely, modelling the interaction of flow and molecular orientation in a complex fluid such as a liquid crystal. Specifically, we consider a nematic liquid crystal in a spatially inhomogeneous flow situation where the orientational order is described by a second rank alignment tensor. The evolution is determined by two coupled equations: a generalised Navier-Stokes equation for flow in which the divergence of the stress tensor also depends on the alignment tensor and its time derivative, and a convectiondiffusion type equation with non-linear terms that stem from a Landau-GinzburgDeGennes potential for the alignment. In this paper, we use a specific model with three viscosity coefficients that allows the contribution of the orientation to the viscous stress to be cast in the form of an orientation-dependent force. This effectively decouples the flow and orientation, with each appearing only on the right-hand side of the other equation. In this way, difficulties associated with solving the fully coupled problem are circumvented and a stand-alone fast solver, such as the state-of-the-art preconditioned iterative solver implemented here, can be used for the flow equation. A time-discretised strategy for solving the flow-orientation problem is illustrated using the example of Stokes flow in a lid-driven cavity.

show abstract

Section: Solution Strategymentioning

confidence: 99%

Section: In-plane Orientationmentioning

confidence: 99%

Computational fluid dynamics for nematic liquid crystals

Ramage

Sonnet

2015

Bit Numer Math

View full text Add to dashboard Cite

show abstract

“…If strong distortions are present biaxial states could be locally entered. Degree of biaxiality is assessed via parameter [26] …”

Section: Free Energymentioning

confidence: 99%

“…Below the finger tip the nematic configuration is positively uniaxial (S > 0) at the symmetry axis. The finger is enclosed within a biaxial shell exhibiting maximal biaxiality [26,30] which joins the finger tip with the upper surface. By topological reasons the nematic order parameter melts only at the finger tip for realistic anchoring strengths.…”

Section: Interaction Between Nps and Topological Defectsmentioning

confidence: 99%

Mixtures Composed of Liquid Crystals and Nanoparticles

Popa-Nita¹,

Barna²,

Repnik³

et al. 2013

Syntheses and Applications of Carbon Nanotubes and Their Composites

View full text Add to dashboard Cite

“…This is achieved via an expansion of a in a standard tensorial basis [13,49]. The resulting components are linked by simple expressions to their cartesian counterparts a αβ (with α, β = x, y, z), that is, a 0 ∝ −(a xx + a yy ), a 1 ∝ a xx − a yy , a 2 ∝ a xy , a 3 ∝ a xz , and a 4 ∝ a yz [13,49]. Thus, a 0 (with negative values), a 1 , and a 2 describe ordering within the shear (x-y) plane, whereas a 3 and a 4 describe out-of-plane ordering.…”

Section: B Explicit Equations Of Motionmentioning

confidence: 99%

Shear-stress-controlled dynamics of nematic complex fluids

Klapp

Hess

2010

Phys. Rev. E

View full text Add to dashboard Cite

Based on a mesoscopic theory we investigate the non-equilibrium dynamics of a sheared nematic liquid, with the control parameter being the shear stress σxy (rather than the usual shear rate, γ). To this end we supplement the equations of motion for the orientational order parameters by an equation forγ, which then becomes time-dependent. Shearing the system from an isotropic state, the stress-controlled flow properties turn out to be essentially identical to those at fixedγ. Pronounced differences occur when the equilibrium state is nematic. Here, shearing at controlleḋ γ yields several non-equilibrium transitions between different dynamic states, including chaotic regimes. The corresponding stress-controlled system has only one transition from a regular periodic into a stationary (shear-aligned) state. The position of this transition in the σxy-γ plane turns out to be tunable by the delay time entering our control scheme for σxy. Moreover, a sudden change of the control method can stabilize the chaotic states appearing at fixedγ.

show abstract

Stability and Instability of an Uniaxial Alignment Against Biaxial Distortions in the Isotropic and Nematic Phases of Liquid Crystals

Cited by 100 publications

References 16 publications

Computational fluid dynamics for nematic liquid crystals

Computational fluid dynamics for nematic liquid crystals

Mixtures Composed of Liquid Crystals and Nanoparticles

Shear-stress-controlled dynamics of nematic complex fluids

Contact Info

Product

Resources

About