The flow-phase diagram of Doi-Hess theory for sheared nematic polymers II: finite shear rates

Forest, M. Gregory; Wang, Qi; Zhou, Ruhai

doi:10.1007/s00397-004-0380-9

Cited by 83 publications

(101 citation statements)

References 14 publications

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“…These simple closure approximations respect the traceless property of the orientational dynamic equation, and have been shown to yield a good approximation of kinetic theory in the dynamics of monodomains at the nematic concentrations of interest here [10,15,16]. These closures are exact when the molecules are aligned perfectly.…”

Section: Continuity Equationmentioning

confidence: 86%

“…The model has been benchmarked in the longwave, monodomain regime with resolved simulations of the Doi kinetic theory [15,16]. Indeed, the motivation for an analytical study of structure properties is to provide guidance for structure simulations of mesoscopic [17] and kinetic [15,16] models, where the parameter space is too large to assimilate any kind of collapse of the numerical data through scaling laws.…”

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confidence: 99%

“…First, we consider a more general physical model to admit anisotropic distortional elasticity (unequal bend, splay, twist elasticity constants). The second-moment orientation model is derived from a recent generalization of the Doi-Hess-Marrucci-Greco kinetic theory [33] and guides our numerical studies [15,16], for which there are no preceding numerical or analytical results. Second, the asymptotic analysis is extended from plate-driven Couette cell properties to pressure-driven Poiseuille flows.…”

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confidence: 99%

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On Weak Plane Couette and Poiseuille Flows of Rigid Rod and Platelet Ensembles

Cui¹,

Forest²,

Wang³

et al. 2006

SIAM J. Appl. Math.

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On weak plane Couette and Poiseuille flows of rigid rod and platelet ensembles (with Z. Cui, M.G. Forest and Q. Wang), SIAM J. Appl. Math. , 66 (4), 2006 Abstract. Films and molds of nematic polymer materials are notorious for heterogeneity in the orientational distribution of the rigid rod or platelet macromolecules. Predictive tools for structure length scales generated by shear-dominated processing are vitally important: both during processing because of flow feedback phenomena such as shear thinning or thickening, and postprocessing since gradients in the rod or platelet ensemble translate to nonuniform composite properties and to residual stresses in the material. These issues motivate our analysis of two prototypes for planar shear processing: drag-driven Couette and pressure-driven Poiseuille flows. Hydrodynamic theories for high aspect ratio rod and platelet macromolecules in viscous solvents are well developed, which we apply in this paper to model the coupling between short-range excluded volume interactions, anisotropic distortional elasticity (unequal elasticity constants), wall anchoring conditions, and hydrodynamics. The goal of this paper is to generalize scaling properties of steady flow molecular structures in slow Couette flows with equal elasticity constants [M. G. Forest et al., J. Rheol., 48 (2004), pp. 175-192] in several ways: to contrast isotropic and anisotropic elasticity; to compare Couette versus Poiseuille flow; and to consider dynamics and stability of these steady states within the asymptotic model equations.

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Section: Continuity Equationmentioning

confidence: 86%

mentioning

confidence: 99%

mentioning

confidence: 99%

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On Weak Plane Couette and Poiseuille Flows of Rigid Rod and Platelet Ensembles

Cui¹,

Forest²,

Wang³

et al. 2006

SIAM J. Appl. Math.

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“…First we set a nematic concentration N = 6, for which stable quiescent equilibria satisfying F (Q) = 0 are uniaxial (β = 0), ordered phases with Flory order parameter s given below, equation (7). We select a = 0.8, or aspect ratio r = 3, which for the Doi closure gives excellent agreement with the full kinetic theory in the longwave limit of sheared monodomains [10,11,12]. Finally we set α = 2.0, µ 1 = 2.3867 × 10 −4 , µ 2 = 3.1667 × 10 −3 , µ 3 = 3.5 × 10 −3 , consistent with our previous papers [1,9] so that we identify anchoring distortion effects; similarly, we use a constant rotational diffusivity.…”

Section: Hong Zhou and M Gregory Forestmentioning

confidence: 94%

Anchoring distortions coupled with plane Couette & Poiseuille flows of nematic polymers in viscous solvents: Morphology in molecular orientation, stress & flow

Zhou

Forest²

2005

DCDS-B

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Abstract. The aim of this work is to model and simulate processing-induced heterogeneity in rigid, rod-like nematic polymers in viscous solvents. We employ a mesoscopic orientation tensor model due to Doi, Marrucci and Greco which extends the small molecule, liquid crystal theory of Leslie-Ericksen-Frank to nematic polymers. The morphology has various physical realizations, all coupled through the model equations: the orientational distribution of the ensemble of rods, anisotropic viscoelastic stresses, and flow feedback. Previous studies in plane Couette & Poiseuille flow (with the exception of [7]) have focused on the coupling between hydrodynamics and the orientational distribution of rigid rod polymers with identical anchoring conditions at solid boundaries; without flow, the equilibrium structure is homogeneous. Here we explore steady structures that emerge with mismatch anchoring conditions at the walls, which couple an equilibrium elastic distortion across the channel, short and long range elasticity potentials, and hydrodynamics. In plane Couette (where moving plates drive the flow) and Poiseuille flow (where a pressure gradient drives the flow), in the regime of weak flow and strong distortional elasticity, asymptotic analysis yields closed-form steady solutions and scaling laws with identical wall conditions. We focus simulations in this regime to expose the effects due to wall anchoring conflicts, and illustrate the induced morphology of the orientational distribution, stored viscoelastic stresses, and non-Newtonian flow. A remarkably simple diagnostic emerges in this physical parameter regime, in which salient morphology features are controlled by the amplitude and sign of the difference in plate anchoring angles of the director field at the two plates.

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“…From these properties of the function f (η), we draw conclusions listed below related to equation (12):…”

Section: Equilibrium States Of a Nematic Polymer Ensemblementioning

confidence: 99%

Stability of equilibria of nematic liquid crystalline polymers

Zhou

Wang

2011

Acta Mathematica Scientia

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We provide an analytical study on the stability of equilibria of rigid rodlike nematic liquid crystalline polymers (LCPs) governed by the Smoluchowski equation with the Maier-Saupe intermolecular potential. We simplify the expression of the free energy of an orientational distribution function of rodlike LCP molecules by properly selecting a coordinate system and then investigate its stability with respect to perturbations of orientational probability density. By computing the Hessian matrix explicitly, we are able to prove the hysteresis phenomenon of nematic LCPs: when the normalized polymer concentration b is below a critical value b * (6.7314863965), the only equilibrium state is isotropic and it is stable; when b * < b < 15/2, two anisotropic (prolate) equilibrium states occur together with a stable isotropic equilibrium state. Here the more aligned prolate state is stable whereas the less aligned prolate state is unstable. When b > 15/2, there are three equilibrium states: a stable prolate state, an unstable isotropic state and an unstable oblate state.

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The flow-phase diagram of Doi-Hess theory for sheared nematic polymers II: finite shear rates

Cited by 83 publications

References 14 publications

On Weak Plane Couette and Poiseuille Flows of Rigid Rod and Platelet Ensembles

On Weak Plane Couette and Poiseuille Flows of Rigid Rod and Platelet Ensembles

Anchoring distortions coupled with plane Couette & Poiseuille flows of nematic polymers in viscous solvents: Morphology in molecular orientation, stress & flow

Stability of equilibria of nematic liquid crystalline polymers

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