A continuum model for flows of cholesteric liquid crystal polymers and permeation flows

Cui, Zhenlu; Wang, Qi

doi:10.1016/j.jnnfm.2006.04.005

Cited by 5 publications

(9 citation statements)

References 30 publications

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“…cosωt. For steady shear flow, the dimensionless flow rate F s and the dimensionless apparent viscosity η s are given by the following relations [5,7]:…”

Section: Fig 32 the Profiles Of The Director Rotation Components Imentioning

confidence: 99%

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Small amplitude oscillatory shear permeation flow of cholesteric liquid crystal polymers

Cui¹

2010

Communications in Mathematical Sciences

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Abstract. We investigate the small amplitude oscillatory shear permeation flow (SAOSPF) of cholesteric liquid crystal polymers (CLCPs) using a mesoscopic model obtained from the Doi kinetic theory for flows of CLCPs. We model the system by Stokes hydrodynamic equations coupled with orientational dynamics and study the frequency-locked solutions of the system by employing a coarsegrained approach. The leading order solutions exhibit boundary layers of thickness of the order of the cholesteric pitch in low frequency regimes but in the order of 1 √ ω in high frequency regimes, where ω is the plate driven frequency. The response of CLCPs has been calculated. Viscoelastic behavior is only observed at intermediate frequencies and the material is essentially viscous at low and high frequency regimes. At both low and high frequencies, the real component of complex viscosity controls its magnitude which is of the order of the reciprocal of the cholesteric pitch at low frequencies while the order of 1 at high frequencies.

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“…cosωt. For steady shear flow, the dimensionless flow rate F s and the dimensionless apparent viscosity η s are given by the following relations [5,7]:…”

Section: Fig 32 the Profiles Of The Director Rotation Components Imentioning

confidence: 99%

“…They also pointed out the importance of the secondary flow in their simulation [21,22]. The authors [7] analytically studied permeation flows and resolved a long standing inconsistency in the study of chiral liquid crystal permeation flows.…”

Section: Introductionmentioning

confidence: 96%

Small amplitude oscillatory shear permeation flow of cholesteric liquid crystal polymers

Cui¹

2010

Communications in Mathematical Sciences

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“…Cui-Wang-McMillan model [3] for flowing CLCPs. We present the dimensionless governing system of equations along with the dimensionless parameter group only and refer readers to [3] for the detailed theory, the dimensional parameters, and the derivation.…”

Section: Model Formulationmentioning

confidence: 99%

“…− r 2 +1 parameterizes the aspect ratio r of the spheroidal molecules 0 < a ≤ 1 corresponds to a rod-like molecule and − 1 ≤ a < 0 for a platelet [3].…”

Section: Momentum Balance Equationmentioning

confidence: 99%

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Oscillatory shear rheology of chiral liquid crystal polymers

Cui

Wang

2009

SPIE Proceedings

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We employ a hydrodynamic theory for chiral liquid crystal polymers (CLCPs) to investigate the linear viscoelastic response of CLCPs to small amplitude oscillatory permeation shear flow, when the helix is oriented along the velocity direction and the orientation distortion retain the original planar structure. To predict the linear viscoelasticity, we model the system with Stokes hydrodynamic equations with viscous and nematic as well as cholesteric stresses coupled with orientational dynamics driven by the flow. The key findings are the following: in low frequency limit, both the loss modulus (G") and storage modulus (G i ) exhibit a classical frequency ω dependence (G " ∝ ω, G i ∝ ω 2 ) but their magnitudes are of order O(q/Er 1/2 ), where 2π/q defines the pitch of the chiral liquid crystal and Er is the Ericksen number. In high frequency limit, G i = O(q 2 /Er) is independent of ω while G i = O(1)ω is independent of q and Er.

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Liquid crystal models of biological materials and processes

2010

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This paper presents an overview of liquid crystal (LC) models of phase diagrams, phase transitions, self-assembly, interfaces, defects, and rheology and their integrated applications to biological mesophase materials and processes. Biological liquid crystals, classified into analogues (helicoidal plywoods), biopolymer solutions (in vitro DNA, polypeptides, collagen solutions) and in vivo LCs (membranes, silk, DNA), are discussed in terms of molecular characteristics and the symmetry of the thermodynamic phases. The thermodynamics and self-assembly of biological liquid crystals (BLCs) are discussed in terms of the Doi-Maier-Saupe lyotropic model and its extensions to chiral phases, showing the role of excluded volume and chirality. The defect physics of BLCs is described using the Landau-de Gennes model of chiral and achiral nematostatics to identify (i) thermodynamic phases, and (ii) observed textures and defect lattices under confinement and flow. The rheology and flow properties of BLCs are described using the Leslie-Ericksen and the Landau-de Gennes models of nematodynamics. The applications of integrated thermodynamic/defect/rheology modeling to the experimental characterization of several BLCs, including collagen and DNA solutions, are shown to provide organizing principles and quantitative tools to establish the properties of these natural materials. The phase transitions, tactoidal spherulites, flow-birefringence in dilute solutions, and banded textures in sheared concentrated solutions of collagen show how the principles of LC physics operate in BLC materials. Drying and spreading drops of DNA solutions leading to the formation of nematic monodomain aligned along the contact line are shown to follow self-assembly structuring under the action of interfacial, bulk, and contact line torques. Finally modeling of spider and silkworm LC spinning is presented as an example of biological polymer processing, where a high performance fiber material is produced through a lyotropic LC protein solution. The concerted structuring action of capillary confinement, strong anchoring, and nematic flow leads to predictions in agreement with the reported textural transitions in the duct of spiders and silkworms. The quantitative description of BLC materials and processes using mesoscopic models provides another tool to develop the science and future biomimetic applications of these ubiquitous natural anisotropic soft materials.

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A continuum model for flows of cholesteric liquid crystal polymers and permeation flows

Cited by 5 publications

References 30 publications

Small amplitude oscillatory shear permeation flow of cholesteric liquid crystal polymers

Small amplitude oscillatory shear permeation flow of cholesteric liquid crystal polymers

Oscillatory shear rheology of chiral liquid crystal polymers

Liquid crystal models of biological materials and processes

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