Ericksen number and Deborah number cascade predictions of a model for liquid crystalline polymers for simple shear flow

Klein, David H.; Leal, L. Gary; Garcı́a-Cervera, Carlos J.; Ceniceros, Héctor D.

doi:10.1063/1.2424499

Cited by 22 publications

(32 citation statements)

References 48 publications

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“…It was found in Ref. [61] that the DMG model was able to capture dynamic behaviors in accordance with experimental observations 69 for the Ericksen number and Deborah number cascades. For increasing shear rates within the Ericksen number cascade, where gradient elasticity is the dominant stress contribution, the DMG model exhibits four distinct flow regimes: stable simple linear shear flow at low shear rates; stable roll cells at intermediate shear rates; irregular structure followed by large-stain disclination formation and irregular structure preceded by disclination formation at high shear rates.…”

Section: Numerical Simulationsmentioning

confidence: 51%

“…For increasing shear rates within the Deborah number cascade, where the dominant contribution to the stress is viscoelasticity, the DMG model displays a stream-wide banded texture, in the absence of roll cells and disclinations, followed by a shear alignment where the mean orientation lies within the shear plane throughout the monodomain. Very recently Klein et al extended their calculations 61 to three-dimensional sheardriven dynamics to study polydomain textures and disclination loops in liquid crystalline polymers. 62 Finally, we want to point out that numerical simulations based on the Leslie-Ericksen theory on liquid crystals have also been carried out extensively.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…[66] the orientation tensor is restricted to be a two-by-two matrix and the coupled flow calculations are one-dimesional, in Ref. [61] the behavior of the Doi-Marrucci-Greco (DMG) model for nematic liquid crystalline polymers in planar shear flow is investigated where the 2D assumption of no spatial gradients in the flow direction is retained in the computations. It was found in Ref.…”

Section: Numerical Simulationsmentioning

confidence: 99%

See 2 more Smart Citations

Mathematical Studies and Simulations of Nematic Liquid Crystal Polymers and Nanocomposites

Zhou

Forest²,

Wang

2010

Jnl of Comp & Theo Nano

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Nematic liquid crystal polymers and nanocomposites have wide-ranging applications in modern technology including display devices, ultra-fast switches, high strength fibers, and materials with enhanced multi-functional properties including thermal, dielectric, electrical, and barrier properties. In this review article we provide an overview of selected mathematical issues and numerical simulations of nematic liquid crystal polymers and rigid rod nanocomposites. Some open questions will be addressed.

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Section: Numerical Simulationsmentioning

confidence: 51%

Section: Numerical Simulationsmentioning

confidence: 99%

Section: Numerical Simulationsmentioning

confidence: 99%

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Mathematical Studies and Simulations of Nematic Liquid Crystal Polymers and Nanocomposites

Zhou

Forest²,

Wang

2010

Jnl of Comp & Theo Nano

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“…Notable examples of mean field approaches to anisotropic particle interaction described in the kinetic theory framework are the model initially proposed by Hess in 1976 as mentioned by Doi and Edwards in [12], or the physically more realistic LC models proposed by Marrucci and coworkers [36][37][38][39] and of Beris and Edwards [3,[13][14][15]. In spite of the complexities associated with the constitutive equations resulting from solving the kinetic theory, major advances have been made in the coupled solution of the hydrodynamic field equations and the LC constitutive equation as well as in the evolution of LC structure in given velocity fields [9][10][11][17][18][19][20][21][22]26,35,42,45,48,49].…”

Section: Liquid-crystalline Polymers: the Doi's Modelmentioning

confidence: 99%

Reduced numerical modeling of flows involving liquid-crystalline polymers

Ammar

Prulière

Chinesta

et al. 2009

Journal of Non-Newtonian Fluid Mechanics

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a b s t r a c tKinetic theory models involving the Fokker-Planck equation can be accurately discretized using a mesh support (Finite Elements, Finite Differences, Finite Volumes, Spectral Techniques, . . .). However, these techniques involve a high number of approximation functions. In the finite element framework, widely used in complex flow simulations, each approximation function has only local support and is related to a node that defines the associated degree of freedom. In the technique proposed here, a reduced approximation basis is constructed. The new shape functions have extended support and are defined in the whole domain in an appropriate manner (the most characteristic functions related to the model solution). Thus, the number of degrees of freedom involved in the solution of the Fokker-Planck equation is very significantly reduced. The construction of those new approximation functions is done with an 'a priori' approach, which combines a basis reduction (using the Karhunen-Loève decomposition) with a basis enrichment based on the use of some Krylov subspaces. This paper analyzes the application of model reduction to the simulation of non-linear kinetic theory models involving complex behaviors, such as those coming from stability analysis, complex geometries and coupled models. We apply our model reduction approach to the Doi's classical constitutive equation for viscoelasticity of liquid-crystalline polymer.

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“…The most resolved Doi-Marrucci-Greco tensor model simulations are the two physical space dimension results from Sgalari, Leal, Feng, Klein, Garcia-Cervera, and Ceniceros [42,26,27]. Their studies presume strong anchoring along the vorticity direction, aimed at modeling the roll cell instability [30].…”

mentioning

confidence: 99%

Anchoring-induced texture & shear banding of nematic polymers in shear cells

Zhou

Forest²,

Wang³

2007

Discrete &Amp; Continuous Dynamical Systems - B

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Abstract. We numerically explore texture (resolved by the second-moment of the orientational distribution) and shear banding of nematic polymers in shear cells, allowing for one-dimensional morphology in the gap between parallel plates. We solve the coupled Navier-Stokes and Doi-Marrucci-Greco orientation tensor model, considering both confined orientation in the plane of shear and full orientation tensor degrees of freedom, and both primary flow and vorticity (in the full tensor model) components. This formulation makes contact with a large literature on analytical and numerical (cf. the review [41]) as well as experimental (cf. the review [45]) studies of nematic polymer texture and flow feedback. Here we focus on remarkable sensitivity of texture & shear band phenomena to plate anchoring conditions on the orientational distribution. We first explore steady in-plane flow-nematic states at low Peclet (P e) and Ericksen (Er) numbers, where asymptotic analysis provides exact texture scaling properties [18,6]. We illustrate that in-plane steady states co-exist with, and are unstable to, out-of-plane steady states, yet the structures and their scaling properties are not dramatically different. Non-Newtonian shear bands arise through orientational stresses. They are explored first for steady states, where we show the strength and gap location of shear bands can be tuned with anchoring conditions. Next, unsteady flow-texture transitions associated with the Ericksen number cascade are explored. We show the critical Er of the steady-to-unsteady transition, and qualitative features of the spacetime attractor, are again strongly dependent on wall anchoring conditions. Other simulations highlight unsteady flow-nematic structures over 3 decades of the Ericksen number, comparisons of shear banding and texture features for in-plane and out-of-plane models, and vorticity generation in out-of-plane attractors.

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Ericksen number and Deborah number cascade predictions of a model for liquid crystalline polymers for simple shear flow

Cited by 22 publications

References 48 publications

Mathematical Studies and Simulations of Nematic Liquid Crystal Polymers and Nanocomposites

Mathematical Studies and Simulations of Nematic Liquid Crystal Polymers and Nanocomposites

Reduced numerical modeling of flows involving liquid-crystalline polymers

Anchoring-induced texture & shear banding of nematic polymers in shear cells

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