Numerical solution of the Ericksen–Leslie dynamic equations for two-dimensional nematic liquid crystal flows

Cruz, Pedro Alexandre da; Tomé, Murilo Francisco; Stewart, Iain W.; McKee, Sean

doi:10.1016/j.jcp.2013.03.061

Cited by 22 publications

(21 citation statements)

References 36 publications

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“…The method enables simulations of the low-Reynolds-number hydrodynamics of simple fluids, of passive liquid crystal flows [65,39,1,2,14], and finally, of active polar viscous gels. Here, we present numerical results of the time-evolution of the polarization and velocity fields in a passive liquid crystal [1,2], in an active polar film [33,32], and in active polar viscous gels with topological defects in the polarization field [33,36].…”

Section: Computational Experimentsmentioning

confidence: 99%

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A hybrid particle-mesh method for incompressible active polar viscous gels

Ramaswamy

Bourantas

Jülicher

et al. 2015

Journal of Computational Physics

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We present a hybrid particle-mesh method for numerically solving the hydrodynamic equations of incompressible active polar viscous gels. These equations model the dynamics of polar active agents, embedded in a viscous medium, in which stresses are induced through constant consumption of energy. The numerical method is based on Lagrangian particles and staggered Cartesian finite-difference meshes. We show that the method is second-order and first-order accurate with respect to grid and time-step sizes, respectively. Using the present method, we simulate the hydrodynamics in rectangular geometries, of a passive liquid crystal, of an active polar film and of active gels with topological defects in polarization. We show the emergence of spontaneous flow due to Fréedericksz transition, and transformation in the nature of topological defects by tuning the activity of the system.

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Section: Computational Experimentsmentioning

confidence: 99%

“…(1), (2), (9), (10), and (11)) of incompressible active polar viscous gels reduce to the Ericksen-Leslie equations governing passive liquid crystals flows [65,39,1,2,14]. Note that when μ = 0, Eqs.…”

Section: Passive Liquid Crystalmentioning

confidence: 99%

A hybrid particle-mesh method for incompressible active polar viscous gels

Ramaswamy

Bourantas

Jülicher

et al. 2015

Journal of Computational Physics

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“…Weinan E [9,10] has established a general nonlinear continuum theory for smectic-A liquid crystals applicable to situations with large deformation and non-trivial flow. It is an application of Ericksen-Leslie's theory of the nematic phase [8,11,12,13,18,23]. We are motivated to use similar methods to formulate a smectic-C fluid dynamics model because both smectic-A and smectic-C are liquid crystalline phases in which there is some degree of orientational order, but also some degree of positional order.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear continuum theory of smectic-C liquid crystals

Tang

Zhang

2015

Communications in Mathematical Sciences

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Here we develop a model of smectic-C liquid crystals by forming their hydrostatic and hydrodynamic theories which are motivated by W.N. E's work [Arch. Rational Mech. Anal., 137 (1997)]. A simplified model is also presented. In order to prove the rationality of the model, we establish the energy dissipative relation of the new model. Meanwhile, we verify that the system can also be obtained using asymptotic analysis when both the fluid and layers are incompressible.

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“…Recentemente, Cruz et al [34] encontraram uma solução analítica para escoamento totalmente desenvolvido em um canal bidimensional. Para obter a solução analítica para este problema foram impostas as hipóteses de escoamento totalmente desenvolvido e, na ausência de torques externos (ver Carou et.…”

Section: Validação Do Método Numérico Bidimensionalunclassified

“…Nessas condições, o sistema de equações resultantes foi resolvido analiticamente e obteve-se expressões para a velocidade u, para o ângulo de orientação do diretor φ e consequentemente, obteve-se expressões para as componentes do tensor das tensões não-newtoniano Φ ij . Detalhes de como essa solução analítica foi obtida são apresentados a seguir (para mais detalhes ver [34] ).…”

Section: Validação Do Método Numérico Bidimensionalunclassified

Solução numérica de escoamentos de cristais líquidos nemáticos

Cruz¹

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Numerical solution of the Ericksen–Leslie dynamic equations for two-dimensional nematic liquid crystal flows

Cited by 22 publications

References 36 publications

A hybrid particle-mesh method for incompressible active polar viscous gels

A hybrid particle-mesh method for incompressible active polar viscous gels

Nonlinear continuum theory of smectic-C liquid crystals

Solução numérica de escoamentos de cristais líquidos nemáticos

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