Steady Flow of a Nematic Liquid Crystal in a Slowly Varying Channel

Carou, J. Quintans; Duffy, Brian; Mottram, Nigel J.; Wilson, S. K.

doi:10.1080/15421400590955569

Cited by 7 publications

(5 citation statements)

References 6 publications

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“…The normal stress boundary condition in these papers neglects the contribution of the elastic stress tensor, which leads to a change in sign of the elastic contribution in the free surface evolution equation. A third approach used by Carou et al [25][26][27] scales the nematic elasticity such that, to leading order, the free surface is unaffected by the elasticity, and one recovers the Newtonian thin Second, as for isotropic liquids with film thickness below about 100 nm, long-and short-range effective intermolecular forces between the substrate and the free surface have to be taken into account possibly through a Derjaguin or disjoining pressure that describes wettability effects 39 .…”

Section: Discussionmentioning

confidence: 99%

“…One can see that the nematic elasticity as well as viscosity only have influence on the mobility function Q, and thus have no influence on the stability of a free surface. This formulation has been studied extensively by Carou et al [25][26][27] both analytically and numerically under the assumption of small director variation.…”

Section: A Weak Elasticity ( = δ)mentioning

confidence: 99%

“…Another long-wave model was introduced by Carou et al to study blade coating and cavity filling flows of NLC in 2D [25][26][27] . However, none of these long-wave evolution equations agree with models that use energy arguments 9 , when it comes to identifying the effect of the elastic distortion energy on the film dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…7, 22-24, but in Refs. [25][26][27] it is predicted to have no influence on the stability of the film.…”

Section: Introductionmentioning

confidence: 99%

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Note on the hydrodynamic description of thin nematic films: Strong anchoring model

et al. 2013

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We discuss the long-wave hydrodynamic model for a thin film of nematic liquid crystal in the limit of strong anchoring at the free surface and at the substrate. We rigorously clarify how the elastic energy enters the evolution equation for the film thickness in order to provide a solid basis for further investigation: several conflicting models exist in the literature that predict qualitatively different behaviour. We consolidate the various approaches and show that the long-wave model derived through an asymptotic expansion of the full nemato-hydrodynamic equations with consistent boundary conditions agrees with the model one obtains by employing a thermodynamically motivated gradient dynamics formulation based on an underlying free energy functional. As a result, we find that in the case of strong anchoring the elastic distortion energy is always stabilising. To support the discussion in the main part of the paper, an appendix gives the full derivation of the evolution equation for the film thickness via asymptotic expansion.

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Section: Discussionmentioning

confidence: 99%

Section: A Weak Elasticity ( = δ)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…7, 22-24, but in Refs. [25][26][27] it is predicted to have no influence on the stability of the film.…”

Section: Introductionmentioning

confidence: 99%

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Note on the hydrodynamic description of thin nematic films: Strong anchoring model

et al. 2013

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“…These solutions can be viewed as the limiting profiles as the elastic constant tends to zero of the antisymmetric nematic field in the channel observed numerically in [40], cf. in particular with the approximate formula ( 29) therein, see also [41]. In the presence of active terms, some of the found passive solutions continue to exist and exhibit non-zero flow that can be spontaneously initiated from zero, for example, by increasing the film thickness, similar to the effect observed in [9,12].…”

Section: Introductionmentioning

confidence: 56%

Thin-film models for an active gel

2018

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In this study we present a free-boundary problem for an active liquid crystal based on the Beris-Edwards theory that uses a tensorial order parameter and includes active contributions to the stress tensor to analyse the rich defect structure observed in applications such as the Adenosinetriphosphate (ATP) driven motion of a thin film of an actin filament network. The small aspect ratio of the film geometry allows for an asymptotic approximation of the free-boundary problem in the limit of weak elasticity of the network and strong active terms. The new thin film model captures the defect dynamcs in the bulk as well as wall defects and thus presents a significant extension of previous models based on the Lesli-Erickson-Parodi theory. Analytic expression are derived that reveal the interplay of anchoring conditions, film thickness and active terms and their control of transitions of flow structure. *

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On the simulation of nematic liquid crystalline flows in a 4:1 planar contraction using the Leslie–Ericksen and Beris–Edwards models

Fedorowicz

Prosser²

2022

Journal of Non-Newtonian Fluid Mechanics

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Steady Flow of a Nematic Liquid Crystal in a Slowly Varying Channel

Cited by 7 publications

References 6 publications

Note on the hydrodynamic description of thin nematic films: Strong anchoring model

Note on the hydrodynamic description of thin nematic films: Strong anchoring model

Thin-film models for an active gel

On the simulation of nematic liquid crystalline flows in a 4:1 planar contraction using the Leslie–Ericksen and Beris–Edwards models

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