Modeling flow of nematic liquid crystal down an incline

Lam, Michael; Cummings, L. J.; Lin, Te-Sheng; Kondic, Lou

doi:10.1007/s10665-014-9697-2

Cited by 13 publications

(26 citation statements)

References 26 publications

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“…In the work of Sharma & Verma (2004), the solution that satisfies the above far-field conditions is referred to as a pancake solution. We will refer to this solution as a front solution since (4.22) and (4.23) are analogous to the far-field conditions used for a travelling front solution in our previous work (see Lam et al 2014). Note that the same nomenclature is used by Thiele et al (2001); the derivation of the front solution in that work is slightly different to that presented here, however, the two methods yield the same result.…”

Section: Metastability: Analytical Findingsmentioning

confidence: 83%

“…where ∇G(h) is the gradient of the free surface anchoring energy. The derivation of G(h) is nontrivial and we refer the reader to our previous work for further details (Lam et al 2014;Lin et al 2013b). Since the second term on the right hand side of the last equation in (2.22) is always stabilising, instability arises from the gradients of the free surface anchoring energy (the last term in (2.22)), present only for non-constant m(h) (i.e., only for weak anchoring).…”

Section: Comparison To Other Modelsmentioning

confidence: 99%

“…Note 1: The speed of the propagating front, (4.19), may alternatively be obtained by using pinch point analysis, with a key difference of how the complex integral path is chosen in the Fourier representation (4.10). Our previous results (see Lam et al 2014) for the flow of an NLC film down an inclined plane relied on the results of such analysis to derive the velocity of the wave packet boundaries (V in the MSC analysis). In that work, analytical and numerical simulations confirmed the existence of three stability regimes behind the front travelling down the inclined plane: stable, convectively unstable, and absolutely unstable.…”

Section: Marginal Stability Criterion: Outlinementioning

confidence: 99%

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Stability of thin fluid films characterised by a complex form of effective disjoining pressure

2018

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We discuss instabilities of fluid films of nanoscale thickness, with a particular focus on films where the destabilising mechanism allows for linear instability, metastability, and absolute stability. Our study is motivated by nematic liquid crystal films; however we note that similar instability mechanisms, and forms of the effective disjoining pressure, appear in other contexts, such as the well-studied problem of polymeric films on twolayered substrates. The analysis is carried out within the framework of the long-wave approximation, which leads to a fourth order nonlinear partial different equation for the film thickness. Within the considered formulation, the nematic character of the film leads to an additional contribution to the disjoining pressure, changing its functional form. This effective disjoining pressure is characterised by the presence of a local maximum for nonvanishing film thickness. Such a form leads to complicated instability evolution that we study by analytical means, including application of marginal stability criteria, and by extensive numerical simulations that help us develop a better understanding of instability evolution in the nonlinear regime. This combination of analytical and computational techniques allows us to reach novel understanding of relevant instability mechanisms, and of their influence on transient and fully developed fluid film morphologies. arXiv:1704.03919v1 [cond-mat.soft]

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Section: Metastability: Analytical Findingsmentioning

confidence: 83%

Section: Comparison To Other Modelsmentioning

confidence: 99%

Section: Marginal Stability Criterion: Outlinementioning

confidence: 99%

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Stability of thin fluid films characterised by a complex form of effective disjoining pressure

2018

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“…17, to give U = w p R/H. As an inclined plane and channel flows (see, for example, [23][24][25][26][27]).…”

Section: Boundary Conditionsmentioning

confidence: 99%

“…(65), and integrate with respect tor and impose the condition on the pressure gradient, Eq. (26), which leads to…”

Section: The Limit Of Small Ericksen Numbermentioning

confidence: 99%

Squeezing a drop of nematic liquid crystal with strong elasticity effects

et al. 2019

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The One Drop Filling (ODF) method is widely used for the industrial manufacture of liquid crystal devices. Motivated by the need for a better fundamental understanding of the reorientation of the molecules due to the flow of the liquid crystal during this manufacturing method, we formulate and analyse a squeeze-film model for the ODF method. Specifically, we consider a nematic squeeze film in the asymptotic regime in which the drop is thin, inertial effects are weak, and elasticity effects are strong for four specific anchoring cases at the top plate and the substrate (namely, planar, homeotropic, hybrid aligned nematic (HAN), and π-cell infinite anchoring conditions) and for two different scenarios for the motion of the top plate (namely, prescribed speed and prescribed force). Analytical expressions for the leading-and first-order director angles, radial velocity, vertical velocity, and pressure are obtained. Shear and couple stresses at the top plate and the substrate are calculated and are interpreted in terms of the effect that flow may have on the alignment of the molecules at the plates, potentially leading to the formation of spurious optical defects ("mura").

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Nonlinear emergent macroscale PDEs, with error bound, for nonlinear microscale systems

Bunder

Roberts

2021

SN Appl. Sci.

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Many multiscale physical scenarios have a spatial domain which is large in some dimensions but relatively thin in other dimensions. These scenarios includes homogenization problems where microscale heterogeneity is effectively a ‘thin dimension’. In such scenarios, slowly varying, pattern forming, emergent structures typically dominate the large dimensions. Common modelling approximations of the emergent dynamics usually rely on self-consistency arguments or on a nonphysical mathematical limit of an infinite aspect ratio of the large and thin dimensions. Instead, here we extend to nonlinear dynamics a new modelling approach which analyses the dynamics at each cross-section of the domain via a multivariate Taylor series (Roberts and Bunder in IMA J Appl Math 82(5):971–1012, 2017. 10.1093/imamat/hxx021). Centre manifold theory extends the analysis at individual cross-sections to a rigorous global model of the system’s emergent dynamics in the large but finite domain. A new remainder term quantifies the error of the nonlinear modelling and is expressed in terms of the interaction between cross-sections and the fast and slow dynamics. We illustrate the rigorous approach by deriving the large-scale nonlinear dynamics of a thin liquid film on a rotating substrate. The approach developed here empowers new mathematical and physical insight and new computational simulations of previously intractable nonlinear multiscale problems.

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Modeling flow of nematic liquid crystal down an incline

Cited by 13 publications

References 26 publications

Stability of thin fluid films characterised by a complex form of effective disjoining pressure

Stability of thin fluid films characterised by a complex form of effective disjoining pressure

Squeezing a drop of nematic liquid crystal with strong elasticity effects

Nonlinear emergent macroscale PDEs, with error bound, for nonlinear microscale systems

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