Computational fluid dynamics for nematic liquid crystals

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Due to recent advances in fast iterative solvers in the field of computational fluid dynamics, more complex problems which were previously beyond the scope of standard techniques can be tackled. In this paper, we describe one such situation, namely, modelling the interaction of flow and molecular orientation in a complex fluid such as a liquid crystal. Specifically, we consider a nematic liquid crystal in a spatially inhomogeneous flow situation where the orientational order is described by a second rank alignment tensor. The evolution is determined by two coupled equations: a generalised Navier-Stokes equation for flow in which the divergence of the stress tensor also depends on the alignment tensor and its time derivative, and a convection-diffusion type equation with non-linear terms that stem from a Landau-Ginzburg-DeGennes potential for the alignment. In this paper, we use a specific model with three viscosity coefficients that allows the contribution of the orientation to the viscous stress to be cast in the form of an orientation-dependent force. This effectively decouples the flow and orientation, with each appearing only on the right-hand side of the other equation. In this way, difficulties associated with solving the fully coupled problem are circumvented and a stand-alone fast solver, such as the state-of-the-art preconditioned iterative solver implemented here, can be used for the flow equation. A time-discretised strategy for solving the flow-orientation problem is illustrated using the example of Stokes flow in a lid-driven cavity.
LanguageEnglish
Pages1-14
Number of pages15
JournalBIT Numerical Mathematics
Volume56
Issue number2
Early online date13 Nov 2015
DOIs
Publication statusPublished - 1 Jun 2016

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Nematic liquid crystals
Nematic Liquid Crystal
Computational Fluid Dynamics
Tensors
Computational fluid dynamics
Alignment
Molecular orientation
Liquid crystals
Navier Stokes equations
Tensor
Viscosity
Derivatives
Iterative Solver
Lid-driven Cavity
Complex Fluids
Iterative Solvers
Coupled Problems
Fluids
Convection-diffusion
Ginzburg-Landau

Keywords

  • computational fluid dynamics
  • nematic liquid crystal
  • complex fluids
  • iterative solvers
  • alignment tensor

Cite this

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title = "Computational fluid dynamics for nematic liquid crystals",
abstract = "Due to recent advances in fast iterative solvers in the field of computational fluid dynamics, more complex problems which were previously beyond the scope of standard techniques can be tackled. In this paper, we describe one such situation, namely, modelling the interaction of flow and molecular orientation in a complex fluid such as a liquid crystal. Specifically, we consider a nematic liquid crystal in a spatially inhomogeneous flow situation where the orientational order is described by a second rank alignment tensor. The evolution is determined by two coupled equations: a generalised Navier-Stokes equation for flow in which the divergence of the stress tensor also depends on the alignment tensor and its time derivative, and a convection-diffusion type equation with non-linear terms that stem from a Landau-Ginzburg-DeGennes potential for the alignment. In this paper, we use a specific model with three viscosity coefficients that allows the contribution of the orientation to the viscous stress to be cast in the form of an orientation-dependent force. This effectively decouples the flow and orientation, with each appearing only on the right-hand side of the other equation. In this way, difficulties associated with solving the fully coupled problem are circumvented and a stand-alone fast solver, such as the state-of-the-art preconditioned iterative solver implemented here, can be used for the flow equation. A time-discretised strategy for solving the flow-orientation problem is illustrated using the example of Stokes flow in a lid-driven cavity.",
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Computational fluid dynamics for nematic liquid crystals. / Ramage, Alison; Sonnet, Andre M.

In: BIT Numerical Mathematics , Vol. 56, No. 2, 01.06.2016, p. 1-14.

Research output: Contribution to journalArticle

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