Computational fluid dynamics for nematic liquid crystals

Ramage, Alison and Sonnet, Andre M. (2016) Computational fluid dynamics for nematic liquid crystals. BIT Numerical Mathematics, 56 (2). pp. 1-14. ISSN 0006-3835 (https://doi.org/10.1007/s10543-015-0586-5)

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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.

ORCID iDs

Ramage, Alison ORCID logoORCID: https://orcid.org/0000-0003-4709-0691 and Sonnet, Andre M. ORCID logoORCID: https://orcid.org/0000-0003-2583-7897;
  • Item type:Article
    ID code:54752
    Dates:
    Date
    Event
    1 June 2016
    Published
    13 November 2015
    Published Online
    23 October 2015
    Accepted
    Notes:The final publication is available at Springer via http://dx.doi.org/10.1007/s10543-015-0586-5
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:11 Dec 2015 01:27
    Last modified:11 Nov 2024 11:14
    Related URLs:
    URI:https://strathprints.strath.ac.uk/id/eprint/54752
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