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Steady-state hydrodynamic instabilities of active liquid crystals: Hybrid lattice Boltzmann simulations

D. Marenduzzo1, E. Orlandini2, M. E. Cates1, and J. M. Yeomans3

  • 1SUPA, School of Physics, University of Edinburgh, Mayfield Road, Edinburgh EH9 3JZ, Scotland
  • 2Dipartimento di Fisica and Sezione INFN, Università di Padova, Via Marzolo 8, 35131 Padova, Italy
  • 3The Rudolf Peierls Centre for Theoretical Physics, 1 Keble Road, Oxford OX1 3NP, England

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Phys. Rev. E 76, 031921 – Published 24 September, 2007

DOI: https://doi.org/10.1103/PhysRevE.76.031921

Abstract

We report hybrid lattice Boltzmann (HLB) simulations of the hydrodynamics of an active nematic liquid crystal sandwiched between confining walls with various anchoring conditions. We confirm the existence of a transition between a passive phase and an active phase, in which there is spontaneous flow in the steady state. This transition is attained for sufficiently “extensile” rods, in the case of flow-aligning liquid crystals, and for sufficiently “contractile” ones for flow-tumbling materials. In a quasi-one-dimensional geometry, deep in the active phase of flow-aligning materials, our simulations give evidence of hysteresis and history-dependent steady states, as well as of spontaneous banded flow. Flow-tumbling materials, in contrast, rearrange themselves so that only the two boundary layers flow in steady state. Two-dimensional simulations, with periodic boundary conditions, show additional instabilities, with the spontaneous flow appearing as patterns made up of “convection rolls.” These results demonstrate a remarkable richness (including dependence on anchoring conditions) in the steady-state phase behavior of active materials, even in the absence of external forcing; they have no counterpart for passive nematics. Our HLB methodology, which combines lattice Boltzmann for momentum transport with a finite difference scheme for the order parameter dynamics, offers a robust and efficient method for probing the complex hydrodynamic behavior of active nematics.

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Outline

Information

Phys. Rev. E 76, 031921– Published 24 September, 2007
  • Received 16 February 2007

© 2007 American Physical Society

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