Lattice Boltzmann Simulations of Active Liquid Crystals Under Confinement

Nonlinear systems out of equilibrium are characterised by the emergence of spatiotemporal patterns. When these systems are subjected to confining boundaries, the interplay between the nonlinearities and boundaries creates even richer behaviour. This is especially relevant in biological materials such as tissues and organoids which grow and develop under confinement. Here, we perform lattice Boltzmann simulations of an active nematic liquid crystal in a two dimensional cavity with a moving lid. By systematically varying the activity and lid velocity, we map out the possible steady states in the isotropic as well as nematic regimes. In both regimes, the flow field consists of a circular vortex in the centre of the cavity. The activity and shear induce ordering in the isotropic phase, with the extent of ordering increasing with activity. In the nematic phase, a spectrum of static and time-dependent states is observed. In particular, for high activities, a pair of circulating +1/2 defects appears in the centre of the cavity while -1/2 defects are observed to oscillate near the walls. Our results are summarised in a detailed phase diagram.