Advection of nematic liquid crystals by chaotic flow

Consideration is given to the effects of inhomogeneous shear flow (both regular and chaotic) on nematic liquid crystals in a planar geometry. The Landau-de Gennes equation coupled to an externally prescribed flow field is the basis for the study: this is solved numerically in a periodic spatial domain. The focus is on a limiting case where the advection is passive, such that variations in the liquid-crystal properties do not feed back into the equation for the fluid velocity. The main tool for analyzing the results (both with and without flow) is the identification of the fixed points of the dynamical equations without flow, which are relevant (to varying degrees) when flow is introduced. The fixed points are classified as stable/unstable and further as either uniaxial or biaxial. Various models of passive shear flow are investigated. When tumbling is present, the flow is shown to have a strong effect on the liquid-crystal morphology; however, the main focus herein is on the case without tumbling. Accordingly, the main result of the work is that only the biaxial fixed point survives as a solution of the Q-tensor dynamics under the imposition of a general flow field. This is because the Q-tensor experiences not only transport due to advection but also co-rotation relative to the local vorticity field. A second result is that all families of fixed points survive for certain specific velocity fields, which we classify. We single out for close study those velocity fields for which the influence of co-rotation effectively vanishes along the Lagrangian trajectories of the imposed velocity field. In this scenario, the system exhibits coarsening arrest, whereby the liquid-crystal domains are "frozen in" to the flow structures, and the growth in their size is thus limited. Published by AIP Publishing.