Fluid-flow-induced pattern formation in liquid crystals in a rotating magnetic field

We present a numerical study of pattern formation in the asynchronous regime of a homeotropically aligned nematic liquid crystal under the influence of an in-plane continuously rotating magnetic field. Experimentally, this system has been shown to produce several pattern-forming states. Here, we test the hypothesis that these dynamic patterns exist due to a coupling between spatial gradients in the nematic director and gradients in the fluid flow. We derive the equations of motion coupling the director and hydrodynamic flow from the Leslie-Erickson equations and numerically integrate them in the asynchronous regime. We show that there are two pathways by which a sample that is initially in a homogeneous state can evolve into a dynamic pattern. The first path is through a large external disturbance which nucleates pattern formation and the second is through the amplification of thermal fluctuations, both of which are experimentally observed. We find that the fluid-flow coupling is essential in order to reproduce the experimental behavior. Intuitively, the coupling of the director with the flow creates a lower effective viscosity than in the absence of the flow.