Molecular representation of the 4-Cyano-4'-pentylbiphenyl (5CB) and its corresponding molecular director . The 5CB molecule can be represented by a rodlike ellipsoid; and average of molecular orientations give the system director . The LCs can adopt perpendicular (homeotropic) or parallel (planar) configurations at a confining surface.
Lid-driven cavity flow geometry, where the “lid” at y/H = 1.0 moves at a constant speed V. (a) Velocity field for a Newtonian fluid at a Reynolds number 100. This velocity field was calculated using RBF (Ref. 57). (b) Wall anchoring (strong) and initial orientation of the LC.
Cavity with a stationary lid. Scalar order parameter contours, local directors and streamlines at various times. (a) After a short time, defects form at each corner and near the center of the walls at y/H = 0, 1. (b) As the meta-stable state begins to collapse, the two defects near the wall approach the diagonal corners. (c) The wall and corner defects begin to join. (d) The final stable state has defects in all corners, and the system has zero net topological charge.
Cavity with a lid moving at Er = 2. Scalar order parameter contours, local directors and streamlines at various times. (a) After a short time, disordered areas form near the lid (y/H = 1) and bottom (y/H = 0) of the cavity. (b) The moving lid prevents any defect from forming near the lid center, and the flow pushes the defect at the bottom surface off-center. (c) At the moving lid, no defects are present away from the corners, and the bottom surface shows the defect displaced far off-center. (d) The final stable defect configuration has defects in all corners, and the system has zero net topological charge. This steady state is reached far more quickly with the lid moving at this moderate speed.
Thin film of a LC with an initial rotation of the director in the center. This rotation produces two defects of opposing strength that annihilate each other in order to adopt a uniform orientation.
Defect displacements versus time. In all cases, the distances plotted are s = +1/2 defect displacement (◯), s = −1/2 defect displacement (△), and the defect separation (□) versus time for different scenarios. (a) 2D, no flow. (b) 3D, no flow. The two defects are indistinguishable in their relaxation when flow effects are omitted. They relax at the same rate an meet at the x/H = 3 midplane of the thin film. (c) 2D, flow. (d) 3D, flow. When flow is included, the defects meet at a position off-center of the original x/H = 3 midplane. Additionally, the overall relaxation and annihilation process occurs faster when flow is included.
Order parameter contours and velocity streamlines at various times during the relaxation of two line defects in a thin film of liquid crystal. (a) At the flow exhibits vortices near defects and a net flow in the positive x-direction. (b) At the vortices appear to follow the defects as they move. (c) At the defects are in close proximity, and the flow disturbances interact to form a new structure.
Shear stress maps at , where a flow has developed but no noticeable defect motion has occurred. (a) , the shear component of the viscous stress. (b) . This elastic stress forms lobes that surround and follow the defects as they relax. (c) , the shear stress of largest magnitude which drives a flow in the +x direction, away from the s = +1/2 defect. (d) .
Shear stress maps at . (a) . (b) . The lobes around each defect begin interacting and displace slightly. (c) . (d) . These final two stress components are only present in the central region with a rotation of the director, and as this region recedes, so does the region of high stress.
Shear stress maps at . (a) . (b) . The lobes have been completely displaced from the original positions, leaving an eight lobe stress structure surrounding the region of low order parameter where the defects have met to combine. (c) . (d) . These nonequilibrium stresses diminish and eventually disappear as the order parameter S returns to the bulk value dictated by the temperature parameter U.
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