Journal of Rheology, Vol.53, No.3, 589-615, 2009
Dynamic defect morphology and hydrodynamics of sheared nematic polymers in two space dimensions
Dynamic (unsteady) defect structures arising in the hydrodynamics of sheared nematic polymers are investigated by numerical simulations and real-time diagnostics in two space dimensions. We simulate the Larson-Mead experiments on roll-cell formation and breakup, following recent numerical studies with a similar model [Klein et al., Phys. Fluids 19, 023101 (2007a); Klein, D. H., Ph.D. thesis, University of California, Santa Barbara (2007b)]. The simulations are blindly monitored on the basis of tensorial defect metrics defined by eigenvalue degeneracies, which are local in space and time, and monitored cost free. The focus in the defect detection is shifted from topology to local conditions, yet the nonlocality of defect domains is recovered by graphics of metric level sets. These tools reveal the spawning of an array of oblate defect core domains, which then deform, propagate, collide, merge, and split in a dynamic process that numerically continues ad infinitum. Next, we paint topological features onto snapshots of the level set texture of the oblate metric, using the remainder of the tensor information: first, the full tensor morphology (triaxial ellipsoids per grid point), and then the principal axis (where identifiable) of each orientation ellipsoid. These enhanced textures yield the traditional topological defect metric based on nonlocal winding number of the principal axis and the regularization of each apparent half integer and integer degree singularity. The most compelling predictions of these simulations and diagnostics are persistence of interacting oblate defect domains, while topology is highly transient, and coincidence of topological transitions with oblate domain merger and splitting. Finally, the coupling between orientation features and the transient primary and secondary flow are amplified with additional graphics. (C) 2009 The Society of Rheology. [DOI: 10.1122/1.3089622]