Nonhomogenous patterns with core defects in elongational flows of liquid crystal polymers

The interaction between flow and orientation of liquid crystalline polymers (LCPs) creates remarkable heterogeneous patterns in which defects, or sing ular solutions, serve to mediate a confluence of ordered nematic phases. Th e origin of defects remains a mystery. It is therefore valuable to have mod els for LCP flows that provide some evidence of defects, and of the corresp onding physical competition between flow and LCP properties. In this direct ion, the flow-orientation moment-averaged Doi model is studied with an impo sed elongational flow. Nonhomogeneous, biaxial nematic patterns are discove red in both axial and planar elongation. These exact solutions consist of s patially varying directors in the plane orthogonal to the flow axis, couple d with homogeneous biaxial order parameter equilibria fixed by the LCP conc entration (N) and elongation rate (nu). For each (N, nu), the following pat terns coexist all with identical order parameter values: the homogeneous pa tterns of Rey [Macromol. Theory Simul. 4, 857-872 (1995)]; radially symmetr ic director patterns; and finally, director patterns periodic in the cylind rical azimuthal angle. The nonhomogeneous structures are distinguished by t he presence of core defects along the axis of flow symmetry, characterized by a logarithmic pressure singularity at the core. (C) 1999 The Society of Rheology. [S0148-6055(99)01506-0].