Simulating Complex Flows of Liquid Crystalline Polymers Using the Doi Theory

J. Feng and L. G. Leal

*J. Rheol*. **41**, 1317-1335
(1997)

**Abstract** - We simulate the startup flow of lyotropic liquid
crystalline polymers (LCPs) in an eccentric cylinder geometry. The objectives
are to explore the mechanisms for the generation of disclinations in a
non-homogeneous flow and to study the coupling between the flow and the polymer
configuration. The Doi theory, generalized to spatially varying flows and
approximated by the quadratic closure, is used to model the evolution of
LCP configurations. This, along with the equations of motion for the fluid,
is solved by a finite element method. The flow modification by the polymer
stress is mild for the parameters used, but the LCP exhibits complex
orientational behavior in different regions of the flow domain. For relatively
weak nematic strength, a steady state is reached in which the director is
oriented either along or transverse to the streamline depending upon local
flow conditions and the deformation history. A pair of disclinations, with
strength ±1/2, are identified in the steady state and the LCP configuration
at the disclinations confirms the model of a structured defect core proposed
by Greco & Marrucci (1992). For strong nematic strength, director tumbling
occurs in the more rotational regions of the flow field, giving rise to a
polydomain structure. The boundary of the tumbling domain consists of two
disclinations of ±1/2 strength, a structure very similar to previous
experimental observations of LCP domains.