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Abstract
The aim of this work is to model and simulate processing-induced
heterogeneity in rigid, rod-like nematic polymers in viscous
solvents. We employ a mesoscopic orientation tensor model due to
Doi, Marrucci and Greco which extends the small molecule, liquid
crystal theory of Leslie-Ericksen-Frank to nematic polymers. The
morphology has various physical realizations, all coupled through
the model equations: the orientational distribution of the ensemble
of rods, anisotropic viscoelastic stresses, and flow feedback.
Previous studies in plane Couette & Poiseuille flow (with the
exception of [7]) have focused on the coupling between hydrodynamics
and the orientational distribution of rigid rod polymers with
identical anchoring conditions at solid boundaries; without flow,
the equilibrium structure is homogeneous. Here we explore steady
structures that emerge with mismatch anchoring conditions at the
walls, which couple an equilibrium elastic distortion across the
channel, short and long range elasticity potentials, and
hydrodynamics. In plane Couette (where moving plates drive the
flow) and Poiseuille flow (where a pressure gradient drives the
flow), in the regime of weak flow and strong distortional
elasticity, asymptotic analysis yields closed-form steady solutions
and scaling laws with identical wall conditions. We focus
simulations in this regime to expose the effects due to wall
anchoring conflicts, and illustrate the induced morphology of the
orientational distribution, stored viscoelastic stresses, and
non-Newtonian flow. A remarkably simple diagnostic emerges in this
physical parameter regime, in which salient morphology features are
controlled by the amplitude and sign of the difference in plate
anchoring angles of the director field at the two plates.
Mathematics Subject Classification: 37C45.
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