RESUMEN
Films and molds of
nematic polymer materials are notorious for heterogeneity in the
orientational distribution of the rigid rod or platelet macromolecules.
Predictive tools for structure length scales generated by shear-dominated processing
are vitally important: both during processing because of flow feedback
phenomena such as shear thinning or thickening, and postprocessing since
gradients in the rod or platelet ensemble translate to nonuniform
composite properties and to residual stresses in the material. These
issues motivate our analysis of two prototypes for planar shear
processing: drag-driven Couette and pressure-driven Poiseuille flows.
Hydrodynamic theories for high aspect ratio rod and platelet
macromolecules in viscous solvents are well developed, which we
apply in this paper to model the coupling between short-range
excluded volume interactions, anisotropic distortional elasticity
(unequal elasticity constants), wall anchoring conditions, and hydrodynamics.
The goal of this paper is to generalize scaling properties of
steady flow molecular structures in slow Couette flows with equal
elasticity constants [M. G. Forest et al., J. Rheol., 48 (2004), pp.
175-192] in several ways: to contrast isotropic and anisotropic
elasticity; to compare Couette versus Poiseuille flow; and to
consider dynamics and stability of these steady states within the
asymptotic model equations.