Resumen
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.
The linear stability of perturbed simple shear in a ductile plastic material which can strain-soften is analyzed on a finite time interval. An asymptotic study is made of the influence of two small dimensionless coefficients, which are shown to be connected by a similarity parameter. The first coefficient is a dimensionless group of parameters which can be interpreted as the ratio of the momentum flux to the plastic flow stress, while the second coefficient gives the scale of the viscous damping. A criterion is derived for the minimum strain rate where the early-time behavior changes from oscillatory to exponential.