On weak plane Couette and Poiseuille flows of rigid rod and platelet ensembles
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Author
Zhou, Hong
Cui, Zhenlu
Forest, Gregory
Wang, Qi
Date
2006Metadata
Show full item recordAbstract
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.
Description
SIAM J. Appl. Math., Volume 66, Issue 4, 1227-1260, 2006.
The article of record as published may be found at http://dx.doi.org/10.1137/04061934x
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.Collections
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