On weak plane Couette and Poiseuille flows of rigid rod and platelet ensembles
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Authors
Zhou, Hong
Cui, Zhenlu
Forest, Gregory
Wang, Qi
Subjects
liquid crystals
nematic polymers
asymptotic expansions
partial differential equations
instability
nematic polymers
asymptotic expansions
partial differential equations
instability
Advisors
Date of Issue
2006
Date
Publisher
Society for Industrial and Applied Mathematics
Language
Abstract
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.
Type
Article
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
The article of record as published may be found at http://dx.doi.org/10.1137/04061934x
Series/Report No
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NPS Report Number
Sponsors
Air Force Office of Scientific Research, Air Force Materials Command
National Science Foundation
Army Research Office, Materials Division
National Science Foundation
Army Research Office, Materials Division
Funding
Grant F49620-02-1-0086
Grant F49620-03-1-0098
Grant DMS-0204243
Grant DMS-0308019
Grant F49620-03-1-0098
Grant DMS-0204243
Grant DMS-0308019
Format
Citation
On weak plane Couette and Poiseuille flows of rigid rod and platelet ensembles (with Z. Cui, M.G. Forest and Q. Wang), SIAM J. Appl. Math. , 66 (4), 1227-1260, 2006.
Distribution Statement
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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.