Fourier decomposition of polymer orientation in large-amplitude oscillatory shear flow
Abstract
In our previous work, we explored the dynamics of a dilute suspension of rigid dumbbells as a model for polymeric liquids in large-amplitude oscillatory shear flow, a flow experiment that has gained a significant following in recent years. We chose rigid dumbbells since these are the simplest molecular model to give higher harmonics in the components of the stress response. We derived the expression for the dumbbell orientation distribution, and then we used this function to calculate the shear stress response, and normal stress difference responses in large-amplitude oscillatory shear flow. In this paper, we deepen our understanding of the polymer motion underlying large-amplitude oscillatory shear flow by decomposing the orientation distribution function into its first five Fourier components (the zeroth, first, second, third, and fourth harmonics). We use three-dimensional images to explore each harmonic of the polymer motion. Our analysis includes the three most important cases: (i) nonlinear steady shear flow (where the Deborah number λω is zero and the Weissenberg number λγ 0 is above unity), (ii) nonlinear viscoelasticity (where both λω and λγ 0 exceed unity), and (iii) linear viscoelasticity (where λω exceeds unity and where λγ 0 approaches zero). We learn that the polymer orientation distributionmore »
- Authors:
-
- Queen's Univ., Kingston, ON (Canada)
- Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Chemical Diagnostics and Engineering.
- Publication Date:
- Research Org.:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Org.:
- USDOE
- OSTI Identifier:
- 1212189
- Grant/Contract Number:
- AC52-06NA25396
- Resource Type:
- Journal Article: Accepted Manuscript
- Journal Name:
- Structural Dynamics
- Additional Journal Information:
- Journal Volume: 2; Journal Issue: 2; Journal ID: ISSN 2329-7778
- Publisher:
- American Crystallographic Association/AIP
- Country of Publication:
- United States
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; polymers; shear flows; nonlinear viscoelasticity; suspensions; linear viscoelasticity
Citation Formats
Giacomin, A. J., Gilbert, P. H., and Schmalzer, A. M. Fourier decomposition of polymer orientation in large-amplitude oscillatory shear flow. United States: N. p., 2015.
Web. doi:10.1063/1.4914411.
Giacomin, A. J., Gilbert, P. H., & Schmalzer, A. M. Fourier decomposition of polymer orientation in large-amplitude oscillatory shear flow. United States. https://doi.org/10.1063/1.4914411
Giacomin, A. J., Gilbert, P. H., and Schmalzer, A. M. 2015.
"Fourier decomposition of polymer orientation in large-amplitude oscillatory shear flow". United States. https://doi.org/10.1063/1.4914411. https://www.osti.gov/servlets/purl/1212189.
@article{osti_1212189,
title = {Fourier decomposition of polymer orientation in large-amplitude oscillatory shear flow},
author = {Giacomin, A. J. and Gilbert, P. H. and Schmalzer, A. M.},
abstractNote = {In our previous work, we explored the dynamics of a dilute suspension of rigid dumbbells as a model for polymeric liquids in large-amplitude oscillatory shear flow, a flow experiment that has gained a significant following in recent years. We chose rigid dumbbells since these are the simplest molecular model to give higher harmonics in the components of the stress response. We derived the expression for the dumbbell orientation distribution, and then we used this function to calculate the shear stress response, and normal stress difference responses in large-amplitude oscillatory shear flow. In this paper, we deepen our understanding of the polymer motion underlying large-amplitude oscillatory shear flow by decomposing the orientation distribution function into its first five Fourier components (the zeroth, first, second, third, and fourth harmonics). We use three-dimensional images to explore each harmonic of the polymer motion. Our analysis includes the three most important cases: (i) nonlinear steady shear flow (where the Deborah number λω is zero and the Weissenberg number λγ 0 is above unity), (ii) nonlinear viscoelasticity (where both λω and λγ 0 exceed unity), and (iii) linear viscoelasticity (where λω exceeds unity and where λγ 0 approaches zero). We learn that the polymer orientation distribution is spherical in the linear viscoelastic regime, and otherwise tilted and peanut-shaped. We find that the peanut-shaping is mainly caused by the zeroth harmonic, and the tilting, by the second. The first, third, and fourth harmonics of the orientation distribution make only slight contributions to the overall polymer motion.},
doi = {10.1063/1.4914411},
url = {https://www.osti.gov/biblio/1212189},
journal = {Structural Dynamics},
issn = {2329-7778},
number = 2,
volume = 2,
place = {United States},
year = {Thu Mar 19 00:00:00 EDT 2015},
month = {Thu Mar 19 00:00:00 EDT 2015}
}
Web of Science
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Time‐Dependent Flows of Dilute Solutions of Rodlike Macromolecules
journal, April 1972
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Normal stress in a solution of a plane–polygonal polymer under oscillating shearing flow
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Dilute rigid dumbbell suspensions in large-amplitude oscillatory shear flow: Shear stress response
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Works referencing / citing this record:
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