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Title: 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 » 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.« less

Authors:
 [1];  [1];  [2]
  1. Queen's Univ., Kingston, ON (Canada)
  2. 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}
}

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Cited by: 19 works
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Works referenced in this record:

Komplexe Viskosit�t
journal, June 1935


The conception of a complex viscosity and its application to dielectrics
journal, January 1935


Who conceived the “complex viscosity”?
journal, March 2012


Rheometers for Molten Plastics
book, February 1985


A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (LAOS)
journal, December 2011


A novel sliding plate rheometer for molten plastics
journal, April 1989


Molecular origins of nonlinear viscoelasticity
journal, March 1998


Large-amplitude oscillatory shear flow from the corotational Maxwell model
journal, October 2011


Time‐Dependent Flows of Dilute Solutions of Rodlike Macromolecules
journal, April 1972


Viscous dissipation with fluid inertia in oscillatory shear flow
journal, September 1999


Fluid inertia in large amplitude oscillatory shear
journal, August 1998


Using large-amplitude oscillatory shear
book, January 1998


Defining nonlinear rheological material functions for oscillatory shear
journal, January 2013


Dynamics of rigid dumbbells in confined geometries Part II. Time-dependent shear flow
journal, January 1985


Kinetic theory and rheology of dumbbell suspensions with Brownian motion
book, January 1971


Non‐Newtonian Viscoelastic Properties of Rod‐Like Macromolecules in Solution
journal, April 1956


Hydrodynamic Properties of a Plane‐Polygonal Polymer, According to Kirkwood–Riseman Theory
journal, August 1969


Normal stress in a solution of a plane–polygonal polymer under oscillating shearing flow
journal, December 1977


Calculation of the nonlinear stress of polymers in oscillatory shear fields
journal, July 1982


Dilute rigid dumbbell suspensions in large-amplitude oscillatory shear flow: Shear stress response
journal, February 2014


Normal stress differences in large-amplitude oscillatory shear flow for dilute rigid dumbbell suspensions
journal, August 2015


Orientation in Large-Amplitude Oscillatory Shear: Orientation in LAOS
journal, December 2014


Large-amplitude oscillatory shear rheology of dilute active suspensions
journal, October 2014


A novel sliding plate rheometer for molten plastics
journal, April 1989


Calculation of the nonlinear stress of polymers in oscillatory shear fields
journal, July 1982


Who conceived the “complex viscosity”?
journal, March 2012


Large-amplitude oscillatory shear rheology of dilute active suspensions
journal, October 2014


Dynamics of rigid dumbbells in confined geometries Part II. Time-dependent shear flow
journal, January 1985


Normal stress differences in large-amplitude oscillatory shear flow for dilute rigid dumbbell suspensions
journal, August 2015


A review of nonlinear oscillatory shear tests: Analysis and application of large amplitude oscillatory shear (LAOS)
journal, December 2011


The conception of a complex viscosity and its application to dielectrics
journal, January 1935


Hydrodynamic Properties of a Plane‐Polygonal Polymer, According to Kirkwood–Riseman Theory
journal, August 1969


Time‐Dependent Flows of Dilute Solutions of Rodlike Macromolecules
journal, April 1972


Non‐Newtonian Viscoelastic Properties of Rod‐Like Macromolecules in Solution
journal, April 1956


Normal stress in a solution of a plane–polygonal polymer under oscillating shearing flow
journal, December 1977


Dilute rigid dumbbell suspensions in large-amplitude oscillatory shear flow: Shear stress response
journal, February 2014


Defining nonlinear rheological material functions for oscillatory shear
journal, January 2013


Works referencing / citing this record:

Exact Analytical Solution for Large-Amplitude Oscillatory Shear Flow: Exact Analytical Solution for Large-Amplitude…
journal, May 2015


Orientation Distribution Function Pattern for Rigid Dumbbell Suspensions in Any Simple Shear Flow
journal, November 2018


Exact analytical solution for large-amplitude oscillatory shear flow from Oldroyd 8-constant framework: Shear stress
journal, April 2017


Power series for normal stress differences of polymeric liquids in large-amplitude oscillatory shear flow
journal, March 2019


Macromolecular tumbling and wobbling in large-amplitude oscillatory shear flow
journal, February 2019


Macromolecular architecture and complex viscosity
journal, August 2019


Small-angle light scattering in large-amplitude oscillatory shear
journal, October 2019