Fourier decomposition of polymer orientation in large-amplitude oscillatory shear flow

Journal Article · Thu Mar 19 00:00:00 EDT 2015 · Structural Dynamics

DOI:https://doi.org/10.1063/1.4914411· OSTI ID:1212189

Giacomin, A. J. ^[1]; Gilbert, P. H. ^[1]; Schmalzer, A. M. ^[2]

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1. Queen's Univ., Kingston, ON (Canada)
2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States). Chemical Diagnostics and Engineering.

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.

• Research Organization: Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
• Sponsoring Organization: USDOE
• Grant/Contract Number: AC52-06NA25396
• OSTI ID: 1212189
• Journal Information: Structural Dynamics, Vol. 2, Issue 2; ISSN 2329-7778
• Publisher: American Crystallographic Association/AIP
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
polymers
shear flows
nonlinear viscoelasticity
suspensions
linear viscoelasticity