Complex polymer orientation

Gilbert, Peter H.; Giacomin, A. Jeffrey

doi:10.1016/j.polymer.2016.05.046

Cited by 10 publications

(8 citation statements)

References 26 publications

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“…Figure 16B and Figure 16C show the orientation distributions associated with the fourth harmonic components in and out-of-phase with cos 4ωt , respectively. Figure 16 corrects Figure 7 of [23]. To study the fourth harmonic contribution to tumbling and wobbling of the total orientation distribution, we plot the side and top views of Figure 16 shown in Figure 17 and Figure 18.…”

Section: Fourth Harmonicmentioning

confidence: 83%

“…(15) of [8]; Eq. (14.4-1) of [9]; see [10], [11], [12], [13], [14], [15] to explore diffusion equation and application; see also Table I. of [16], Table I.…”

Section: Introductionmentioning

confidence: 99%

“…(81) and (82) of [22]). In this paper, we use these general results as a starting point to derive the Fourier solution for the special case of largeamplitude oscillatory shear flow [23].…”

Section: Introductionmentioning

confidence: 99%

“…(19) through (20) of [17] or Eqs. (12) through (20) of [23]). This prior analysis of the molecular dynamics included the three most important regimes: nonlinear steady shear flow λω ,λ !…”

Section: Introductionmentioning

confidence: 99%

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Macromolecular tumbling and wobbling in large-amplitude oscillatory shear flow

Jbara

Giacomin

2019

Physics of Fluids

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For a suspension of rigid dumbbells, in any simple shear flow, we recently solved for the diffusion equation for the orientation distribution function by a power series expansion in the shear rate magnitude. In this paper, we focus specifically on large-amplitude oscillatory shear flow (LAOS), for which we extend the orientation distribution function to the 6th power of the shear rate amplitude. We arrive at the Fourier solution for each harmonic contribution to the total orientation distribution function, separating each harmonic into its coefficients in and out-of-phase with cosnωt , ′ ψ n and ′′ ψ n , respectively. We plot, for the first time, the evolving normalized alternant macromolecular orientation. Moreover, to deepen our understanding of the macromolecular motions, we distinguish and study the two types of possible rotations, tumbling and wobbling.*Corresponding author (giacomin@queensu.ca) CONTENTS

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Section: Fourth Harmonicmentioning

confidence: 83%

“…(15) of [8]; Eq. (14.4-1) of [9]; see [10], [11], [12], [13], [14], [15] to explore diffusion equation and application; see also Table I. of [16], Table I.…”

Section: Introductionmentioning

confidence: 99%

“…(81) and (82) of [22]). In this paper, we use these general results as a starting point to derive the Fourier solution for the special case of largeamplitude oscillatory shear flow [23].…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Macromolecular tumbling and wobbling in large-amplitude oscillatory shear flow

Jbara

Giacomin

2019

Physics of Fluids

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“…; see refs. to explore diffusion equation and application; see also Table I of ref. , Table I of ref.…”

Section: Introductionmentioning

confidence: 99%

Orientation Distribution Function Pattern for Rigid Dumbbell Suspensions in Any Simple Shear Flow

Jbara

Giacomin

2018

Macro Theory & Simulations

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For rigid dumbbells suspended in a Newtonian solvent, the viscoelastic response depends exclusively on the dynamics of dumbbell orientation. The orientation distribution function ψ(θ, φ, t) represents the probability of finding dumbbells within the range (θ, θ + dθ) and (φ, φ + dφ). This function is expressed in terms of a partial differential equation (the diffusion equation), which, for any simple shear flow, is solved by postulating a series expansion in the shear rate magnitude. Each order of this expansion yields a new partial differential equation, for which one must postulate a form for its solution. This paper finds a simple and direct pattern to these solutions. The use of this pattern reduces the amount of work required to determine the coefficients of the power series expansion of the orientation distribution function, ψ i . To demonstrate the usefulness of this new pattern, new expressions for these coefficients are derived up to and including the sixth power of the shear rate magnitude. This work also completes previous findings that ended at the fourth power of the shear rate magnitude.

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