Padé approximants for large-amplitude oscillatory shear flow

Giacomin, A. Jeffrey; Saengow, Chaimongkol; Guay, Martin; Kolitawong, Chanyut

doi:10.1007/s00397-015-0856-9

Cited by 22 publications

(19 citation statements)

References 75 publications

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“…The truncation of the power series of Eq. (7) can be usefully approximated with ratios of polynomials 6) , and this is especially useful for molecular theory where extending these series can be prohibitively laborious (compare Eq. (20) of [25] with Eq.…”

Section: Increasing Either the Weissenberg Number Or Thementioning

confidence: 99%

“…More and more, physicists deepen their understanding of complex fluids this way. The present paper aims to help this growing community of scholars, both scientists and engineers, to exploit contemporary rheological theory that, with few exceptions [3][4][5] , takes the form of expansions truncated after one of the first few harmonics of the shear stress, or of the normal stress difference responses 6) .…”

Section: Introductionmentioning

confidence: 99%

“…(2) (Eq. (2) of [10]): (4) where the dimensionless Deborah and Weissenberg numbers are given by: (5), (6) each of which reflects both a property of the fluid, λ and property of the flow. In this paper, we follow Dealy et al 22) in plotting loops of shear stress versus shear rate, since these best bring out material nonlinearities as distortions from ellipticity [22][23][24] .…”

Section: Introductionmentioning

confidence: 99%

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Simple Accurate Expressions for Shear Stress in Large-Amplitude Oscillatory Shear Flow

Saengow

Giacomin

Khalaf

et al. 2017

J. Soc. Rheol., Jpn

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Analytical solutions for shear stress in large-amplitude oscillatory shear flow (LAOS), for continuum or molecular models, often take the form of the first few terms of a power series in the shear rate amplitude. For corotational models, we get this truncated series using the Goddard-Miller integral expansion (GIE). Our previous work shows that the best Padé approximants for this truncated series, and specifically for the corotational Maxwell model in LAOS, can agree closely with the corresponding exact solution. We observe this close agreement, even for the Padé approximant for the series truncated after the fifth shear stress harmonic. In this paper, we begin with the extension of the GIE truncated after the next, seventh, order in the shear rate amplitude [Phys. Fluids 29, 043101 (2017)], and we then explore its Padé approximants. We uncover its best approximant, the [2,4], and compare it with both the GIE and the exact solution [Macromol. Theory Simul. 24, 352 (2015)]. We use Ewoldt grids to show the stunning accuracy of the [2,4] approximant in LAOS. We quantify this accuracy with an objective function and then map this function onto Pipkin space. We find the [2,4] approximant (from the GIE truncated after the seventh order in the shear rate amplitude) to be a simple accurate expression for the shear stress in LAOS. Our worked examples illustrate how researchers can use our new approximant reliably. For this, we use the Spriggs relations to extend the Padé approximant to multimode.

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Section: Increasing Either the Weissenberg Number Or Thementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Simple Accurate Expressions for Shear Stress in Large-Amplitude Oscillatory Shear Flow

Saengow

Giacomin

Khalaf

et al. 2017

J. Soc. Rheol., Jpn

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“…of [16], Table I. of [17], Table 3 of [18], Table I. of [ 19 ]) in the following power series expansion in λ !…”

Section: Introductionmentioning

confidence: 99%

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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“…Chai focused on oscillatory shear performed at large amplitudes (LA), where the molecules are grossly distorted from their shapes at rest. Chai arrived at the first exact mathematical equations for interpreting the stresses associated with these gross distortions in LAOS …”

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confidence: 99%

2017 winner of The Canadian Journal of Chemical Engineering award for best graduate student paper

2017

Can J Chem Eng

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Padé approximants for large-amplitude oscillatory shear flow

Cited by 22 publications

References 75 publications

Simple Accurate Expressions for Shear Stress in Large-Amplitude Oscillatory Shear Flow

Simple Accurate Expressions for Shear Stress in Large-Amplitude Oscillatory Shear Flow

Macromolecular tumbling and wobbling in large-amplitude oscillatory shear flow

2017 winner of The Canadian Journal of Chemical Engineering award for best graduate student paper

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