Normal stress differences from Oldroyd 8-constant framework: Exact analytical solution for large-amplitude oscillatory shear flow

Saengow, Chaimongkol; Giacomin, A. Jeffrey

doi:10.1063/1.4994866

Cited by 42 publications

(37 citation statements)

References 108 publications

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“…where m is defined after Equation (33). We begin with steady shear flow, by applying Equation (44) to Equation (39). We find that S T passes the ratio test when:…”

Section: Convergencementioning

confidence: 99%

“…which can be used to arrive at corrections for flow-field heterogeneity in parallel-disk flow for LAOS, following the method of Giacomin et al [38] Following this same method, starting with Saengow and Giacomin, [39] we can arrive at a power series for the normal stress difference responses for the Oldroyd 8-constant framework in LAOS; however, we will leave this for another day.…”

Section: Steady Shear Flowmentioning

confidence: 99%

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Series expansion for shear stress in large‐amplitude oscillatory shear flow from oldroyd 8‐constant framework

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When polymeric liquids undergo large-amplitude oscillatory shear flow, the shear stress responds as a Fourier series, the higher harmonics of which are caused by the fluid nonlinearity, and the first harmonic of which is a nonlinear function of both the frequency and the shear rate amplitude. The Oldroyd 8-constant framework for continuum constitutive theory contains a rich diversity of popular special cases for polymeric liquids. The shear stress response for the Oldroyd 8-constant framework has recently yielded to exact analytical solution. However, in its closed form, Bessel functions appear 24 times, each within infinite summations. In this paper, to simplify the exact solution, we expand it in a Taylor series. We truncate the series after its 16th power of the shear rate amplitude. Our main result reduces to the well known expression for the corotational Jeffreys and corotational Maxwell fluids. Whereas these special cases yielded to the Goddard integral expansion (GIE), the more general Oldroyd 8-constant framework does not. We use Ewoldt grids to show our main result to be highly accurate, for the corotational Jeffreys and corotational Maxwell fluids. For these two special cases, our solutions agree closely with the exact solutions so long as Wi=De < 7 2 . We apply our main result for the special case of the Johnson-Segalman fluid to describe the measured frequency sweep and shear rate amplitude sweep responses of molten atactic polystyrene. For this, we use the Spriggs relations to generalize our main result to multimode, which then agrees closely with the measured responses.

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“…where m is defined after Equation (33). We begin with steady shear flow, by applying Equation (44) to Equation (39). We find that S T passes the ratio test when:…”

Section: Convergencementioning

confidence: 99%

Section: Steady Shear Flowmentioning

confidence: 99%

Series expansion for shear stress in large‐amplitude oscillatory shear flow from oldroyd 8‐constant framework

et al. 2019

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“…(29)- (35) are much more compact than Eqs. (66)-(70) of [19] (or than (56)-(62) of [39]). We find Eqs.…”

Section: Exact Solutionsmentioning

confidence: 99%

“…For SAOS, for the Oldroyd 8-constant framework, and thus, for all of its special cases, the expression for the real part and minus the imaginary part of both complex normal stress coefficients are given by (Eqs. (32)-(34) of [39]):…”

Section: Introductionmentioning

confidence: 99%

Exact solutions for oscillatory shear sweep behaviors of complex fluids from the Oldroyd 8-constant framework

Saengow

Giacomin

2018

Physics of Fluids

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Large-amplitude oscillatory shear flow (LAOS) is a popular for studying the nonlinear physics of complex fluids. Specifically, the strain rate sweep (also called the strain sweep) is used routinely to identify the onset of nonlinearity. In this paper, we give exact expressions for the nonlinear complex viscosity and the corresponding nonlinear complex normal stress coefficients for the Oldroyd 8-constant framework for oscillatory shear sweeps. We choose the Oldroyd 8-constant framework for its rich diversity of popular special cases (we list 18 of these). We evaluate the Fourier integrals of our previous exact solution to get exact expressions for the real and imaginary parts of the complex viscosity, and for the complex normal stress coefficients, as functions of both test frequency and shear rate amplitude. For our comparisons with data, we use the Spriggs relations to generalize the Oldroyd 8-constant framework to multimode. We explore the role of infinite shear rate viscosity on strain rate sweep responses for the special case of the corotational Jeffreys fluid. We find that raising η ∞ , raises the real part of the complex viscosity, and lowers the imaginary. In our worked examples, we thus first use the corotational Jeffreys fluid, and then, for greater accuracy, we use the Johnson-Segalman fluid, to describe the strain rate sweep response of molten atactic polystyrene. Our generalization yields unequivocally, a longest fluid relaxation time, used to assign Weissenberg and Deborah numbers to each oscillatory shear flow experiment. We then locate each experiment in Pipkin space. () are the real and minus [10] the imaginary parts of the nonlinear complex viscosities, η n * , and first and second normal stress coefficients, Ψ 1,n * and Ψ 2,n * . Some prefer to write Eq. (6) as (see Eq.(3) of [11]):

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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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Normal stress differences from Oldroyd 8-constant framework: Exact analytical solution for large-amplitude oscillatory shear flow

Abstract: This report is circulated to persons believed to have an active interest in the subject matter; it is intended to furnish rapid communication and to stimulate comment, including corrections of possible errors.

Cited by 42 publications

References 108 publications

Series expansion for shear stress in large‐amplitude oscillatory shear flow from oldroyd 8‐constant framework

Series expansion for shear stress in large‐amplitude oscillatory shear flow from oldroyd 8‐constant framework

Exact solutions for oscillatory shear sweep behaviors of complex fluids from the Oldroyd 8-constant framework

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

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