In this paper, we provide a new exact framework for analyzing the most commonly measured behaviors in large-amplitude oscillatory shear flow (LAOS), a popular flow 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. By the strain rate sweep, we mean a sequence of LAOS experiments conducted at the same frequency, performed one after another, with increasing shear rate amplitude. 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. 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. For our comparisons with data, we use the Spriggs relations to generalize the Oldroyd 8-constant framework to multimode. 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 the Pipkin space.
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March 2018
Research Article|
February 14 2018
Exact solutions for oscillatory shear sweep behaviors of complex fluids from the Oldroyd 8-constant framework
Special Collection:
Papers from the 8th Meeting of the Hellenic Society of Rheology
Chaimongkol Saengow
;
Chaimongkol Saengow
1
Polymers Research Group, Chemical Engineering Department, Queen’s University
, Kingston, Ontario K7L 3N6, Canada
2
College of Integrated Science and Technology, Rajamangala University of Technology Lanna
, Doisaket, Chiangmai 50220, Thailand
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A. Jeffrey Giacomin
A. Jeffrey Giacomin
a)
1
Polymers Research Group, Chemical Engineering Department, Queen’s University
, Kingston, Ontario K7L 3N6, Canada
3
Mechanical and Materials Engineering Department, Queen’s University
, Kingston, Ontario K7L 3N6, Canada
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a)
Author to whom correspondence should be addressed: giacomin@queensu.ca
Physics of Fluids 30, 030703 (2018)
Article history
Received:
May 15 2017
Accepted:
July 10 2017
Citation
Chaimongkol Saengow, A. Jeffrey Giacomin; Exact solutions for oscillatory shear sweep behaviors of complex fluids from the Oldroyd 8-constant framework. Physics of Fluids 1 March 2018; 30 (3): 030703. https://doi.org/10.1063/1.5023586
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