## Exact Solutions for Oscillatory Shear Sweep Behaviors of Complex Fluids from the Oldroyd 8-constant Framework

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##### Date

2017-05

##### Authors

Saengow, Chaimongkol

Giacomin, A. Jeffrey

##### Keyword

Strain rate sweep , Strain sweep , Frequency sweep , Nonlinear complex viscosity , Oldroyd 8-constant framework , Exact solutions , Large-amplitude oscillatory shear flow , LAOS , Lost modulus , Storage modulus , Finite difference

##### Abstract

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.