(468f) Padé Approximants for Shear Stress in Large-Amplitude Oscillatory Shear Flow

Giacomin, A. J. - Presenter, Queen's University
Saengow, C., Queen's University
Guay, M., Queens University
Analytical solutions for shear stress in large-amplitude oscillatory shear flow, both for continuum or molecular models, often take the form of the first few terms of a power series in the shear rate amplitude. We get this series using the Goddard-Miller integral expansion. Our previous work shows that the Padé approximants for this truncated series, and specifically for the corotational Maxwell model, can agree closely with the corresponding exact solution. We observe this close agreement, even for the Padé approximant of the truncation that contains only the fifth harmonic of the shear stress response. Here we begin with our recent extension of the power series to the next order in the shear rate amplitude [Phys. Fluids 29, 043101 (2017)]. We then use this extension to explore its Padé approximants. We uncover its best approximant, compare it with the Goddard-Miller integral expansion, and also with the exact solution [Macromol. Theory Simul. 24, 352 (2015)]. We use Ewoldt fingerprints to show the stunning accuracy of our new Padé approximant. We quantify this accuracy with the objective functions introduced in this paper. Our worked examples illustrate how researchers can use our new approximant reliably.