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Padé approximants for large-amplitude oscillatory shear flow

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Abstract

Analytical solutions for either the shear stress or the normal stress differences 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. Here, we explore improving the accuracy of these truncated series by replacing them with ratios of polynomials. Specifically, we examine replacing the truncated series solution for the corotational Maxwell model with its Padé approximants for the shear stress response and for the normal stress differences. We find these Padé approximants to agree closely with the corresponding exact solution, and we learn that with the right approximants, one can nearly eliminate the inaccuracies of the truncated expansions.

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Acknowledgments

We thank R. Byron Bird, Professor Emeritus of Chemical and Biological Engineering, of the Rheology Research Center of the University of Wisconsin-Madison for his encouragement and helpful discussions. The financial support of the Royal Golden Jubilee Program of the Thailand Research Fund for (contract no. PHD/0116/2554) is also greatly appreciated. A.J. Giacomin is indebted to the Faculty of Applied Science and Engineering of Queen’s University at Kingston, for its support through a Research Initiation Grant (RIG). This research was undertaken, in part, thanks to funding from the Canada Research Chairs program of the Government of Canada of the Natural Sciences and Engineering Research Council of Canada (NSERC) Tier 1 Canada Research Chair in Rheology.

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  1. Chemical Engineering Department, Queen’s University, Kingston, Ontario, K7L 3N6, Canada

    A. Jeffrey Giacomin & Martin Guay

  2. Polymers Research Group, Queen’s University, Kingston, Ontario, K7L 3N6, Canada

    A. Jeffrey Giacomin & Chaimongkol Saengow

  3. Mechanical and Aerospace Engineering Department, Polymer Research Center, King Mongkut’s University of Technology North Bangkok, Bangkok, 10800, Thailand

    Chaimongkol Saengow & Chanyut Kolitawong

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  1. A. Jeffrey Giacomin
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Correspondence to A. Jeffrey Giacomin.

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Giacomin, A.J., Saengow, C., Guay, M. et al. Padé approximants for large-amplitude oscillatory shear flow. Rheol Acta 54, 679–693 (2015). https://doi.org/10.1007/s00397-015-0856-9

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