Padé Approximants for Large-Amplitude Oscillatory Shear Flow

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 that, in this way, we learn that in this way, one can nearly eliminate the inaccuracies of the truncated expansions.