A. J. Giacomin

Exact analytical solution for large-amplitude oscillatory shear flow from Oldroyd 8-constant framework: Shear stress

The Oldroyd 8-constant model is a continuum framework containing, as special cases, many important constitutive equations for elastic liquids. When polymeric liquids undergo large-amplitude oscillatory shear flow, the shear stress responds as a Fourier series, the higher harmonics of which are caused by the fluid nonlinearity. We choose this continuum framework for its rich diversity of special cases (we tabulate 14 of these). Deepening our understanding of this Oldroyd 8-constant framework thus at once deepens our understanding of every one of these special cases. Previously [C. Saengow et al., Macromol. Theory Simul. 24, 352 (2015)], we arrived at an exact analytical solution for the corotational Maxwell model. Here, we derive the exact analytical expression for the Oldroyd 8-constant framework for the shear stress response in large-amplitude oscillatory shear flow. Our exact solution reduces to our previous solution for the special case of the corotational Maxwell model, as it should. Our worked exampl...

Reflections on Inflections

In plastics processing, the single most important rheological property is the steady shear viscosity curve: the logarithm of the steady shear viscosity versus the logarithm of the shear rate. This curve governs the volumetric flowrate through any straight channel flow, and thus governs the production rate of extruded plastics. If the shear rate is made dimensionless with a characteristic time for the fluid (called the Weissenberg number, Wi), then we can readily identify the end of the Newtonian plateau of a viscosity curve with the value Wi≈1. Of far greater importance, however, is the slope at the point where the viscosity curve inflects, (n-1), where n is called the shear power-law index. This paper explores the physics of this point and related inflections, in the first and second normal stress coefficients. We also discuss the first and second inflection pairing times, λ′B and λ″B. First, we examine the generalized Newtonian fluid (Carreau model). Then, we analyze the more versatile model, the corotational Oldroyd 8-constant model, which reduces to many simpler models, for instance, the corotational Maxwell and Jeffreys models. We also include worked examples to illustrate the procedure for calculating inflection points and power-law coefficients for all three viscometric functions,

Normal stress differences from Oldroyd 8-constant framework: Exact analytical solution for large-amplitude oscillatory shear flow

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Strain sweeps from Oldroyd 8-constant framework

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Power series for shear stress of polymeric liquid in large-amplitude oscillatory shear flow

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Molecular origins of higher harmonics in large-amplitude oscillatory shear flow: Shear stress response

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