Reflections on Inflections
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Authors
Saengow, Chaimongkol
Giacomin, A. Jeffrey
Gilbert, Peter H.
Kolitawong, Chanyut
Date
2015-11-11
Type
technical report
Language
en
Keyword
Steady shear flow , Viscosity curve , Viscosity inflection , Normal stress coefficients , Normal stress differences
Alternative Title
Abstract
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, η (γ! ), Ψ1 (γ! ) and Ψ2 (γ! ).