Journal
JOURNAL OF NON-NEWTONIAN FLUID MECHANICS
Volume 166, Issue 19-20, Pages 1081-1099Publisher
ELSEVIER
DOI: 10.1016/j.jnnfm.2011.04.002
Keywords
Large-amplitude oscillatory shear; Corotational Maxwell model; Corotational Jeffreys model; Ewoldt coefficients; Weissenberg number; Deborah number
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Funding
- Placon Corporation of Fitchburg, Wisconsin
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Using the single relaxation time corotational Maxwell fluid, we derive explicit analytical expressions for the first, third, and fifth harmonics of the alternating shear stress response in large-amplitude oscillatory shear (LAOS). We also derive corresponding expressions for the zeroth, second, and fourth harmonics of both the first and second normal stress differences. These harmonics are found to depend upon just two dimensionless groups: the Deborah and Weissenberg numbers, each of which causes non-Newtonian behavior. The form of the solution for the corotational Maxwell model in LAOS matches the forms of the analytical solutions for two molecular models for dilute solutions and one for concentrated solutions or melts. We also derive an analytical solution for the corotational Maxwell model after startup of LAOS. For this we find that both small and large amplitude cases approach a periodic limit cycle (alternance) at the same rate for both the shear stress response and for the normal stress differences. For molten high density polyethylene that is lightly filled with carbon black, we find good quantitative agreement with measured LAOS behavior when our analytical solution is superposed for multiple relaxation times. (C) 2011 Elsevier B.V. All rights reserved.
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