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Predicting nonlinear viscosity and elasticity from zero‐shear parameters in the Pao‐Rouse model
Author(s) -
Fruh S. M.,
Rodriguez F.,
Manning A. J.
Publication year - 1970
Publication title -
journal of applied polymer science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.575
H-Index - 166
eISSN - 1097-4628
pISSN - 0021-8995
DOI - 10.1002/app.1970.070141213
Subject(s) - shear modulus , materials science , shear rate , simple shear , shear thinning , creep , elasticity (physics) , shear stress , constitutive equation , thermodynamics , shear flow , shear (geology) , stress relaxation , viscoelasticity , apparent viscosity , viscosity , mechanics , composite material , physics , finite element method
When the Rouse distribution of relaxation times is inserted into Pao's constitutive equation as expressed by Huseby and Blyler, a simple two‐parameter model results. The parameters can be fitted using the limiting values of viscosity and modulus at low shear rates. The modulus in this case is defined as the ratio of shear stress during steady flow to the recovered shear during creep recovery with the stress removed. The mathematical model, is then used to predict the behavior at high shear rates where flow is pseudoplastic and elasticity is non‐Hookean. A sample of polyisobutylene and several high molecular weight poly(dimethylsiloxanes) can be fitted reasonably well. Silicones of lower molecular weight (3.7 and 5.5 × 10 5 ) are not correlated successfully, perhaps because not all the “recoverable shear” stored during flow can actually be recovered experimentally. The Rouse distribution can be generalized for added flexibility.