First normal stress growth coefficient

Figure 9.9 Normalized shear stress growth coefficient (s, ) and normalized first normal stress growth coefficient (s, ) as a function of the normalized time s at a shear rate of 2s (T = 20°C, 15%-MDMA0-HN03, pH = 3.5). Predictions of the Giesekus model...

In start-up of steady simple shear, the measured stresses are divided by the imposed shear rate or its square to obtain the shear stress growth coefficient and the first normal stress growth coefficient, which are defined as follows ... 

Figure 11.10 Predictions of shear stress and first normal stress growth coefficients by the CCR model of Likhtman etal. modified to include chain stretch by Graham eta/. [37] in start-up of steady shearing compared to data [53] for a 7% solution of nearly monodisperse polybutadiene (M = 350,000) at the shear rates shown, where the parameters = 4.156 -10" s,M = 51779, and Gg = (5/4) G 5 = 51770 Pa are obtained from linear viscoelastic measurements, and = 0.1 sets the rate of constraint release.The longest Rouse orientational relaxation time should be given by the theoretical relationship to =Z however, the retraction rate is artificially doubled (equivalent to taking xj, =0.5 Z T )tooffsetthe error introduced by a closure approximation and to give a better fit to the data. From Graham et al. [37].

Vtit,/) first normal stress growth coefficient Eq. 10.48... 

Viscosity T), first normal-stress coefficient /i, second normal-stress coefficient /2 Shear stress growth coefficient T1+, first normal-stress growth coefficient t t[, second normal-stress growth coefficient /J Shear stress decay coefficient Tj", first normal-stress decay coefficient /f, second normal-stress decay coefficient /j Shear creep compliance J... 

Figure 8.15 First normal stress difference coefficient growth function of a low density polyethylene filled with two different fillers. (Reprinted from Ref. 91 with kind permission from Gulf Publishing Co.. Houston, Texas. USA.)...

As in the equation for evolution of fiber orientation, a closure approximation is needed in Eq. 3.102 to express A4 in terms of A. Using Eq. 3.102 it is straightforward to show that the shear stress growth coefficient, +, and the first normal stress growth function, N, are... 

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