View - Martin Kröger - ETH Zürich

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1312 FANG, KRÖGER, AND ÖTTINGER FIG. 15. The strain-hardening parameter as a function of the Hencky strain at the dimensionless elongational rate ˙ d 100 with the parameter values as for Fig. 13. seen in the uniaxial extension, except that i the second regime of steady-state viscosity is absent and ii it is ‘‘softer’’ and less strain hardening than uniaxial extension Nishioka et al. 2000. Simulations of planar extension of our model are also performed. The steady-state planar viscosity p1 ( zz xx )/(4˙ ) direction of extension z and p2 ( yy xx )/(2˙ ) neutral direction y are plotted in Fig. 17. The viscosity p2 decays much faster than the p1 does in the intermediate region, 1/ d ˙ 1/ s . Again, there is no second regime for both of them. In Fig. 18 we show the transient FIG. 16. Dimensionless uniaxial extensional viscosity vs dimensionless time after startup of steady uniaxial elongation at the dimensionless elongational rate ˙ d 200 for 1 2 1/, Z 20, and three different values of max .
THERMODYNAMICALLY ADMISSIBLE REPTATION MODEL 1313 FIG. 17. Steady-state values of the dimensionless planar extensional viscosity p1 along the direction of extension z and p2 along the neutral direction y as functions of dimensionless extensional rate with the parameter values as for Fig. 13. viscosity p2 not shown is the p1 , which is similar to the transient viscosity in uniaxial extension. The model predicts overshoots at medium and high extensional rates. V. CONCLUSION A new thermodynamically admissible reptation model that includes chain stretching, double reptation, and convective constraint release, and that avoids IA approximation is numerically investigated for transient and steady properties in shear and extensional flows. Quantitative comparisons are made with experimental data of entangled PS solution in shear flows. We find that the model is able to capture qualitatively, or quantita- FIG. 18. Dimensionless planar extensional viscosity p2 along the neutral direction y versus dimensionless time after startup of steady planar elongation at many dimensionless elongational rates with the parameter values as for Fig. 13.
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View - Martin Kröger - ETH Zürich

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