View - Martin Kröger - ETH Zürich

More documents

Recommendations

Info

1306 FANG, KRÖGER, AND ÖTTINGER FIG. 5. Magnitude of the strain p at which the maximum in the stress overshoot occurs as functions of shear rate for shear stress under startup of steady shear flow predicted by the models and experiment. reptation represented by a smaller value of d in the MLDS model. This behavior is also in accordance with the other experimental results Attane et al. 1985; Menezes and Graessley 1982. C. Steady shear flow In Fig. 7 the steady-state values of the shear stress xy and the first normal stress difference N 1 are plotted as functions of shear rate. Our model and the FCS model predict a slight decrease of the shear stress over a range of shear rates that extends from roughly ˙ 0.3 to ˙ 2s 1 , where the MLDS model predicts a slight increase which is consistent with the experimental data. This new observation of the MLDS model may be attributed to the fact that we use a relatively small ratio d / s 10 here. Over the same range of shear rates, all the model predictions for the first normal stress difference FIG. 6. Relaxation of the shear stress reduced by its value at steady state as a function of time after cessation of steady shear flow at two shear rates predicted by experiment and the models.
THERMODYNAMICALLY ADMISSIBLE REPTATION MODEL 1307 FIG. 7. Steady-state values of the shear stress and first normal stress difference as functions of shear rate predicted by the models and experiment. N 1 increase gradually with shear rate, which are consistent with the experimental data. For the shear stress at rates after the range, our model predicts an increase, the FCS model shows a lesser increase, and the MLDS model shows a decrease. This decreasing behavior of MLDS is caused by the exponential switch function used and the additional term accounting for the CCR effect in the equation for stretch. We examine the behavior of the steady-state shear stress and its dependence on choice of our model parameters in more detail in order to understand how to avoid the prediction of an instability region as mentioned earlier. In Fig. 8, we see that the inclusion of chain FIG. 8. Steady-state values of the dimensionless shear stress as functions of dimensionless shear rate predicted by the DE model, the model without any constraint release effects 1 0, 2 0, the model with double reptation effect 1 1/, 2 0, the model with double reptation and convective constraint release effects ( 1 2 1/), and the model with double reptation and enhanced convective constraint release effects ( 1 1/, 2 2/. The other parameters of the model are set as Z 20, and max 10.
Page 1 and 2: A thermodynamically admissible rept
Page 3 and 4: THERMODYNAMICALLY ADMISSIBLE REPTAT
Page 13: THERMODYNAMICALLY ADMISSIBLE REPTAT
Page 25: THERMODYNAMICALLY ADMISSIBLE REPTAT

View - Martin Kröger - ETH Zürich

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?