Shear rate apparent

Between 50 and 300°C, PTEE obeys the relationship between stress T and the apparent shear rate 7 r =. Melting of PTEE begins near... 

Since it is recognised that the fluid is Non-Newtonian, this is often referred to as the apparent shear rate to differentiate it from the true shear rate. If the pressure drop, P, across the die is also measured then the shear stress, r, may be calculated from... 

This leads to a definition of apparent viscosity as the ratio of shear stress to apparent shear rate... 

For a rectangular slot, as shown earlier, the apparent shear rate, y at A i is given by... 

The correction factor for converting apparent shear rates at the wall of a circular cylindrical capillary to true shear rates is (3n + l)/4n, where n is the power law index of the polymer melt being extruded. 

Derive a similar expression for correcting apparent shear rates at the walls of a die whose cross-section is in the form of a very long narrow slit. 

Now the cone and plate gives true shear rate whereas the ram extruder uses apparent shear rate. The Non-Newtonian correction factor is... 

The simple result is attained when dependence of viscosity on shear rateq(Yapp)can be ignored in the interval of apparent shear rates realized along channel axis. Then,... 

Before the viscosity can be calculated from capillary data, as mentioned above, the apparent shear rate, 7 , must be corrected for the effect of the pseudoplastic nature of the polymer on the velocity profile. The calculation can be made only after a model has been adopted that relates shear stress and shear rate for this concept of a pseudoplastic shear-thinning material. The model choice is a philosophical question [11] after rheologlsts tried numerous models, there are in general two simple models that have withstood substantial testing when the predictions are compared with experimental data [1]. The first Is ... 

Figure 3.18 Apparent shear rate as a function of the wall stress (tJ. The first derivative of the function is used to perform the Weissenberg-Rabinowitsch correction. The data are for the HDPE resin at 190°C as shown in Fig. 3.17...

The calculation of the shear rate at the capillary wall, 7 , is computed from the function slope of Fig 3.18 and the apparent shear rate using Eq. 3.36. The derivative of the function appears relatively constant over the shear stress range for Fig. 3.18. Many resin systems will have derivatives that vary from point to point. The corrected viscosity can then be obtained by dividing the shear stress at the wall by the shear rate i ,. Equation 3.36 is known as the Weissenberg-Rabinowitsch equation [9]. 

For this power law model n is the slope of the shear stress at the wall with respect to the apparent shear rate at the wall as shown in Fig. 3.19. The value of n is also not always a constant, but can change point to point. 

Figure 3.19 Calculation of power law index n from the shear stress at the wall (tJ as a function of the apparent shear rate ()...

The shear rate at the capillary wall is then calculated from the apparent shear rate at the wall as follows ... 

The pressure change is measured for each capillary at the apparent shear rate. Regression analysis is then used to obtain the slope and intercept for the function of pressure change (column two) in Table 3.5 with respect to the length divided by the radius (L/R, column six). The slope of the function is 0.376 MPa, and the intercept is 1.5 MPa. The regressed pressure change is obtained from the slope and the intercept, and the pressure change corrected for the end effects are as follows ... 

The iocai vaiue for n at an apparent shear rate of 10 1/s is caicuiated using the data points at apparent shear rates of 50 and 5 1/s as follows ... 

Notice that the corrected shear rate at the wall is about twice the apparent shear rate at the wall for this case. This set of calculations must be repeated with the other data sets until the total shear rate and temperature range is covered. A typical set of data is presented Table 3.6. 

The melt Index test measures the flow property at a fixed wall shear stress In the capillary. The shear stress depends on the load specified for the condition and it is provided in Table 3.8. The apparent shear rate at the capillary wall that the resin experiences depends on the Ml value measured, and it can be calculated using a modification of Eq. 3.33 as follows ... 

Where // is referred to as the Newtonian viscosity. The apparent shear rate is often used when deaiing with a non-Newtonian poiymer ... 

Viscosity of 12% PVB solutions. Solutions were prepared with 0.1185Kinematic viscosities were measured in a size 400 Cannon-Zhukov viscometer. In this viscometer, the apparent shear rate at the wall, y =T /iy, ranged from 2.5 to 40 sec". It is possible tliat non-Newtonian effects were present even at these low shear rates. However, such effects would only alter the data quantitatively—but not qualitatively—and the qualitative features of the data are the focus of this investigation. For further details about equipment and procedures, see Ref. 35. 

Figure 1 shows how the viscosity of low density polyethylene-containing titanium dioxide changes as a function of apparent shear rate [18]. Similar results are shown in Fig. 2 for polystyrene filled with carbon black [19]. 

Equations of interest are the relations between apparent shear rate Ds and volumetric output rate Q and between the shear stress aw at the large side wall and the mentioned pressure gradient dpjdz along the slit capillary. One obtains ... 

In this respect, additional results, as obtained on polymer melts 40), seem of interest. Fig. 1.9 shows results obtained on a polystyrene melt (Styron 666 at 190° with the aid of the discussed slit-apparatus. In this figure the total path difference is plotted in the form (P/d) against apparent shear rate Ds. Extrusion defect occurs only at the highest... 

Fig. 1.9. Total path difference P, divided by slit width d, as a function of apparent shear rate D, for a polystyrene melt (Styron 666) at 190° C [Wales (40)]...

Q = Volume flow rate D = pipe diameter t w = wall shear stress Y = Apparent shear rate... 

Melt flow rheology measurements were obtained on the MBAS polymer using an Instron capillary rheometer. The data reported were obtained using an 0.056-inch capillary, 90° included angle, with an L/D of 36. In Figure 5 the maximum shear stress (lb/in2) is plotted vs. the apparent shear rate (sec 1). The apparent viscosity (lb-sec/in2) vs. tem-... 

Corporation film-grade Ziegler-Natta linear low density polyethylenes will be presented. They are Resin E, Nova FP-015-A, MFI = 0.55, p = 0.9175 g/cc, and Resin C, Nova PF-120-F, MFI = 1.00, p = 0.9170 g/cc. Their capillary-flow behavior in terms of apparent shear stress vs. apparent shear rate are shown on Fig. 12.24. The melt fracture onset is also noted in Figure 12.24 and the data presented in the table below, indicate that resin E undergoes both sharkskin and gross melt fracture at lower apparent shear rates and stresses. 

C (LLDPE FP-120-F) Apparent shear rate Apparent shear stress 100 0.24 1100 0.42... 

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