Shear flow Shift factor

Fig. 2.5. Steady-state and dynamic oscillatory flow measurements on a 2 wt. per cent solution of polystyrene S 111 in Aroclor 1248 according to Philippoff (57). ( ) steady shear viscosity (a) dynamic viscosity tj, ( ) cot 1% from flow birefringence, (A) cot <5 from dynamic measurements, all at 25° C. (o) cot 8 from dynamic measurements at 5° C. Steady-state flow properties as functions of shear rate q, dynamic properties as functions of angular frequency m. Shift factor aT which is equal to unity for 25° C, is explained in the text, cot 2 % and cot 8 are expressed in terms of shear (see eqs. 2.11 and 2.22)...

The experimental ranges of strain rates (or strains) are summarized in Table 2 for the various types of experiments. Time-temperatiire superposition was successfully applied on the various steady shear flow and transient shear flow data. The shift factors were foimd to be exactly the same as those obtained for the dynamic data in the linear viscoelastic domain. Moreover, these were found to be also applicable in the case of entrance pressure losses leading to an implicit appUcation to elongational values. 

The Ellul group reported the shear flow behavior and oil distribution between phases in TPVs (55). The distribution of the high temperature oil between the PP melt and the EPDM was a key parameter because this affected the viscosity of the PP/oil medium. Several PP/oU mixtures were prepared and their viscosity curves were correlated with the neat PP melt viscosity curves by means of shift factors varying with oil concentration. The oil distribution between the PP and EPDM phases was estimated from TEM micrographs of the TPV blends. It was found that the PPs are mixed with oil in different proportions in different TPVs and that the viscosity curves of these mixtures exhibit the same trends in magnitude as the corresponding TPV viscosity curves. Hence, the shear flow of TPVs could be understood more readily in terms of the effective PP/oil medium flow behavior than in terms of the neat PP melt flow. 

At finite concentrations, the frequency dependence of G and G" — (aris can be examined directly without scaling the coordinates as in preceding figures. However, measurements at different temperatures may be combined by reduction to a standard temperature To G and G" — coris are multiplied by Toco/Tc and u> is multiplied by a shift factor aj which is given by rjo Vs)ocT/ t]o — Vs)coTq. Here r]o is the steady-flow (vanishing shear rate) viscosity and the subscript 0 otherwise refers to the reference temperature. This is the method of reduced variables which will be discussed fully in Chapter 11 with explanation of its rationale, and affords an extension of the effective frequency range. 

Figure 21 SALS (scale on left ordinate axis) and SANS (right ordinate axis) profiles measured for PS 200/DOP 8.0 wt.% at various shear rates and at a given temperature of 22°C (a) parallel (b) perpendicular to the flow direction. The SALS profiles were multiplied by a common shift factor in order to compare them with the SANS profiles, although the SANS profiles are shown in the absolute intensity scale (cm ). Based on Salto, S. Hashimoto, T. Morfin, I. etal. Macromolecules2002, 35, 445. ...

From this relatively simple test, therefore, it is possible to obtain complete flow data on the material as shown in Fig. 5.3. Note that shear rates similar to those experienced in processing equipment can be achieved. Variations in melt temperature and hypostatic pressure also have an effect on the shear and tensile viscosities of the melt. An increase in temperature causes a decrease in viscosity and an increase in hydrostatic pressure causes an increase in viscosity. Topically, for low density polyethlyene an increase in temperature of 40°C causes a vertical shift of the viscosity curve by a factor of about 3. Since the plastic will be subjected to a temperature rise when it is forced through the die, it is usually worthwhile to check (by means of Equation 5.64) whether or not this is signiflcant. Fig. 5.2 shows the effect of temperature on the viscosity of polypropylene. 

From the above discussion, it is clear that convection with or without an environment independent response of chains to shear is not enough to shift the conditions for stabihty of concentration fluctuations in the one-phase region. Its usefulness as a theory hes in its abihty to predict the anisotropic q dependence of the structure factor in the one-phase region, which can be measured using scattering techniques. In order to predict apparent shifts in phase boimdaries an extra ingredient is required - stress and flow rate variations within the blend. 

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