The Second Newtonian Region

Flow curve for various concentrations of polystyrene (Mw=2106g/mol) in decalin solutions at 25 °C obtained with a low-shear viscometer (A), a mechanical spectrometer ( ) and a high-shear concentric-cylinder viscometer (O) 

In order to obtain solutions with the desired flow properties, shear-induced degradation should be avoided. From mechanical degradation experiments it has been shown that chain scission occurs when all coupling points are loose and the discrete chains are subjected to the velocity field. Simple considerations lead to the assumption that this is obtained when T sp( y) is equal to r sp(c- [r ]) (Fig. 18). The critical shear rate can then easily be evaluated [22]. 

The molar mass of the degraded sample can easily be calculated by assuming that the overlap parameter is equal to the intersection point of the horizontal with the line of slope 1. 

Normally (3 is used without considering the solvent quality. However, a master low curve can only be established using such a method. In Table 5 a comparison of the model prediction with the experimental findings, obtained by laser light scattering measurements, is given. 

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There is a reasonable correspondence between the experimental and calculated viscosity values at a shear rate of 10 s-1. The calculated 77 value at y 103 s-1 is too low, however, because at this shear rate the second Newtonian region is approached. To estimate rj Eq. (16.51) can be applied with... 

Finally a phenomenon should be mentioned which polymer solutions show more often than polymer melts viz. a second Newtonian region. This means that with increasing shear rate the viscosity at first decreases, but finally approaches to another constant value. As the first Newtonian viscosity is denoted by rjor the symbol // x, is generally used for the second Newtonian viscosity. Empirical equations as those presented in Chap. 15 now need an extra term r oo to account for this second Newtonian region. This leads to ... 

Continuing in the pseudoplastic region it is often found that an upper threshold can be reached beyond which no further reduction in viscosity occurs. The curve then enters a second linear region of proportionality the slope of which is the second Newtonian viscosity. 

Polymer melts are almost invariably of the pseudoplastic type, and the existence of first and second Newtonian regions has long been recognized. The pseudoplastic behavior appears to arise from the elastic nature of the melt and from the fact that under shear, polymers tend to be oriented. 

Figure 7-5. Generalized flow curve with the first Newtonian region (N), pseudoplastic region (st), second Newtonian region (N2), dilatant region (d), and onset of turbulence or melt break (t).

The phenomena described above are the basis of the structural viscosity and viscoelastic behavior mentioned in Sec. il. The region of elastic response and the region of viscous flow depicted in Fig. 33 correspond to the lirsi and to the second Newtonian plateau of Fig. 5, respectively. Further, the floe destruction region shown in Fig. 34 corresponds to the shear-thinning portion between both plateaus of Fig. 

The molecular dynamics theories need to make a proper combination to describe the rheological behaviors of polymer melt in various regions of shear rates (Bent et al. 2003). Above 1/t the convective constraint release dominates the rheological behaviors of polymers in shear flow, and thus explains the shear-thinning phenomenon. Beyond 1/t, the extensional deformation reaches saturation, and the shear flow becomes stable, entering the second Newtonian-fluid region, as demonstrated in Fig. 7.6. 

Solution. Fig. 5.14 presents a graph of Qx-Hoo) vs. shear rate. In the absence of data at lower shear rates, it is assumed that the shear rate of 0.945 seconds" is the end of the lower Newtonian region. The shear-thinning region is present from about 15 to 128.4 seconds ", as indicated by the linear relationship between /a. and y. A long transition region is present between -y=0.945 and 15 seconds" for this solution. 

Figure H1.1.4 A complete flow curve for a time-independent non-Newtonian fluid. r 0 and i , are the viscosities associated with the first and second Newtonian plateaus, respectively. Regions (1) and (2) correspond to viscosities relative to low shear rates induced by sedimentation and leveling, respectively. Regions (3) and (4) correspond to viscosities relative to the medium shear rates induced by pouring and pumping, respectively. Regions (5) and (6) correspond to viscosities relative to high shear rates by rubbing and spraying, respectively.

Up to now, two regions of shear flow have been discussed Newtonian flow at low shear rates and non-Newtonian flow at high shear rates. In the first region, the viscosity is independent of the shear rate, while in the second region the viscosity decreases with increasing shear rate. 

The shear rate dependence of the viscosity and that of the normal stress difference Ni for a viscoelastic fluid follow opposite trends. Thus the first parameter decreases with increasing values of k, while the second increases. It is noteworthy to remark once more that viscoelastic fluids may present nonlinear effects, expressed by the normal stresses, in regions in which the shear stress is a linear function of the shear rate. However, these viscoelastic systems are still called Newtonian fluids due to the fact that the viscosity is independent of the shear rate. 

Polyester BB1 was run twice in steady mode at 290°C (Figure 10), and shows that the orientational effect of the first run has a drastic effect on steady shear viscosity. In the first run the log viscosity vs. log shear rate had a slope of -0.92 (solid like behaviour, yield stress), but in the second run a pseudo-Newtonian plateau was reached from approx. 1 sec 1. Capillary viscosity values corresponded reasonably well with the second run steady shear data. The slope at high shear rates was close to -0.91 which corresponds nicely to the first-run steady shear run. All this could suggest, that this system is not completely melted, but still has some solid like regions incorporated. At 300°C capillary viscosity data showed an almost pseudo-Newtonian plateau. This corresponds quite well to the fact that fiber spinning as mentioned earlier was difficult and almost impossible below 290°C, but easy at 300°C. At an apparent shear rate of 100 sec 1, a die-swell was found to be approximately 0.95. 

The liquid crystalline PBLG sample is characterized by a stress relaxation which depends on shear rate, even in the Newtonian region (Moldenaers, P. Mewis, J. J. Non—Newtonian Fluid Mech., in press). This proves the existence of a shear rate dependent structure in the linear shear rate region. It was also found that the stress relaxation curve could be divided in two different sections. The temperature dependence of the initial part scales with the viscosity and does not depend on shear rate in the Newtonian region. The second part does not depend on temperature but scales with the inverse of the previous shear rate. 

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