Second Newtonian region

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 ... 

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... 

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).

FIG. 12 Plot of apparent viscosity r/ vs apparent shear rate / for HDPE at 230°C L /D = 40.1, Instron capillary rheometer II, specially designed capillary rheometer III, first non-Newtonian region IV, second Newtonian region V, second non-Newtonian region. (From Ref. 31.)... 

Figure 5.3 (b) Apparent viscosity versus apparent shear rate for HDPE at 230 "C LjD = 40). I Instron capillary rheometer II specially designed capillary rheometer IE first non-Newtonian region IV second Newtonian region V second non-Newtonian region [2]... 

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.

Sisko (predicts power law region and second Newtonian plateau) Tl=TL+k yn"1... 

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. 

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. 

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. 

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