Lower Newtonian region

Fig. 11-28. Typical rheometer shear rate ranges and polymer melt flow curve. The lower shear rate region of the flow curve exhibits viscosities that appear to be independent of y. This is the lower Newtonian region.

Similarly, the two models could be reduced by neglecting the lower Newtonian region. This has been done by Sisko for the Cross model in order to account for the rheological properties of grease in bearings ... 

Considering that in many cases the viscosity measured is significantly smaller than that of the lower Newtonian region (i] upper Newtonian region (i] > i]oo), the Cross model can be further simplified ... 

The molecular entanglements increase as the average molecular weight increases. The lower Newtonian region becomes smaller because the interactions occur at lower shear rates, and the non-Newtonian region persists to higher shear rates, as illustrated in Fig. 3.38. 

Chauveteau s research produced an important result. Apparent viscosities in Fountainbleau sandstone were significantly less than found in rheological measurements. This is particularly evident in the lower Newtonian region where apparent viscosities range from 17% to 38% lower than solution viscosities. The largest differences were observed at the... 

Figure 12 The Cross model with m = 1 and typical values ofthe parameters, showing the apparent yield stress region and upper and lower Newtonian regions.

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. 

The lower Newtonian region will be encountered when the Darcy velocity is 0.019 ft/D. If flow is radial,... 

The lower Newtonian region will be reached in the low-permeability zone if the Darcy velocity decreases to Ud in the region contacted by polymer. The injection rate at any time is related to the radius and the Darcy velocity by Eq, 5.57 modified by the factor 5.615 ft /bbl with qf in B/D,... 

At low shear rates (or stresses), a lower Newtonian region is reached with a so-called zero-shear viscosity rjo-... 

A lower Newtonian region exists at low shear rates or stresses, and this leads to the definition of zero-shear viscosity (// ), i.e., value of / as y -> 0. 

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