Viscosity lower-Newtonian

In viscoelastic systems the lower Newtonian viscosity is several orders of magnitude smaller than the upper one, rj, and is frequently neglected. At high deformation rates Eq. (2.13) reverts to the power-law dependence ... 

Viscosities for molecular weight determination are usually measured in glass capillary viscometers, in which the solution flows through a capillary under its own head. Two common types, the Ostwald and Ubbelohde, are sketched in Figure 5.6. (Since polymer solutions are non-Newtonian, intrinsic viscosity must be defined, strictly speaking, in terms of the zero-shear or lower-Newtonian viscosity (see Chapter 14). This is rarely a problem, because the low shear rates in the usual glassware viscometers give just that. Occasionally, however, extrapolation to zero-shear conditions is required.)... 

The predicted effect of the Newtonian viscosity on the film blowing stability is depicted in Figure 6a. It is clearly shown that an increase in the Newtonian viscosity leads to the increase in the film blowing processing window. In particular, the model predicts that an increase in the Newtonian viscosity (i.e. Mw) of the melt increases the capability to achieve much higher final film thickness for certain BUR a condition which is very desirable for heavy-duty bags production. On the other hand the model predicts that an increase in the Newtonian viscosity enhances the ability of the melt to stretch i.e. one can produce lower final film thickness compared to the case where the material has lower Newtonian viscosity. 

The viscosities of most real shear-thinning fluids approach constant values both at very low shear rates and at very high shear rates that is, they tend to show Newtonian properties at the extremes of shear rates. The limiting viscosity at low shear rates mq is referred to as the lower-Newtonian (or zero-shear /x0) viscosity (see lines AB in Figures 3.28 and 3.29), and that at high shear rates Mo0 is the upper-Newtonian (or infinite-shear) viscosity (see lines EF in Figures 3.28 and 3.29). 

Bueche-Ferry theory describes a very special second order fluid, the above statement means that a validity of this theory can only be expected at shear rates much lower than those, at which the measurements shown in Fig. 4.6 were possible. In fact, the course of the given experimental curves at low shear rates and frequencies is not known precisely enough. It is imaginable that the initial slope of these curves is, at extremely low shear rates or frequencies, still a factor two higher than the one estimated from the present measurements. This would be sufficient to explain the shift factor of Fig. 4.5, where has been calculated with the aid of the measured non-Newtonian viscosity of the melt. A similar argumentation may perhaps be valid with respect to the "too low /efi-values of the high molecular weight polystyrenes (Fig. 4.4). 

Melt Viscosity. Low shear melt viscosities were measured by Kepes cone-plate viscometer (7) at 150°, 170°, and 190°C. No stabilizer was added to the sample. The flow curves are shown in Figure 6. The viscosities of NMWD are in good agreement with those observed by others (8) the viscosities of BMWD by our measurements are somewhat lower. The Newtonian viscosities, y0, were observed with NMWD sample. With BMWD sample, vo was estimated by extrapolation shown in the figure. The extrapolated values are uncertain they may have been underestimated. The Newtonian viscosities are listed in Table III. 

A lack of experimental data in the literature makes the check-up-of Eqs. (2.1)—(2.3) rather difficult to perform, most of the data have been obtained for Newtonian liquids, 2, 4). Equation (2.3) was shown to be valid at f = qv/cr = 0.3255 at f > 2.4 the formation of waves and disturbances of liquid flow was observed. The lower the viscosity of a system, the easier these phenomena are to be observed. The value of K was experimentally shown14> to be equal to 0.657, i.e. rather close to the theoretically predicted value K = 2/3. 

If a = 0, the non-Newtonian viscosity is temperature independent and the equations of motion and energy can be solved independently from each other if, however, a/0, they are coupled. Next, we assume that viscous dissipation is negligible Br —> 0, and that the moving plate at velocity Vo is T and the lower stationary plate is Tq. The equations of motion and energy reduce to... 

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.

For aqueous solutions, say, at 25°C the lower limit of the critical Reynolds number will not be reached as long as V/Rt is well below 30. Thus for all practical purposes this complication will not arise in routine viscosity measurements. On the other hand if the non-Newtonian viscosity measurements are extended to a very high range of the shearing stress, it is desirable to check the possibility of this effect. 

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 ... 

Dilatant Flows Krieger and Choi [1984] smdied the viscosity behavior of sterically stabilized PMMA spheres in silicone oil. In high viscosity oils, thixotropy and yield stress was observed. The former was well described by Eq 7.41. The magnimde of Oy was found to depend on ( ), the oil viscosity, and temperature. In most systems, the lower Newtonian plateau was observed for the reduced shear stress value = Oj d / RT > 3 (d is the... 

The theory of hydrodynamics similarly describes an ideal liquid behavior making use of the viscosity (see Sect 5.6). The viscosity is the property of a fluid (liquid or gas) by which it resists a change in shape. The word viscous derives from the Latin viscum, the term for the birdlime, the sticky substance made from mistletoe and used to catch birds. One calls the viscosity Newtonian, if the stress is directly proportional to the rate of strain and independent of the strain itself. The proportionality constant is the viscosity, q, as indicated in the center of Fig. 4.157. The definitions and units are listed, and a sketch for the viscous shear-effect between a stationary, lower and an upper, mobile plate is also reproduced in the figure. Schematically, the Newtonian viscosity is represented by the dashpot drawn in the upper left comer, to contrast the Hookean elastic spring in the upper right. 

Limiting viscosity at infinite shear rate, i.e., at the lower Newtonian plateau... 

The parameter a was obtained empirically by assiiming the shear rate for the onset of shear-thinning behavior in the viscometric data is equal to the shear rate at the velocity where the onset of shear-thinning is observed in the rock. A critical shear rate is found for each polymer system from the intersection of tangents to the viscosity shear rate curve in the lower Newtonian and shear-thinning regions. This critical shear, is l/Xj. from Equation 2. A similar procedure is used to find the critical velocity, u, from apparent viscosity-Darcy velocity data. 

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... 

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