Newtonian viscosities

In connection with a discussion of the Eyring theory, we remarked that Newtonian viscosity is proportional to the relaxation time [Eqs. (2.29) and (2.31)]. What is needed, therefore, is an examination of the nature of the proportionality between the two. At least the molecular weight dependence of that proportionality must be examined to reach a conclusion as to the prediction of the reptation model of the molecular weight dependence of viscosity. 

From plots of these data, estimate the Newtonian viscosity of each of the solutions and the approximate rate of shear at which non-Newtonian behavior sets in. Are these two quantities better correlated with the molecular weight of the polymer or the molecular weight of the arms ... 

At 200°C the Newtonian viscosities of polystyrene samples of different molecular weights were studied by Spencer and Dillont and the following results were reported ... 

The Newtonian viscosity is given by the product of the relaxation time and the Hookean modulus. This result was anticipated in the discussion of Eqs. (2.29) and (2.31). 

A significant heat-transfer enhancement can be obtained when a nonckcular tube is used together with a non-Newtonian fluid. This heat-transfer enhancement is attributed to both the secondary flow at the corner of the nonckcular tube (23,24) and to the temperature-dependent non-Newtonian viscosity (25). Using an aqueous solution of polyacrjiamide the laminar heat transfer can be increased by about 300% in a rectangular duct over the value of water (23). 

The other models can be appHed to non-Newtonian materials where time-dependent effects are absent. This situation encompasses many technically important materials from polymer solutions to latices, pigment slurries, and polymer melts. At high shear rates most of these materials tend to a Newtonian viscosity limit. At low shear rates they tend either to a yield point or to a low shear Newtonian limiting viscosity. At intermediate shear rates, the power law or the Casson model is a useful approximation. 

The Williamson equation is useful for modeling shear-thinning fluids over a wide range of shear rates (15). It makes provision for limiting low and high shear Newtonian viscosity behavior (eq. 3), where T is the absolute value of the shear stress and is the shear stress at which the viscosity is the mean of the viscosity limits TIq and, ie, at r = -H... 

Fig. 11. Newtonian viscosity vs chain length in terms of the number of carbon atoms for a series of molten polyethylenes. To convert Pa-s to P, multiply...

The constant of proportionality is K/fx, where K is the permeability and is Newtonian viscosity. The dielectric properties of the resin are also measured using sensors. These measurements were correlated with viscosity and used as a part of the FRTM control system. 

Appearance of rheological effects — yield stress, non-Newtonian viscosity, thixotropy... 

Concrete calculations carried out via formula (10) for different values of constant have shown that it reflects the behavior of flow curves quite really. However, a series doubt remains for such a system (with a yield stress) it is not obvious how to determine the initial Newtonian viscosity (is it necessary to determine it and does it exist ). 

Viscosity is usually understood to mean Newtonian viscosity in which case the ratio of shearing stress to the shearing strain is constant. In non-Newtonian behavior, which is the usual case for plastics, the ratio varies with the shearing stress (Fig. 8-5). Such ratios are often called the apparent viscosities at the corresponding shearing stresses. Viscosity is measured in terms of flow in Pa s, with water as the base standard (value of 1.0). The higher the number, the less flow. 

The viscosity level in the range of the Newtonian viscosity r 0 of the flow curve can be determined on the basis of molecular models. For this, just a single point measurement in the zero-shear viscosity range is necessary, when applying the Mark-Houwink relationship. This zero-shear viscosity, q0, depends on the concentration and molar mass of the dissolved polymer for a given solvent, pressure, temperature, molar mass distribution Mw/Mn, i.e. 

The measurement of viscosity is important for many food products as the flow properties of the material relate directly to how the product will perform or be perceived by the consumer. Measurements of fluid viscosity were based on a correlation between relaxation times and fluid viscosity. The dependence of relaxation times on fluid viscosity was predicted and demonstrated in the late 1940 s [29]. This type of correlation has been found to hold for a large number of simple fluid foods including molten hard candies, concentrated coffee and concentrated milk. Shown in Figure 4.7.6 are the relaxation times measured at 10 MHz for solutions of rehydrated instant coffee compared with measured Newtonian viscosities of the solution. The correlations and the measurement provide an accurate estimate of viscosity at a specific shear rate. 

These data show clearly that that the intrinsic behavior in pure metals is visco-elastic with the velocity proportional to the applied stress (Newtonian viscosity). Although there is a large literature that speaks of a quasi-static Peierls-Nabarro stress, this is a fiction, probably resulting from studying of insufficiently pure metals. 

De Witt T., Mezner. W. A rheological equation of state which predicts non-Newtonian viscosity, normal stresses and dynamics module. J. Appl.Phys., 1985, v. 26, p. 889-892. 

For this simple geometry the shear rate, 7, is equal to the difference between the velocity at the top of the element, U, and the velocity at the bottom of the element, zero, divided by the height of element H. The shear stress is again r = F/A, the element surface area divided by the force. The viscosity, q, is the ratio of shear stress, r, divided by shear rate, 7, at any shear rate, q = rjq. For Newtonian materials such as water, molasses, or gasoline at the nominal shear rates found in everyday life, the slope of the shear stress with shear rate curve is a constant and equal to the Newtonian viscosity. 

Note that if n = 1 then this is the Newtonian viscosity and therefore m = p, and the viscosity is not a function of the shear rate and does not need to be corrected. The viscosity as a function of the corrected shear rate for the HDPE resin at 190°C is shown in Fig. 3.20. 

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