Non-Newtonian viscosity measurement

Here M is the molecular weight and V the partial specific volume of the solute, N the Avogadro number, k the Boltzmann constant, and T the absolute temperature s and D are the sedimentation and translational diffusion coefficients (after extrapolation to infinite dilution). The translational frictional coefficients from both measurements are regarded as identical, i.e., f, = fd. The rotary frictional coefficient, designated as f, can be determined from either flow birefringence or non-Newtonian viscosity measurements. 

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. 

Non newtonian viscosity measurements performed on the WSR 301 solutions after degradation lead to an intrinsic viscosity... 

The unsuitable nature of many commercial instruments which are in common use clearly illustrates the confusion prevalent in the field of viscometric measurements. Many instruments measure some combination of properties which depend only partly on the fluid consistency since the flow is not laminar. In others the shear rates are indeterminate and the data cannot be interpreted completely. Examples of such units include rotational viscometers with inserted baffles, as in the modified Stormer instruments in which the fluid flows through an orifice, as in the Saybolt or Engler viscometers instruments in which a ball, disk, or cylinder falls through the fluid, as in the Gardiner mobilometer. Recently even the use of a vibrating reed has been claimed to be useful for measurement of non-Newtonian viscosities (M14, W10), although theoretical studies (R6, W10) show that true physical properties are obviously not obtainable in these instruments for such fluids. These various instru-... 

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). 

Evaluating the Flow Curve from Experimental Data The flow rate of 3% CMC solution in water was measured in a long capillary as a function of pressure drop. Based on the results given in the following table, compute the non-Newtonian viscosity versus the shear-rate curve. 

There is Newtonian and Non-Newtonian viscosity. With Newtonian viscosity the ratio of shearing stress to the shearing strain is constant such as, theoretically, water. In non-Newtonian behavior, which is the case for plastics, the ratio varies with the shearing stress. Such ratios are often called the apparent viscosities at the corresponding shearing stresses. Viscosity is measured in terms of flow in Pas (P), with water as the base standard value of 1.0. The higher the number, the less flow. 

The viscosity of Newtonian liquids can be measured simply, by one-point determinations with viscometers, such as rotational, capillary, or falling ball viscometers. For non-Newtonian materials, measurement of... 

Equations (19d and e) have been extensively used in flow birefringence measurements and, more recently, in non-Newtonian viscosity studies. (For an ellipsoid there are three translational and rotary frictional coefficients,... 

As mentioned earlier, ideally the best answer should come from the determination of the 5-function. Unfortunately at present the rotary diffusion coefficient is usually the least reliable quantity in all hydrodynamic measurements because of errors inherent in the physical methods of flow birefringence and perhaps also non-Newtonian viscosity (see Section IV). (Electric birefringence also may not give the same rotary diffusion coefficient as the other two methods, since the equivalent ellipsoids can be different under shearing stress and under electrical field.) Edsall (1954) has also illustrated the impossibility of evaluating the axial ratio from the 5-function. The latter was about 0.80 for fibrinogen which corresponded to a prolate ellipsoid with an axial ratio of more than 300. If the rotary diffusion coefficient were only about 15% greater than that listed in Table V the calculated axial ratio would decrease to between ten and twenty. 

With the development of the non-Newtonian viscosity theories it is now possible to compare the rotary diffusion coefficient and thereby the calculated length (or diameter) of the rigid particles as obtained from this technique with that from the commonly used flow birefringence method. Since both measurements depend upon the same molecular distribution function (Section III) they should give an identical measure of the rotary diffusion coefficient. Differences, however, will arise if the system under study is heterogeneous. The mean intrinsic viscosity is calculated from Eq. (7) whereas the mean extinction angle, x, for flow birefringence is defined by the Sadron equation (1938) ... 

In this review we have briefly discussed the theoretical and experimental aspects of both Newtonian and non-Newtonian viscosities of polymer solutions. To protein chemists one of the interesting developments is no doubt the re-examination of the (Newtonian) viscosity treatments of protein solutions. There are many assumptions involved in the effective use of intrinsic viscosity measurements for evaluating the asymmetry of the protein molecules, however attractive the conventional treatment may have appeared for the past two decades. Carefully interpreted, the intrinsic viscosity (at zero gradient) can still provide a reasonable estimate of the axial ratios of the protein molecules. The concept of equivalent hydrodynamic volume, sound in principle, has put the viscometry of protein solutions in a proper perspective, although the quantitative aspects of this new approach still... 

Experimental data for polymer solutions have been reported by Osaki, Tamura, Kurata, and Kotaka (60), by Booij (12), and by Macdonald (50). Osaki et al. used polystyrene in toluene, polymethylmethacrylate in diethylphthalate, and poly-n-butylmethacrylate in diethylphthalate. Booij s data were for aluminum dilaurate in decalin and a rubbery ethylene-propylene copolymer in decalin. Macdonald s experiments were performed on several polystyrenes in several Aroclors and on polyisobutylene in Primol. Shortly after the original publication of the Japanese group, Macdonald and Bird (51) showed that a nonlinear viscoelastic constitutive equation was capable of describing quantitatively their data on both the non-Newtonian viscosity and the superposed-flow material functions. Other measurements and continuum model calculations have been described by Booij (12 a). 

If flocculation occurs slowly, the viscosity, measured at low rates of shear, increases with time during the rest period after an efficient shearing. When this happens the paint is said to be thixotropic. If there is no dependence on time or on the previous treatment of the paint and if the viscosity decreases as the rate of shear increases, then the paint is said to be pseudo-plastic. If there is a minimum stress required before any flow can occur at all, the viscosity behaviour is said to be plastic. All these types of behaviour are, of course, contrary to Newton s equation and are grouped together under the heading of non-Newtonian viscosity. 

We have measured by quasi-elastic light scattering the hydro-dynamic radius of PEO s samples in 2 solvents water and water-isopropanol mixture (90%/10%) as a function of the age of the solutions. We study the influence of the solvent on the properties of the 2 higher molecular weight samples (WSR 301 and Coagulant) in laminar (non-newtonian viscosity) and turbulent (drag reduction) flow conditions. 

In most studies dealing with heat and mass transfer, it has been generally assumed that the thermo-physical properties, such as thermal conductivity, specific heat, molecular diffusivity of non-Newtonian polymer solutions, are the same as that for water, except for their non-Newtonian viscosity. Intuitively, one would expect the surface tension to be an important variable by way of influence on bubble dynamics and shape, but only a few investigators have controlled/measured/included it in their results. The available correlations can be broadly classified into two types first, those which directly relate the volumetric mass transfer coefficient with the liquid viscosity and gas velocity. The works of Deckwer et al. [36], Godbole et al. [42] and Ballica and Ryu [60] illustrate the applicability of this approach. All of them have correlated their results in the following form ... 

The Gladstone pipeline uses Wilson-Snyder positive displacement pumps. At the weight concentration of 60-64%, the slurry acted as a Bingham mixture, with non-Newtonian viscosity characteristics. However, it did feature clay, sand, and iron, as the materials were formulated for the manufacture of clinker cement. The pipeline operation speed was maintained at 2 m/s and the pressure drop was around 300 kPa/km. API 5LX steel with a high yield strength was used. Corrosion rates as high as 0.25 mm/year were measured during the initial phase of operation of the pipeline. 

Table 2 Viscosity correction factors for non-Newtonian liquids measured in wide-gap concentric cylinder viscometers.

In molecular theories for non-Newtonian viscosity (Section El of Chapter 10), the reciprocal of a characteristic time r, is a measure of the shear rate above which non-Newtonian viscosity is observed (for example, where 77/170 falls to about 0.8). It follows from equation 12 that d log r,/rf log M - and in the above investi-... 

Optimising the balance of Newtonian to non-Newtonian viscosity within a grade has been shown to give measurable benefits in foel economy. 

This flow is shown in Figure 2(a) where the velocity distribution is given by Vx = yy,Vy = 0,V2 = 0 and y = dv /dy is a constant. For this flow it is possible to measure a shear stress a first normal stress difference x — and a second normal stress difference These three quantities are in general strong functions of the shear rate y — dVx/dyl It is conventional to define three viscometric functions , namely the (non-Newtonian) viscosity rj (equation 1), the first normal stress coefficient Pi (equation 2) and the second normal stress coefficient 2 (equation 3), as follows... 

The dramatic decrease in the non-Newtonian viscosity with shear rate was one of the first properties to be measured extensively for polymeric liquids, because of its great importance in the description and prediction of polymer-melt flow in industrial problems. Clearly if the viscosity of a fluid is varying by several orders of magnitude in a flow field, this is an important effect that cannot be ignored. 

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