True Viscosity

Reynolds numbers are an order of magnitude below turbulence. The D/1 ratios are less than 1/10 except for the 10 hi" pore membrane in which Foiseuille flow formulas need to be corrected for end effects to determine true viscosities or shear rates. 

Orifice. Orifice viscometers, also called efflux or cup viscometers, are commonly used to measure and control flow properties in the manufacture, processing, and application of inks, paints, adhesives, and lubricating oils. Their design answered the need for simple, easy-to-operate viscometers in areas where precision and accuracy are not particularly important. In these situations knowledge of a true viscosity is unnecessary, and the efflux time of a fixed volume of liquid is a sufficient indication of the fluidity of the material. Examples of orifice viscometers include the Ford, Zahn, and Shell cups used for paints and inks and the Saybolt Universal and Furol instruments used for oils (Table 5). 

Linear equations of the type v = ct — C, where c and C are constants, relate kinematic viscosity to efflux time over limited time ranges. This is based on the fact that, for many viscometers, portions of the viscosity—time curves can be taken as straight lines over moderate time ranges. Linear equations, which are simpler to use in determining and applying correction factors after calibration, must be applied carefully as they do not represent the true viscosity—time relation. Linear equation constants have been given (158) and are used in ASTM D4212. 

Several methods of correlating film thickness data have been published in the literature. Thus, several investigators have plotted the film thickness b as a function of the Reynolds number 2VRe this yields a different curve for each liquid and is not very convenient. Hopf (H18) presented his film thickness results in the form of an apparent liquid viscosity as a function of IVbo. This type of plot makes it possible to see very clearly the value of IVrc at which turbulence commences, since at this point the apparent viscosity begins to differ from the true viscosity. 

In the food industry it has often been difficult to obtain true viscosity measurements (unithj.j) of complex fluid foods such as coarse fruit suspensions. These are usually non-Newtonian suspensions. Fruit concentrates are dispersions of solid particles (pulp) in aqueous media (serum). Their rheological properties are of interest in practical applications related to processing, storage stability, and sensory properties. Expensive rheometers are often not available in quality control and product development laboratories. However, viscosity is nonetheless an important quality factor of these products. 

The raw data from the capillary rheometer measurements are subject to four important corrections to obtain true viscosity and shear rate values. These corrections, which are fully described in Kwag (1998) and Kwag et al. 

Viscosity index, the customary basis for comparison of change of viscosity in hydrocarbon oils, becomes less satisfactory when applied to silicone oils, because the viscosity index varies with viscosity as well as with the temperature coefficient. In silicone oils the variation of viscosity with temperature is too small in relation to the viscosity itself. A true viscosity-temperature coefficient (VTC) has been proposed as a more satisfactory criterion [see Wilcock, Mechanical Engineering 66, 739 (1944)1. 

The term apparent viscosity refers to a viscosity that has been back-calculated from impeller torque or horsepower. A true-viscosity reading should be measured at a fixed and known shear rate. The effective shear rate developed by a mixing impeller is really a distribution of different shear rates. This distribution is probably most closely related to the shear between the helix blade and the tank... 

The first consequence of the introduction of two additional viscosities vt and Va to the true viscosity v is that the Reynolds number really seen by the code is ... 

With Eq. (17) find 17 pp for dry air and use this value in Eq. (16) to find the value of K. Now calculate 17 pp for the other gases from Eq. (16) (one can use the approximate value of rj in evaluating the kinetic-energy correction term). Finally, apply the slip correction to obtain the true viscosity. The gas pressure p that appears explicidy in Eq. (19) and implicitly in Eq. (16), where p = pMRT, can be replaced by the average inlet pressure (pj + p()l2. 

Table 3-1. Ratio of inferred-to-true viscosities in a Couette device versus gap width...

Just to give an idea how different are the apparent and true shear rates, we will notice that the higher the shear thinning effect, the larger the difference. For example, at the power-law index n = 0.8, the difference in shear rates and, hence, apparent and true viscosities is 6.25%. For n = 0.2, the difference is 100%. 

This standard covers measurement of the rheological properties of polymers with both stable and unstable melt viscosity parameters at various temperatures and shear rates. The test procedure lists typical test temperature conditions for polyethylene 190°C, for polypropylene 230°C, for poly(vinyl chloride) 170-205°C, however, this indicates that the most useful data are generally obtained at temperatures consistent with processing experience. The test method also prescribes using the Rabinowitsch shear rate correction (see above) and indicates that the basic rheology equations (17.10), (17.15) and (17.16) yield true shear rate and true viscosity for Newtonian fluids only for non-Newtonian fluids only the apparent shear rate and viscosity are obtained. 

These facts indicate that, from the chemical point of view, there is only a single actomyosin complex of composition three parts of myosin to one of actin and that mixtures in any other proportion contain one component in excess. If this is so, the maximum in true viscosity should be at the 3 1 ratio, a point which should be tested in the Couette viscometer. Since artificial actomyosin solutions contain several very rapidly sedimenting fractions (H. H. Weher, 1947 Snellman and Gelotte, 1950 Johnson and Landolt, 1950), and since their viscosities are very variable (Jaisle, 1951 see Section III, 4d), it would have to be assumed that the same 3 1 complex forms threads of very vaiiable length and thickness. This may be so, but the problem requires further elucidation. It is possible that actomyosins with different physical properties represent sharply defined stages in the interaction of the two components. 

Mr. Goldstein, In the commercial use of karaya the gum is designed to fulfill a specific purpose. If a manufacturer of a salad dressing wants a thickening of his product he adds karaya and measures viscosity, usually by a pipet method. This may not be a true viscosity, but it seems to fit the needs of the situation. 

Unlike hard, noninteractive particles, however, shear rate affects viscosity as a result of bond breakage of the large fractal aggregates during viscosity measurement [18]. Hence, the viscosity values of this derivation should be considered the true viscosity of solution with negligible shear rate effects. 

Since equation (11.10) yields a constant for Newtonian fluids, these form the basis for calculating the apparent viscosity t] pp, in a second step, a correction is applied to calculate the true viscosity of the system in question. 

The effect of crystallization on the measured viscosity, which is not equal to the true viscosity of the melt, depends upon the details of the crystallization process. If a sample crystallizes via growth of crystals from the surface, the sample is essentially encapsulated in a shell of crystals which prevent deformation, and the viscosity appears to... 

In this expression, r is in Pas, T is the temperature in K, Tg is the end point of the glass transition, and A(l/Tg) is equal to (1/Tg-l/Tg). In most cases, this expression will yield a calculated value of the viscosity which is within one order of magnitude or less of the true viscosity, as is shown in Figure 12.8 for a NIST standard glass. The simplicity of this method provides a very useful tool for estimating the viscosity of an unknown melt from a single DSC measurement. 

With floppier viscometers, the time required for a rolling ball to run along an inclined tube is measured. In Cochius tubes, the time taken for an air bubble to rise is a measure of the viscosity. Here, the true viscosities, shear stresses, and shear gradients are also difficult to determine. 

For shear-thinning fluids, the apparent shear rate at the wall is less than the true shear rate, with the converse applying near the centre of the tube [Laim, 1983]. Thus at some radius, x R, the true shear rate of a fluid of apparent viscosity /r, equals that of a Newtonian fluid of the same viscosity. The stress at this radius, is independent of fluid properties and thus the true viscosity... 

The occurrence of this phenomenon may be tested by comparing the viscosity ftmctions obtained using capillaries of similar length-to-radius ratios, L/R, but of different radii. Any apparent wall slip may then be corrected for and the true viscosity of the fluid determined by extrpolating the results obtained to infinite pipe diameter. In the relation developed by Mooney [1931], apparent wall shear rates obtained for constant length-to-radius ratio are plotted against L/K). 

The value of viscosity used to make the particle size calculation may not be the true viscosity. Used in this way the value entered for viscosity should be considered a calibration factor used to report the particle size that has been previously determined by a fully dilute experiment. 

The variation of Qs/Q with the shear stress can be rationalized by observing the variation of viscosity with the shear stress in both suspensions. The true viscosity of the suspensions can be obtained by using Equations 3,4 and 6 in parallel disk torsional flows and nations 8-12 in capillary flows. 

The true viscosity vs. the shear stress behavior of the suspensions are shown in Figures 9 and 10 for suspensions I and II respectively. 

The specific viscosity, introduced in Chap. 2 still depends on the concentration according to Eq. (4.5). In order to obtain the true viscosity enhancing properties of a polymer, the reduced viscosity is introduced ... 

However, the reduced viscosity is also not totally independent of the concentration. Even though viscosimetric measurements are performed in the range of dilute solutions (below the critical concentration c where the single polymer coils start to interpenetrate), small polymer interactions (that are decreasing with a decreasing concentration) have to be considered. The true viscosity enhancing properties of a polymer is therefore the reduced viscosity extrapolated to c—>0 ... 

Capillary and slit-die rheometers are used to determine the dependency of viscosity on shear rate. Since most molten polymers exhibit non-Newtonian behavior, it is important to be able to characterize this behavior. Measurements are made using a piston-driven cylinder that drives the molten polymer through a die of precise dimensions. The pressure drop across the die is measured, as is the flow rate through the die. Temperature is precisely controlled throughout the measurement. This test yields precise viscosity measurements as a function of temperature and shear rate. However, measurements tend to have artifacts in them, which need to be corrected in order to obtain true viscosity using Bagley and Rabinowitsch corrections. Capillary rheometers are also used to determine the effects of slip, a phenomenon in which the velocity of the melt at the capillary wall is nonzero. Slip has important implications for highly filled materials. 

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