Viscosity data

The coefficients B and Tq are obtained either by smoothing the experimental viscosity data, or by Van Velzen s method of contributing groups (see article 4.1.1.2). 

Both the intrinsic viscosity and GPC behavior of random coils are related to the radius of gyration as the appropriate size parameter. We shall see how the radius of gyration can be determined from solution viscosity data for these... 

The viscosity of sulfuric acid solutions is plotted in Figure 7 (55) other viscosity data may be found in References 54—60. Surface tension of sulfuric acid solutions is presented in Figure 8 (61). Surface tension of selected concentrations of sulfuric acid as a function of temperature up to the boiling point is given in Reference 62 other data are also available (58,59,63—65). 

The density of oleum at 20°C (76) and at 25°C (39) has been reported. The boiling points of oleum are presented in Figure 15 (86). Freezing points are shown in Figure 16 (75,87). An excellent discussion on the crystallisation points of oleum is available (69). The solubiUty of sulfur dioxide in oleum has been reported (68,69). Viscosity of oleum is summarized in Figure 17 (55) additional viscosity data are available (76). 

Fig. 1. Relative viscosity data for conventional petroleum, heavy oil, and bitumen.

Curves for the viscosity data, when displayed as a function of shear rate with temperature, show the same general shape with limiting viscosities at low shear rates and limiting slopes at high shear rates. These curves can be combined in a single master curve (for each asphalt) employing vertical and horizontal shift factors (77—79). Such data relate reduced viscosity (from the vertical shift) and reduced shear rate (from the horizontal shift). 

A number of viscometers have been developed for securing viscosity data at temperatures as low as 0 °C (58,59). The most popular instmments in current use are the cone plate (ASTM D3205), parallel plate, and capillary instmments (ASTM D2171 and ASTM D2170). The cone plate can be used for the deterniination of viscosities in the range of 10 to over 10 Pa-s (10 P) at temperatures of 0—70°C and at shear rates from 10 to 10 5 . Capillary viscometers are commonly used for the deterniination of viscosities at 60 —135°C. 

Multicomponent Mixtures No simple, practical estimation methods have been developed for predicting multicomponent hquid-diffusion coefficients. Several theories have been developed, but the necessity for extensive activity data, pure component and mixture volumes, mixture viscosity data, and tracer and binaiy diffusion coefficients have significantly limited the utihty of the theories (see Reid et al.). 

Note the smaller range of temperaaire for SO2 and H2O. This was due to lack of high temperature viscosity data. ... 

For non-New tonian fluids, viscosity data are very important. Every impeller has an average fluid shear rate related to speed. For example, foi a flat blade turbine impeller, the average impeller zone fluid shear rate is 11 times the operating speed. The most exact method to obtain the viscosity is by using a standard mixing tank and impeller as a viscosimeter. By measuring the pow er response on a small scale mixer, the viscosity at shear rates similar to that in the full scale unit is obtained. 

All three methods discussed above appear to provide equally high quality ionic liquid viscosity data. However, the rotational viscometer could potentially provide additional information concerning the Newtonian behavior of the ionic liquids. The capillary method has been by far the most commonly used to generate the ionic liquid viscosity data found in the literature. This is probably due to its low cost and relative ease of use. 

The highly detailed results obtained for the neat ionic liquid [BMIM][PFg] clearly demonstrate the potential of this method for determination of molecular reorienta-tional dynamics in ionic liquids. Further studies should combine the results for the reorientational dynamics with viscosity data in order to compare experimental correlation times with correlation times calculated from hydrodynamic models (cf [14]). It should thus be possible to draw conclusions about the intermolecular structure and interactions in ionic liquids and about the molecular basis of specific properties of ionic liquids. 

Viscosity is normally measured at two different temperatures typically 100°F (38°C) and 210°F (99°C). For many FCC feeds, the sample is too thick to flow at 100°F and the sample is heated to about 130°F. The viscosity data at two temperatures are plotted on a viscosity-temperature chart (see Appendix 1), which shows viscosity over a wide temperature range [4]. Viscosity is not a linear function of temperature and the scales on these charts are adjusted to make the relationship linear. 

ASTM D-2502 is one of the most accurate methods of determining molecular weight. The method uses viscosity measurements in the absence of viscosity data, molecular weight can be estimated using the TOTAL correlation. 

Intermolecular potential functions have been fitted to various experimental data, such as second virial coefficients, viscosities, and sublimation energy. The use of data from dense systems involves the additional assumption of the additivity of pair interactions. The viscosity seems to be more sensitive to the shape of the potential than the second virial coefficient hence data from that source are particularly valuable. These questions are discussed in full by Hirschfelder, Curtiss, and Bird17 whose recommended potentials based primarily on viscosity data are given in the tables of this section. 

The most widely used molecular weight characterization method has been GPC, which separates compounds based on hydrodynamic volume. State-of-the-art GPC instruments are equipped with a concentration detector (e.g., differential refractometer, UV, and/or IR) in combination with viscosity or light scattering. A viscosity detector provides in-line solution viscosity data at each elution volume, which in combination with a concentration measurement can be converted to specific viscosity. Since the polymer concentration at each elution volume is quite dilute, the specific viscosity is considered a reasonable approximation for the dilute solution s intrinsic viscosity. The plot of log[r]]M versus elution volume (where [) ] is the intrinsic viscosity) provides a universal calibration curve from which absolute molecular weights of a variety of polymers can be obtained. Unfortunately, many reported analyses for phenolic oligomers and resins are simply based on polystyrene standards and only provide relative molecular weights instead of absolute numbers. 

It is to be expected that the relative values of the univalent crystal radius would be of significance with respect to physical properties involving atomic sizes. That this is true for the viscosity of the rare gases is seen from the radii evaluated by Herzfeld (Ref. 12, p. 436) from viscosity data He, 0.04 (0.93) Ne, 1.18 (1.12) Ar, 1.49 (1.54) Kr, 1.62 (1.69) Xe, 1.77 (1.90). (The values in parentheses are the univalent crystal radii.)... 

Thus, the enhancement of heat transfer may be connected to the decrease in the surface tension value at low surfactant concentration. In such a system of coordinates, the effect of the surface tension on excess heat transfer (/z — /zw)/ (/ max — w) may be presented as the linear fit of the value C/Cq. On the other hand, the decrease in heat transfer at higher surfactant concentration may be related to the increased viscosity. Unfortunately, we did not find surfactant viscosity data in the other studies. However, we can assume that the effect of viscosity on heat transfer at surfactant boiling becomes negligible at low concentration of surfactant only. The surface tension of a rapidly extending interface in surfactant solution may be different from the static value, because the surfactant component cannot diffuse to the absorber layer promptly. This may result in an interfacial flow driven by the surface tension gradi-... 

The intrinsic viscosity data calculated from the methods of Fluggins, Kramer, Schultz-Blaschke and Martin are shown in Table 1, and how to perform these steps are shown in Figure 1. 

Olivares M.L., Peirotti M.B., Deiber J.A. 2006. Analysis of gelatin chain aggregation in dilute aqueous solutions through viscosity data. Food Hydrocolloids 20, 1039-1049. 

The angular momentum conservation equation couples the viscous and the elastic effects. The angular profiles of the director and the effective viscosity data are computed for one set of material parameters based on published data in literature. The velocity profiles are also attained from the same dataset. The results show that the alignment of molecules has a strong influence on the lubrication properties. 

The scaling results above all pertain to local segmental relaxation, with the exception of the viscosity data in Figure 24.5. Higher temperature and lower times involve the chain dynamics, described, for example, by Rouse and reptation models [22,89]. These chain modes, as discussed above, have different T- and P-dependences than local segmental relaxation. 

The experimental viscosity data were analysed according to the relation... 

The recommended viscosity data for NaCl and KNO3 melts are available for calibration, as mentioned in Section II. There still exists appreciable, though small, disagreement between the data obtained by the two groups, that is, 0ye s group and Nagashima s group. Ejima et al. ... 

We thank J. C. Rowell for the intrinsic viscosity data for the polymer samples used in this study. 

The determined r 0-M-c equations [Eqs. (14) and (15)] are valid over a very wide concentration range, but they are restricted to samples having molar masses greater than approximately 20,000 g/mol. Viscosity data for lower molar masses show a more rapid increase in the riSp—(o [iq]) plot than the general curve, because it is assumed that the number of polymer segments is too low to form a coil. 

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