Viscosity versus temperature

If we look at Figure 3.5, we see that some liquids present a curve of viscosity versus temperature above that of water while others lie below. By systematically varying the a and values in Eq. (3.3) and using these to calculate the /q values versus the temperature, we obtain the information about their influence on the viscosity versus temperature relationship. Those plots that lie below the water curve in Figure 3.5 may represent the rules needed to model liquids such as benzene, methanol, or ethyl acetate. The a and coefficients that produce /q values leading to plots above water in Figure 3.5 are candidates for the modeling of liquids such as ethanol, propanol, or butanol. 

A gel of diesel or crude oil can be produced using a phosphate diester or an aluminum compound with phosphate diester [740]. The metal phosphate diester may be prepared by reacting a triester with phosphorous pentoxide to produce a polyphosphate, which is then reacted with an alcohol (usually hexanol) to produce a phosphate diester [870]. The latter diester is then added to the organic liquid along with a nonaqueous source of aluminum, such as aluminum isopropoxide (aluminum-triisopropylate) in diesel oil, to produce the metal phosphate diester. The conditions in the previous reaction steps are controlled to provide a gel with good viscosity versus temperature and time characteristics. All the reagents are substantially free of water and will not affect the pH. 

The standard process cycle for polymer matrix composites is a two-step cure cycle, as seen in Figure 8.1. In such cycles the temperature of the material is increased from room temperature to the first dwell temperature and this temperature is held constant for the first dwell period ( 1 hour). Afterward, the temperature is increased again to the second dwell temperature and held constant for the second dwell period (2-8 hours). After the second dwell, the part is cooled down to room temperature at a constant rate. Because there are two dwell periods, this type of cure cycle is referred to as a two-step cure cycle. The purpose of the first dwell is to allow gases (e.g., entrapped air, water vapor, or volatiles) to escape and to allow the matrix to flow, which leads to compaction of the part. Thus, the viscosity of the matrix must be low during the first dwell. Typical viscosity versus temperature profiles of polymer matrices show that as the temperature is increased, the viscosity of the polymer decreases until a minimum viscosity is reached. As the temperature is increased further, the polymer begins to cure rapidly and the viscosity increases dramatically. The first dwell temperature must be chosen judiciously so that the viscosity of the resin is low while the cure is kept to a minimum. 

Using the viscosity versus temperature table evaluated from the Chapman-Enskog expression in the previous problem, determine a best fit for the S parameter in the form of a Sutherland viscosity expression. Assume reference values of 7o = 273 K and i o = 1.716 x 10-5 N-s/m2. 

A flow model may be considered to be a mathematical equation that can describe rheological data, such as shear rate versus shear stress, in a basic shear diagram, and that provides a convenient and concise manner of describing the data. Occasionally, such as for the viscosity versus temperature data during starch gelatinization, more than one equation may be necessary to describe the rheological data. In addition to mathematical convenience, it is important to quantify how magnitudes of model parameters are affected by state variables, such as temperature, and the effect of structure/composition (e.g., concentration of solids) of foods and establish widely applicable relationships that may be called functional models. 

Figure 2-14 Applicability of the Arrhenius Model to the Apparent Viscosity versus Temperature Data on a Concentrated Orange Juice Serum Sample (Vitali and Rao, 1984b) is Shown.

The Arrhenius equation did not describe very well the influence of temperature on viscosity data of concentrated apple and grape juices in the range 60-68 °Brix (Rao et al., 1984, 1986). From non-linear regression analysis, it was determined that the empirical Fulcher equation (see Ferry, 1980 p. 289, Soesanto and Williams, 1981) described the viscosity versus temperature data on those juice samples better than the Arrhenius model (Rao et al., 1986) ... 

The WLF equation was also used to correlate viscosity versus temperature data on honeys (Al-Malah et al., 2001 Sopade et al., 2003). Because of the empirical nature of the Fulcher equation and the empirical origin of the WLF equation, their use with... 

Figure 3-23 Apparent Viscosity versus Temperature Data on a Starch Dispersion as a Function of Shear Rate (80-640 s ) and temperature (35-118°C) (From Rao et al. 1999).

The same modeling procedure was applied to 3.5% com SDs and the results used to numerically simulate heat transfer to SDs in a can (Yang, 1997). From recent studies (Yang and Rao, 1998 Liao et al., 1999), the general shape of viscosity versus temperature for native, as opposed to cross-linked, starch dispersions is as shown in Figure 4-20. It is important to note that the values of viscosity of the... 

In general, other native starch dispersions will be exhibit similar viscosity versus temperature profiles as in Figure 8-7, while cross-linked starch dispersions, due to limited granule rupture, will not exhibit a sharp decrease in viscosity of the segment CD. The t] versus 7 profiles of a 5% CWM STD obtained at values of cu from 1.26 to 31.38rads , 3% strain, andaheatingrateof2.1°C min (Figure 8-8)followed the equation (Tattiyakul and Rao, 2000) ... 

The data obtained were plotted as viscosity versus temperature for the different materials and displayed the expected exponential increase in viscosity as the temperature decreased. For most of the slags a characteristic sudden increase in viscosity was noted, as in some related studies (J 3 ). Some typical results are shown and compared with the Watt-Fereday and modified silica ratio projections, assuming only a liquid phase exists, in Figures 1 and 2 (slags 1 12). 

To further investigate the characteristics of the slags, plots of the logarithm of viscosity versus temperature were made. These indicated straight lines or two line segments. For slags with a sudden increase in viscosity at lower temperatures, two segments were observed. Shear rates were not varied and the various types of non-Newtonian behavior were not explored. A related study indicated pseudoplastic behavior for this type of material (9 ). 

Plots of the logarithm of viscosity versus temperature showed one or two straight line segments, consistent with other observations on similar systems in the temperature range studied. 

VISCOSITY VERSUS TEMPERATURE oloy, ACRYLAMIDE GROUT A10% AC-400 GROUT 0.S /d TEA, 0.5% AP, 300 ppm KFe 50% SILICATE GROUT 5% FORMAMIOE 5% ETHYL ACETATE 1 j ... 

FIGURE 5.8 PAMOA75 viscosity versus temperature. Source Zhou and Huang (1997). 

Fig. 2 Viscosity versus temperature characteristics for various glass compositions [7]. 1, Fused silica 2, 96% silica 3, soda lime (plate glass) 4, lead silicate (electrical) 5, high-lead 6, borosilicate (low expansion) 10. aluminosilicate...

Fig. 12. Viscosity versus temperature for tri-a-naphthylbenzene, based on data of Ref. 53. The solid curve is the best fit to (7.2) and (7.6), for the parameters given in Table II. The dashed curve is the best fit (Ref. 53) with...

Figure 31.6 Shear viscosity versus temperature for an unsaturated polyester resin (UP)-clay slurry indicating the temperature for the onset of the gelation reaction. Source Reproduced with permission from Rivera-Gonzaga JA, Sanchez-Solis A, Manero O. J Polym Eng 2012 32,1 [91]. Copyright 2012 De Gruyter.

Figure 24.8. Viscosity versus temperature for liquids (Incropera and DeWitt, 1996 Poling, Prausnitz, and O Connell, 2001 U.S. EPA, 2002a).

Figure 6.18 (a) Viscosity versus temperature for a typical soda-lime glass and (b) plot of In (viscosity) versus... 

A number of specific viscosities have been designated as reference points on the viscosity/temperature curve for melts. These particular viscosities have been chosen because of their importance in various aspects of commercial or laboratory processing of glass forming melts. Several other reference temperatures which occur at approximate viscosities are also routinely used by glass technologists. These reference points are summarized in Table 6.1, and are shown on a typical curve of viscosity versus temperature for a soda-lime-silica melt in Figure 6.1. 

FIGURE 21.21 Viscosity versus temperature for strong and fragiie iiquids. 

When the interfacially active fractions from Daqing crude oil are used as emulsifier, the interfacial shear viseosity of the interfacial film between jet fuel and synthetie formation water is decreased as the temperature is raised. The eurve of the interfacial shear viscosity versus temperature is shown in Fig. 6. 

The specific critical hole free volume, is estimated as the specific volume at 0 K, which in turn is obtained from group contribution methods. The ratio of the molar volumes of the jumping units of components i andj, is computed using the values at 0 K. The pre-exponential factor. Do, and the critical energy needed by a molecule to overcome the attractive force, E, are obtained by fitting the Dullien equation for the self-diffusion coefficient to viscosity versus temperature data. Finally, the average hole-free volume per gram of the mixture, VfH/y, can be estimated from those of the individual species ... 

The free-volume parameters are again obtained by fitting viscosity versus temperature data using either the adopted Doohttle expression (low-molecular-weight species) or the Williams-Landel-Ferry equation (polymers). The glass transition temperature, Tg, is as reported in the literature or can be estimated from the melting temperature. 

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