Viscosity theoretical predictions

In this section, we will show some relevant experimental results for dispersions and compare them mainly to viscosity theoretical predictions. More detailed information on experimental results in the oscillatory regime as well is given in reference [5]. 

The validity of the above conclusions rests on the reliability of theoretical predictions on excited state barriers as low as 1-2 kcal mol . Of course, this required as accurate an experimental check as possible with reference to both the solvent viscosity effects, completely disregarded by theory, and the dielectric solvent effects. As for the photoisomerization dynamics, the needed information was derived from measurements of fluorescence lifetimes (x) and quantum yields (dielectric constant, where extensive formation of ion pairs may occur [60], the observed photophysical properties are confidently referable to the unperturbed BMPC cation. Figure 6 shows the temperature dependence of the... 

A theoretical prediction of water-soluble polymer solutions is difficult to obtain due to their ability to build up aggregations and associations. A prediction of the viscosity yield is much easier to observe for solutions of synthetic polystyrene due to its simple solution structure. These solutions have been well characterized in other studies [19-23] concerning their chemical composition, molar mass and sample polydispersity. 

In contrast to the theoretical predictions, the absolute values of 2(Q), normalized with respect to the solvent viscosity r s and the temperature T, are non-universal. They vary from polymer to polymer and are always smaller than expected from theory... 

The dynamic process of bubble collapse has been observed by Lauter-born and others by ultrahigh speed photography (105 frames/second) of laser generated cavitation (41). As seen in Fig. 4, the comparison between theory and experiment is remarkably good. These results were obtained in silicone oil, whose high viscosity is responsible for the spherical rebound of the collapsed cavities. The agreement between theoretical predictions and the experimental observations of bubble radius as a function of time are particularly striking. 

The viscosity of polymer solutions has been considered theoretically by Flory,130 but although this theory has been applied to cellulose esters,131 no applications have yet been made in the case of the starch components. Theoretical predictions of the effect, on [17], of branching in a polymer molecule have been made,132 and this may be of importance with regard to the viscometric behavior of amylopectin. 

Figure 14.8 Generational dependence of relative viscosity, tv, on solution volume fraction for the first six generations, G, of PAMAM dendrimers in ethylenediamine (EDA) in comparison with theoretical predictions of Krieger (A), Eiler (B) and Mooney (C) hard sphere models (according to ref. [5])...

The theoretical prediction of these properties for branched molecules has to take into account the peculiar aspects of these chains. It is possible to obtain these properties as the low gradient Hmits of non-equilibrium averages, calculated from dynamic models. The basic approach to the dynamics of flexible chains is given by the Rouse or the Rouse-Zimm theories [12,13,15,21]. How-ever,both the friction coefficient and the intrinsic viscosity can also be evaluated from equilibrium averages that involve the forces acting on each one of the units. This description is known as the Kirkwood-Riseman (KR) theory [15,71 ]. Thus, the translational friction coefficient, fl, relates the force applied to the center of masses of the molecule and its velocity... 

The influence of fillers has been studied mostly at hl volume fractions (40-42). However, in addition, it is instructive to study low volume fractions in order to test conformity with theoretical predictions that certain mechanical properties should increase monotonlcally as the volume fraction of filler is Increased (43). For example, Einstein s treatment of fluids predicts a linear increase in viscosity with an increasing volume fraction of rigid spheres. For glassy materials related comparisons can be made by reference to properties which depend mainly on plastic deformation, such as yield stress or, more conveniently, indentation hardness. Measurements of Vickers hardness number were made after photopolymerization of the BIS-GMA recipe, detailed above, containing varying amounts of a sllanted silicate filler with particles of tens of microns. Contrary to expectation, a minimum value was obtained (44.45). for a volume fraction of 0.03-0.05 (Fig. 4). Subsequently, similar results (46) were obtained with all 5 other fillers tested (Table 1). 

As with viscosity, the theoretical predictions become more complex as the atoms themselves become more complex and more dense. For a polyatomic gas, the thermal conductivity is given by extension of Eq. (4.35) ... 

The unperturbed chain dimensions of near-monodisperse atactic PS are evaluated from intrinsic viscosity measurements. Negative values for the temperature coefficient of chain dimensions are found. Under conditions where specific solvent effects are eliminated or minimized, measurements yield results in excellent agreement with the theoretical predictions for atactic PS. 

In this expression, the primary environmental determinant is the viscosity in the denominator. Note that the exponential is slightly larger than in the Stokes-Einstein relation (Eq. 18-52). Since viscosity decreases by about a factor of 2 between 0°C and 30°C, D,w should increase by about the same factor over this temperature range. Furthermore, the influence of the molecule s size is also stronger in Eq. 18-53 than in 18-52 (note r, = constant V 173). In Box 18.4 experimental information on the temperature dependence of D,w is compared with the theoretical prediction from Eqs. 18-52 and 18-53. 

Compared experimental measurements for Newtonian and power law fluids to theoretical predictions and showed, that the apparent viscosity predicted by the Bostwick measurement must be correlated with flow behavior during processing and thus could be very useful to incorporate into food process design and control. 

A lack of experimental data in the literature makes the check-up-of Eqs. (2.1)—(2.3) rather difficult to perform, most of the data have been obtained for Newtonian liquids, 2, 4). Equation (2.3) was shown to be valid at f = qv/cr = 0.3255 at f > 2.4 the formation of waves and disturbances of liquid flow was observed. The lower the viscosity of a system, the easier these phenomena are to be observed. The value of K was experimentally shown14> to be equal to 0.657, i.e. rather close to the theoretically predicted value K = 2/3. 

Figure 6.34 Comparison between experiments and theoretical predictions of maximum pressure between the rolls during the calendering process of an unplasticized PVC film. A power law index, n, of 0.1505 and a consistency index, m, of 155.2 kPa-s were used in the power law model of the viscosity.

From slow-shear-rate solutions of the Smoluchowski equation, Eq. (11-3), with the Onsager potential, Semenov (1987) and Kuzuu and Doi (1983, 1984) computed the theoretical Leslie-Ericksen viscosities. They predicted that ai/a2 < 0 (i.e., tumbling behavior) for all concentrations in the nematic state. The ratio jai is directly related to the tumbling parameter X by X = (1 -h a3/a2)/(l — aj/aa). Note the tumbling parameter X is not to be confused with the persistence length Xp.) Thus, X < I whenever ai/a2 < 0. As discussed in Section 10.2.4.1, an approximate solution of Eq. (11-3) predicts that for long, thin, stiff molecules, X is related to the second and fourth moments Sa and S4 of the molecular orientational distribution function (Stepanov 1983 Kroger and Sellers 1995 Archer and Larson 1995) ... 

Figure 12.7 Relative viscosity r)r = versus hydrated micellar volume fraction

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