Viscosities variation

At the saturation pressure, the viscosity variation with temperature follows a law analogous to that of Clapeyron for the vapor pressure f ) ... 

Incorporation of viscosity variations in non-elastic generalized Newtonian flow models is based on using empirical rheological relationships such as the power law or Carreau equation, described in Chapter 1. In these relationships fluid viscosity is given as a function of shear rate and material parameters. Therefore in the application of finite element schemes to non-Newtonian flow, shear rate at the elemental level should be calculated and used to update the fluid viscosity. The shear rale is defined as the second invariant of the rate of deformation tensor as (Bird et at.., 1977)... 

The properties of a botanical gum are determined by its source, the climate, season of harvest, and extraction and purification procedures. Table 6 illustrates one of the important basic properties of all gums, ie, the relationship between concentration and solution viscosity. The considerable viscosity variation observed among gums from different sources determines, in part, their uses. 

Although the viscosity index is useful for characterizing petroleum oils, other viscosity—temperature parameters are employed periodically. Viscosity temperature coefficients (VTCs) give the fractional drop in viscosity as temperature increases from 40 to 100°C and is useful in characterizing behavior of siHcones and some other synthetics. With petroleum base stocks, VTC tends to remain constant as increasing amounts of VI improvers are added. Constant B in equation 9, the slope of the line on the ASTM viscosity—temperature chart, also describes viscosity variation with temperature. 

The value of the first coefficient b, for the dispersion of spherical particles is well known and generally accepted. This is Einstein coefficient b, = 2.5, taking into account the viscosity variation of the dispersion medium upon introducing noninteracting solid particles of spherical form into it. Thus, for tp [Pg.83]

For an incompressible fluid, the density variation with temperature is negligible compared to the viscosity variation. Hence, the viscosity variation is a function of temperature only and can be a cause of radical transformation of flow and transition from stable flow to the oscillatory regime. The critical Reynolds number also depends significantly on the specific heat, Prandtl number and micro-channel radius. For flow of high-viscosity fluids in micro-channels of tq < 10 m the critical Reynolds number is less than 2,300. In this case the oscillatory regime occurs at values of Re < 2,300. 

The treatment of viscosity variations included the possibility of variable density. Equations (8.12) and (8.52) assumed constant density, constant a, and constant otj-. We state here the appropriate generalizations of these equations to account for variable physical properties. 

Some information concerning the intramolecular relaxation of the hyperbranched polymers can be obtained from an analysis of the viscoelastic characteristics within the range between the segmental and the terminal relaxation times. In contrast to the behavior of melts with linear chains, in the case of hyperbranched polymers, the range between the distinguished local and terminal relaxations can be characterized by the values of G and G" changing nearly in parallel and by the viscosity variation having a frequency with a considerably different exponent 0. This can be considered as an indication of the extremely broad spectrum of internal relaxations in these macromolecules. To illustrate this effect, the frequency dependences of the complex viscosities for both linear... 

The power of this technique is two-fold. Firstly, the viscosity can be measured over a wide range of shear rates. At the tube center, symmetry considerations require that the velocity gradient be zero and hence the shear rate. The shear rate increases as r increases until a maximum is reached at the tube wall. On a theoretical basis alone, the viscosity variation with shear rate can be determined from very low shear rates, theoretically zero, to a maximum shear rate at the wall, yw. The corresponding variation in the viscosity was described above for the power-law model, where it was shown that over the tube radius, the viscosity can vary by several orders of magnitude. The wall shear rate can be found using the Weissen-berg-Rabinowitsch equation ... 

Effect of PS Latex Particle Size on Adsorbed Layer Thickness. Figure 6 shows the variation of reduced viscosity with volume fraction for 190, 400, and HOOnm-size bare and PVA-covered PS latex particles. The viscosity variation of the different-size bare particles was the same, with an Einstein coefficient of ca. 3.0. The... 

Also plotted is the viscosity variation with HCl added for 0.2 M C14DAO. Maximum viscosity is observed when half of the amine oxide molecules are in the cationic form. However, in the absence of NaOH the change in viscosity with HCl added is... 

Fluids that show viscosity variations with shear rates are called non-Newtonian fluids. Depending on how the shear stress varies with the shear rate, they are categorized into pseudoplastic, dilatant, and Bingham plastic fluids (Figure 2.2). The viscosity of pseudoplastic fluids decreases with increasing shear rate, whereas dilatant fluids show an increase in viscosity with shear rate. Bingham plastic fluids do not flow until a threshold stress called the yield stress is applied, after which the shear stress increases linearly with the shear rate. In general, the shear stress r can be represented by Equation 2.6 ... 

Aqueous solutions of magnesium nitrate are appreciably denser and more viscous than water. Table II illustrates data (9) On the densities (in g/ml) of concentrated solutions at high temperatures. Figure 2 illustrates the viscosity variations in concentrated solutions (9). 

For the foregoing reasons it is seldom possible to obtain reproducible viscosity values for a given sample of sulphur. If, however, pure gas-free sulphur is prepared by distillation first in carbon dioxide and then in high vacuum, reliable values may be obtained. For such sulphur, protected from exposure to air, it has been found 5 that the viscosity between 163° and 169° C., the interval of high viscosity variation, lies on the same curve whatever the previous thermal treatment of the sample may have been. 

Some regularities, similar to Refs. 1718 21>, of viscosity variation in time under conditions of x = const were observed by the authors of Refs. 23,24,32-341 in extension of polyethylene and butadiene rubber (BR). Note that in Ref.34) the linear region of strain reaching the stationary flow was attained in extension of butadiene rubber. With further step-wise increase of x the effective viscosity grew and the time during which the stationary flow was attained increased significantly. References 23,24) will be discussed in more detail below. 

Wall-slip is not an easy phenomenon to detect. Although in principle, the velocity profile should reveal whether or not the fluid velocity is zero at the stationary wall, in reality determining the velocity profile with sufficient resolution near the wall is very difficult. So alternate means, e.g., checking for viscosity variation with appropriate changes in the test geometry, are also widely used in practice. 

Figure 9.1 shows a qualitative plot of the viscosity variation produced during the heating of a thermosetting polymer. Initially, viscosity decreases with the increase in temperature, but as cure progresses, an abrupt increase in viscosity is observed. The processability window is the range of T0 values... 

An additive, such as a polymer, that reduces a fluid s viscosity variations with temperature. 

Both shear thinning and temperature dependence of viscosity strongly affect the melting rate. Their effect on the rate of melting can be estimated by considering a case in which convection is neglected and viscous dissipation is low enough to permit the assumption that the viscosity variation across the film is determined by a linear temperature profile ... 

Figure 3.8. (a) The linear viscosity dependence of the inverse ionization rate in the reaction studied in Ref. 98. Bullets—experimental points solid line—fit performed with the generalized Collins—Kimball model, (b) The effective quenching radius for the same reaction in the larger range of the viscosity variation. Bullets—experimental points solid fine—fit performed with the encounter theory for the exponential transfer rate. The diffusion coefficient D given in A2/ns was calculated from the Stokes—Einstein relationship corrected by Spemol and Wirtz [100]. 

Low flow activation energies ( = temperature influence on viscosity variation)... 

While fuel viscosity variations were large and had a dominant effect on spray formation, differences between SRC-II and No. 2 fuel oil are also consistent with surface tension and liquid density differences. 

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