Relative apparent viscosities

Apply Eq. (2.27) to some of the data points to evaluate the apparent viscosity at different 7 s. The first section of Table 2.2 shows the results of such calculations. Note that the calculated 17 s are constant at low 7 values, indicating Newtonian behavior. Table 2.2 also expresses all 17 values relative to the Newtonian limiting value 17 - Comparison of Eqs. (2.28) and (2.29) shows that t7/t7im values decrease from the Newtonian limit by the fraction sinh" (j37)/j37. 

The native sample E (Fig. 3) contains a relatively large amount of aggregated structures. Most of them appear to rearrange into perfectly matched double-stranded chains after incubation at 80 °C for 2 months (27). This rearrangement is reported to result in a fivefold increase in the apparent viscosity at a shear rate of 1 s-1 (27). A similar rearrangement of xanthan assemblies is also observed in a unpasteurized fermentation broth after exposure of the sample... 

Among other characteristics, non-Newtonian fluids exhibit an apparent viscosity that varies with shear rate. Consequently, the determination of the shear stress-shear rate curve must be an initial consideration. Although the apparent viscosity of a thixotropic or a rheopectic fluid changes with the duration of shearing, meaningful measurements may be made if the change is relatively slow. Viscoelastic fluids also exhibit behaviour that is a function of time but their apparent viscosities can be measured provided conditions of steady shearing are obtained. 

Not all suspensions will exhibit wall slip. Concentrated suspensions of finely ground coal in water have been found to exhibit wall slip [Fitzgerald (1990)]. This is to be expected because the coal suspension has a much higher apparent viscosity than the water. In contrast, when the liquid is a very viscous gum, the addition of solids may have a relatively small effect. In this case, the layer at the wall will behave only marginally differently from the material in the bulk. 

There is an expression that does not truly fit either class of behaviour, for power law fluids which can be expressed in terms of stress, rate or apparent viscosity with relative ease. They can describe shear thickening or thinning depending upon the sign of the power law index n ... 

Because most shear-thinning fluids, particularly polymer solutions and flocculated suspensions, have high apparent viscosities, even relatively coarse particles may have velocities in the creeping-flow of Stokes law regime. Chhabra(35,36) has proposed that both theoretical and experimental results for the drag force F on an isolated spherical particle of diameter d moving at a velocity u may be expressed as a modified form of Stokes law ... 

The fructan has an optical rotation [a] - 47.2. It is non-hygroscopic, unusual in view of its high solubility. Lyophilized sheets of fructan have been maintained under condition of 25 -30°C and 70Z-85Z relative humidity for up to 6 months. The solubility of fructan is very high up to 30Z in cold water, with no apparent viscosity increase. It is extremely soluble in hot water. This high solubility is characteristic of p-(2- 6) linked fructans. 

As noted above, dilute colloidal systems display Newtonian behavior that is, their apparent viscosity is independent of the rate of shear. Accordingly, the capability to measure 77 under conditions of variable shear is relatively superfluous in these systems. However, non-Newtonian behavior is commonplace in charged colloids and coagulated colloids (see Section 4.8). 

Schreiber and co-workers have noted very persistent history effects in linear polyethylenes (69). Fractions which have been crystallized from dilute solution required times of the order of hours in the melt state at 190° C in order to attain a constant die swell behavior upon subsequent extrusion. The viscosity on the other hand reached its ultimate value almost immediately. The authors concluded from this result that different types of molecular interactions were responsible for elastic and viscous response. However, other less specific explanations might also suffice, since apparent viscosity might be relatively intensitive to the presence of incompletely healed domain surfaces, while die swell, requiring a coordinated motion of the entire extrudate, might be affected by planes of weakness. It would... 

FIGURE 10.10 Relative change of the apparent viscosity of heat-treated PP/PU/APP versus temperature and time. (Adapted from Bugajny, M. et al., Fire Mater., 23, 49, 1999.)... 

Viscosity and Plasticity—Viscosity and plasticity are closely related. Viscosity may be defined as the force required to move a unit-area of plane surface with unit-speed relative to another parallel plane surface, from which it is separated by a layer of the liquid of unit-thickness. Other definitions have been applied to viscosity, an equivalent one being the ratio of shearing stress to rate of shear. When a mud or slurry is moved in a pipe in more or less plastic condition the viscosity is not the same for all rates of shear, as in the case of ordinary fluids. A material may be called plastic if the apparent viscosity varies with the rate of shear. The physical behavior of muds and slurries is markedly affected by viscosity. However, consistency of muds and slurries is not necessarily the same as viscosity but is dependent upon a number of factors, many of which are not yet clearly understood. The viscosity of a plastic material cannot be measured in the manner used for liquids. The usual instrument consists of a cup in which the plastic material is placed and rotated at constant speed, causing the deflection of a torsional pendulum whose bob is immersed in the liquid. The Stormer viscosimeter, for example, consists of a fixed outer cylinder and an inner cylinder which is revolved by means of a weight or weights. 

The thixotropic characteristics provided by fumed sihca are due to its ability to develop a loosely woven, latticelike network by hydrogen bonding between particles. This network raises the apparent viscosity of the system, increases the cohesive forces, and contributes to the suspension of the solid. Because the hydrogen bonds themselves are relatively weak, they are easily disrupted through the action of an apphed stress or shearing force and quickly reform when the stress or shearing force is removed. 

Figure 5. Schematic diagram showing the effect of changing the volume fraction of second phase on the apparent viscosity at a fixed rate of shear of a two-phase emulsion. The different dotted lines refer to different viscosities of the pure phases A and B, The solid line suggests the viscosity that may be displayed by a system in which both the viscosities of the pure phases and the relative proportions of phases are changing continuously, as in a pyrolysis run.

Joosten et al.51 explained the data based on the increase in the apparent viscosity of the slurry by the addition of solids. The volumetric mass-transfer coefficients, as a function of the relative viscosity of slurry obtained by them, are shown in Fig. 9-16. These data show that as the density of the solids decreased the value kLaL decreased faster with the increase in the relative viscosity. These data also show that for particle sizes < 250 pm, the suspended solid particles do not significantly affect the gas-liquid volumetric mass-transfer coefficient when the apparent viscosity of the slurry is not higher than four times that in the liquid. At high solids concentration, bubble coalescence and subsequent reduction in gas holdup can be the major cause in the reduction of fcLaL. The data show that kLoL in a three-phase slurry depends on the difference in density between the solids and liquids. The greater inertia of the heavier particles may create a stronger disturbance at the gas-liquid interface and thus affect the value of kL. 

Foam exhibits higher apparent viscosity and lower mobility within permeable media than do its separate constituents.(1-3) This lower mobility can be attained by the presence of less than 0.1% surfactant in the aqueous fluid being injected.(4) The foaming properties of surfactants and other properties relevant to surfactant performance in enhanced oil recovery (EOR) processes are dependent upon surfactant chemical structure. Alcohol ethoxylates and alcohol ethoxylate derivatives were chosen to study techniques of relating surfactant performance parameters to chemical structure. These classes of surfactants have been evaluated as mobility control agents in laboratory studies (see references 5 and 6 and references therein). One member of this class of surfactants has been used in three field trials.(7-9) These particular surfactants have well defined structures and chemical structure variables can be assigned numerical values. Commercial products can be manufactured in relatively high purity. 

Certain dilute lamellar liquid crystalline phases having relatively low apparent viscosities can propagate through this porous medium micromodel without plugging it. Their behavior followed the trends established with isotropic phases. 

The surfactant has two important roles in CO2 foam. First, it increases the apparent viscosity of CO2 so that brine and oil are displaced in a stable manner. Second, the surfactant lowers the interfacial tension between CO2 and brine which promotes brine displacement. Reducing the brine saturation below S c allows bulk-phase CO2 to completely access the oil-filled pore network. A high-saturation brine bank also retards CO2 mobility by relative permeability effects. The brine bank carries surfactant and allows oil reconnection and mobilization ahead of the bulk CO2 phase because of the favorable partitioning of CO2 from brine into oil. 

The role of insoluble solids can be also studied in terms of the relative viscosity [r]t = apparent viscosity of COJ/apparent viscosity of serum) and pulp fraction (Figure 2-12) and, as expected, such a plot has the limiting value of 1.0 at zero pulp fraction (serum). The curve in Figure 2-12 illustrates the strong influence of pulp fraction on the viscosity of COJ. The values of )a,ioo also, as expected, follow a profile similar to that of % (Figure 2-12). The two curves are described by the equations ... 

The viscosity (or apparent viscosity) of a suspension can be related to the viscosity of the continuous medium in terms of the relative viscosity, rjr. ... 

A thin layer of a molten polymer of 2 mm thickness is sandwiched between two plates. If a shear stress of 120 kPa is applied to the melt, and the apparent viscosity of the melt is 4 x 10 kg(m s) calculate the relative sliding velocity of the two plates. 

Mathesoner al. (M7), show that relatively small amounts of fines added to coarse particles sharply decrease the bed viscosity. Based on this evidence, Zenz (Z4) has calculated an optimum size distribution of fluidized particles (as mentioned in Section II,A, 1). The importance of the apparent viscosity in relation to flow characteristics of the bed has been stressed by Matheson et al. (M7), Rice and Wilhelm (R5), Finnerty et al. (F3), Grace (G13), and others. Matheson et al. (M7) have found that the slugging tendencies of a bed can be expressed in terms of the apparent viscosity. Their results for FCC particles containing 20 wt.% of 46-/nm-diameter fine particles gave fit, equal to 6 x 10" g/cm sec this small bed viscosity agreed with the visible high fluidity of the bed. 

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