Viscosity-concentration behavior

Figure 11 shows the relative-viscosity-concentration behavior for a variety of hard-sphere suspensions of uniform-size glass beads. Even though the particle size was varied substantially (0.1 to 440 xm), the relative viscosity is independent of the particle size. However, when the particle diameter was small ( 1 fJLm), the relative viscosity was calculated at high shear rates, so that the effect of Brownian motion was negligible. Figure 8 shows that becomes independent of the particle size at high shear stress (or shear rate). 

Few studies have been conducted heretofore on sulfonated ionomers in solvents which can be considered relatively polar, as defined by a high dielectric constant. A recent study (13) on acrylonitrile-methallyl sulfonate copolymers in dimethyl-formamide is a notable exception. S-PS is readily soluble in a wide variety of solvents, some of them exhibiting rather high values of dielectric constant, such as dimethylformamide (DMF) or dimethylsulfoxide (DMSO). The reduced viscosity-concentration behavior of sulfonated polystyrene is markedly different in polar solvents from that in nonpolar-solvent systems. Typically there is a marked upsweep in reduced viscosity at low polymer concentrations and clearly a manifestation of classic polyelectrolyte behavior. ( 7)... 

Corresponding-states studies of the viscosity-concentration behavior of dilute and semidilute polymer solutions with Robert Simha led one of the authors (JLZ) to their applications in turbulent flows, a phenomenon that is generally called drag reduction. About six decades ago, Mysels [Mysels, 1949 Agoston et al., 1954] and Toms [1949] discovered that small amounts of aluminum soaps and high polymers added to a fluid in turbulent flow could significantly reduce pressure losses. 

Figure 20 Linear polymers and microgels (a) qualitative representation of solution conformations (b) qualitative zero-shear viscosity-concentration behaviors. (Reprinted with permission from Ref. 46.)...

As is evident from Eq. (3-20) or (3-21), the Bingham plastic exhibits a shear thinning viscosity i.e., the larger the shear stress or shear rate, the lower the viscosity. This behavior is typical of many concentrated slurries and suspensions such as muds, paints, foams, emulsions (e.g., mayonnaise), ketchup, or blood. 

Figure 3. Critical concentration behavior of actin self-assembly. For the top diagram depicting the macroscopic critical concentration curve, one determines the total amount of polymerized actin by methods that measure the sum of addition and release processes occurring at both ends. Examples of such methods are sedimentation, light scattering, fluorescence assays with pyrene-labeled actin, and viscosity measurements. Forthe bottom curves, the polymerization behavior is typically determined by fluorescence assays conducted under conditions where one of the ends is blocked by the presence of molecules such as gelsolin (a barbed-end capping protein) or spectrin-band 4.1 -actin (a complex prepared from erythrocyte membranes, such that only barbed-end growth occurs). Note further that the barbed end (or (+)-end) has a lower critical concentration than the pointed end (or (-)-end). This differential stabilization requires the occurrence of ATP hydrolysis to supply the free energy that drives subunit addition to the (+)-end at the expense of the subunit loss from the (-)-end.

Most food particles are not spherical in shape so that the empirical equation (Equation 2.25) that described well (Kitano et al., 1981 Metzner, 1985) the relative viscosity versus concentration behavior of suspensions of spheres and fibers... 

Thus, (f) = 0.01 is in the semidilute concentration regime. (It is actually at the lower end of the concentrated isotropic regime, which begins at a concentration = nd/4L = 0.008. However, even in the concentrated isotropic regime, the viscosity versus concentration behavior does not change much from that of the semidilute until near the transition to the nematic regime at 0 = 3.3d/L = 0.033.)... 

Figure 11. Relative viscosity vs. concentration behavior for suspensions of spheres having narrow size distributions. Particle diameters range from 0.1 to 440 pm. (Reproduced with permission from reference 30. Copyright 1965...

As discussed in the Introduction to this paper, different viscosity versus concentration behavior is observed for SFS solutions in toluene/methanol and in DMF. Folyelectrolyte behavior is observed only in the latter solvent. The ESR spectrum of a 2.65 mole % Mn-SPS in these two solvents was studied at various concentrations. For both lvents, the hyperfine structure characteristic of isolated Mn ions was observed in very dilute solutions and at concentrations for which Lundberg and Phillips(10) observed strong intermolecular interactions. The ESR data indlcat that in dilute solution in both DMF and toluene/methanol, the Mn exists mainly as Isolated cations. In addition, the IR spectra indicated that the cation is removed from the anion to a similar degree in both solvents. Yet, a polyelectrolyte effect is observed experimentally only in DMF solutions. Although there was some dipole-dipole broadening of the toluene/methanol spectrum, the line width and the g-factor (g 2,000) in both cases were ldent fal. The g-factor of 2.000 is characteristic of an isolated Mn in solution ). 

The influence of small amounts of water as a cosolvent for THF solutions is shown in Figure 3. At water contents of 3% or less the reduced viscosity-concentration profiles are similar to Figure 2. However, increasing water levels induces an upsweep in reduced viscosity at low polymer concentrations typical of polyelectrolyte behavior. This behavior has been observed in other mixed solvent systems and is clearly a consequence of specific cation solvation effects. Sodium23-NMR studies have shown that water solvates sodium cations at least ten times more strongly at similar cosolvent levels and the data in Figures 2 and 3 are consistent with those findings. 

It should be noted that the Doi and Ohta theory predicts oifly an enhancement of viscosity, the so called emulsion-hke behavior that results in positive deviation from the log-additivity rule, PDB. However, the theory does not have a mechanism that may generate an opposite behavior that may result in a negative deviation from the log-additivity rule, NDB. The latter deviation has been reported for the viscosity vs. concentration dependencies of PET/PA-66 blends [Utracki et ah, 1982]. The NDB deviation was introduced into the viscosity-concentration dependence of immiscible polymer blends in the form of interlayer slip caused by steady-state shearing at large strains that modify the morphology [Utracki, 1991]. 

It should he pointed out, however, that Eq. (11.3) assumes Newtonian behavior, which the complex polymeric resists and B ARC fluids do not necessarily exhibit. In particular, mass is not lost, neither from the radial flow of material nor from evaporation of solvent. Meyerhofer considered the effects of evaporation on the final film thickness. He reported that the final solid film thickness is inversely proportional to the square root of the rotational velocity. He also developed a model similar to that considered above, but allowed the solvent to evaporate during the spinning process. His central assumption was that the thinning process could be divided into two major stages, namely, one dominated by radial flow outward and another by evaporation of solvent. Effectively, he assumed a constant rate of evaporation and the viscosity concentration relationship expressed as... 

Semidilute Viscometrics. Solution viscometrics at concentrations above the overlap concentration (C ) indicated dramatic effects caused by the associative nature of the hydrophobic groups in the polymer. As shown by the reduced viscosity-concentration profiles of Figure 3, the introduction of only 1.0 mol % N-n-octylacrylamide to polyacrylamide can increase the viscosification efficiency dramatically. Increasing the hydrophobe level to 1.25 mol % further increased solution viscosity. At 2000 ppm, the presence of the hydrophobe caused a greater that 10-fold increase in viscosity. This result was in contrast to the behavior of these polymers in dilute solution see the box in Figure 3). The presence of hydrophobic functionality on the polymer resulted in a decrease in the reduced viscosity at concentrations below C. In dilute solution, intramolecular hydrophobic associations decreased the hydrodynamic radii of the polymer coils and thus reduced the... 

FIGUREl.il S chematic representation of the two types of viscosity-concentration scaling behavior seen in polymer solutions (a) type 1, linear superposition of data for solutions having different polymer molecular weights, M,- according to Eq. (1.61) with D as a fitting... 

The level of reduction in the viscosity, dependent on the concentration of the solution, was measured at different times. High viscosities were observed on the first day and there was no evidence of a strong polyelec-trolyter character. Measurements performed up to 60 days showed a drastic viscosity decrease. It would be interesting to find out whether the anomalous viscosity-time behavior is caused by chain scission or not. Light scattering measurements on polyelectrolytes are only possible in the... 

Jeffery s calculations were supplemented and extended by Boeder Eisenschitz, Kuhn and by Guth and Gold. The result was a great number of relations between specific viscosity, concentration and axial ratio according to the special assumptions and approximations made about the suspended particles and their behavior in the field of flow. 

The dependence of viscosity on volume fraction sohds is shown in Fig. 8.88. At high particle concentrations, viscosity of the suspension increases more rapidly than predicted by the above equation due to interparticle interactions. Several empirical equations are available to relate viscosity to the solid concentration behavior of suspensions. As the volume fraction of solids is increased further, a stage will be reached where the particles will be interlocked and no flow will occur (i.e., viscosity approaches infinity). The volume fraction of sohds at which this occurs is called the maximum packing fraction and its... 

The examination of the viscosity coeffident behavior has shown that for Fe nanopartides, the coefficient r] is at first reduced passing two local minima and then it increases as their concentration is raised. The coeffident tf is varied essentially monotonically, and it has only one local slight minimum. In the presence of Fe203 nanopartides, coefficient is nonmonotonically increased and has a local maximum and a local minimum. At the same time, a higher partide concentration causes the coefficient to nonmonotonically decrease while having two local minima. 

Consistent with the postulated hydrophobic association in aqueous media, addition of organic solvents such as DMSO, DMF and acetone at constant polymer concentration causes a drop in Brookfield viscosity. This behavior is illustrated in Fig. 7.8 for the addition of acetone. There is no effect until about 5% by volume and then there is a dramatic 3-30 fold decrease at an acetone concentration of 15%. Similar effects are observed for the addition of urea and ionic and nonionic surfactants (Fig. 7.9). In the latter case however, the viscosity vs additive profile is more complicated. There is a sharp initial decrease followed by an increase. The nature of this increase at higher surfactant concentration is unclear at present. The sharp decrease is consistent with association of the... 

These normal stresses are more pronounced for polymers with a very broad molecular weight distribution. Viscosities and viscoelastic behavior decrease with increasing temperature. In some cases a marked viscosity decrease with time is observed in solutions stored at constant temperature and 2ero shear. The decrease may be due to changes in polymer conformation. The rheological behavior of pure polyacrylamides over wide concentration ranges has been reviewed (5). 

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