Viscosity, apparent determination

For non-Newtonian liquids and suspensions, an apparent viscosity is determined using correlations which include power input and the Reynolds number. Scale-up comparisons based on heat generation data only were determined by comparison of results from RC1 experiments and from a 675-liter reactor [208]. In the experiments, a Bingham plastic fluid was used to determine the film heat transfer coefficient. This presents a worst case because of the low thermal conductivity of the Bingham plastic. Calculated inside film heat transfer coefficients determined in the RC1 tests were about 60% lower than the values determined in the pilot plant reactor, even though substantial effort was made to obtain both geometric and kinematic similarity in the pilot reactor. 

Viscosity Measurements. Viscosity measurements were made in filtered DMF and IN NaOH at 25 =t 0.05°C. The DMF was dried over molecular sieve. Flow times were measured in Cannon-Ubbelohde dilution viscometers, and intrinsic viscosities were obtained from the extrapolation of rjsp/c from the Huggins equation to zero concentration. When an apparent polyelectrolyte effect was found in DMF, the intrinsic viscosities were determined by adding CaCl2 to the DMF or by extrapolation from the higher concentration portion of the Huggins curve. Intrinsic viscosities are probably accurate to about 5%. 

For a nematic polymer in a transition region from LC to isotropic state, maximal viscosity is observed at low shear rates j. For a smectic polymer in the same temperature range only a break in the curve is observed on a lgq — 1/T plot. This difference is apparently determined by the same reasons that control the difference in rheological behaviour of low-molecular nematics and smectics 126). A polymeric character of liquid crystals is revealed in higher values of the activation energy (Ef) of viscous flow in a mesophase, e.g., Ef for a smectic polymer is 103 kJ/mole, for a nematic polymer3 80-140kJ/mole. 

The apparent viscosity is determined from Eq. 4. The value of shear rate that corresponds to this viscosity is obtained from the known viscosity vs shear rate rheogram for the non-Newtonian fluids generated using the cone-and-plate method. The value of k is determined from Eq. 5. 

The viscosity of thixotropic materials that exhibit a shear rate dependency is usually determined by the procedure described in ASTM D 2556. The viscosity is determined at different shear rates, and from this plot, apparent viscosity associated with a particular rotational speed and spindle shape can be obtained. Materials with thixotropic characteristics include Vaseline jelly and toothpaste. They are materials that tend to have very high viscosity characteristics and exhibit no flow at low shear rates. However, when pressure is applied (higher shear rates), the material flows easily, exhibiting a characteristic of lower viscosity. Such materials are very common in the adhesive and sealant industries. Thixotropic materials can be pumped through a nozzle, mixed, or applied to a surface with little resistance. However, when applied to a vertical surface, they will not flow under their own weight. 

Finally, the information on the pressure gradient and flow rate is used for an assessment of the viscosity buildup during the foaming stage. The apparent viscosity is determined by ... 

Apparent viscosities were determined using a falling sphere method on samples that had been matured for more than a year. 

One encounters the following difficulties in the interpretation of the data from the experiments with interfacial dilatation. As discussed in Ref. 58, the shear viscosity, T jh, does not influence the total stress, 67, only for interfacial flow of perfect spherical symmetry. If the latter requirement is not fulfilled by a given experimental technique, its output data will be influenced by a mixture of dissipative effects (not only -r d but also -qsh and tr). The apparent interfacial viscosity thus determined is not a real interfacial property insofar as it depends on the specific method of measurement. For example, the apparent interfacial viscosity measured by the capillary-wave methods [189-196] depends on the frequency the apparent interfacial viscosity measured by the Langmuir trough method [197,198] is a sum of the dilatational and shear viscosities ("q + -q h) for the methods employing nonspherical droplet deformation, like the spinning-drop method [199-201], the apparent surface viscosity is a complex function of the dilatational and shear interfacial viscosities. 

Temperatme dependence of viscosity is determined by one more factor - the thickness of an adsorption layer, which also depends on temperature. The thickness diminishes with rising temperature and with shear stress. This fact is explained by the differences in chain mobilities at various distances from the surface more remote layers begin to take part in flow, whereas macromolecules bound to the surface do not participate in this flow. At higher shear stresses, macromolecides with lower mobdity begin to take part in flow, which is confirmed by the dependence of the apparent activation energy on the filler content. Thus, current hydrodynamic theories and experimental data show that the vis-... 

Interpretation of Fig. 5.54 requires consideration of polymer flow characteristics. When steady-slate displacement tests are conducted with a polymer solution, as discussed in Sec. 5.4, the polymer mobility is extracted from the experimental data. Permeability to polymer can be calculated if the apparent viscosity of the polymer solution is known at the Darcy velocity of the polymer phase. For the core in Fig. 5.54, the apparent viscosity was determined with Eq. 5.18 to be 2.3 cp at S r from the polymer mobility with kp=kwp. Because the effective polymer viscosity at Spr did not vary significantly with flow rate, the apparent viscosity for relative permeability computations was assumed to be constant throughout the steady-state tests. The relative permeability curve for polymer solution is significantly less than the corresponding relative permeability curve for the displacement of water before contact of the core with polymer solution. 

The simplest way to test for this phenomenon is to compare viscosity functions determined by capillaries of similar L/R but different R. This is shown in Figure 6.2.5. We see that the smaller diameter ctq >illaries have lower apparent viscosities. 

Jones, et al. examined 50 nm silica spheres coated with covalently-bound stearyl alcohol dissolved in Shellsol T(55). Viscosities were determined with Ubbelohde viscometers and with three different cone and plate instruments. Sphere volume fractions were taken as high as 0.635, corresponding to T]r as large as 9.2 10 . Shear thinning was apparent at concentrations above 0.4. Systems with (p > 0.64 could not be taken into the low-shear limit in which 17 (/c) becomes independent from /c, so the low-shear rj remains indeterminate at these very large concentrations. 

A solution of 0.9% sodium chloride in water was used as the swelling fluid. The experimental set up consisted of a 1000 mL beaker into which was suspended the 1 spindle of a Brookfield LVT Viscometer. Seven hundred fifty milliliters of 0.9% NaCI solution was put into the beaker and stirred at a constant speed with a magnetic stirrer. The viscometer spindle was offset in the beaker so that the reading was not affected by the stirring vortex. The viscometer was started and a zero time reading obtained. Then 7.50 g of polymer powder was added to the stirring solution, and the timer was started. The viscosity was determined at various times until no further increase was apparent. 

For the salt forms, there is no correspondence between the steady state apparent viscosity and the absolute value of the complex viscosity as determined in dynamic shear. As can be seen in Figure 7, the steady shear viscosities are significantly higher than the corresponding dynamic viscosities. It is important to note that this particular material is neutralized to about 70%. In this case, the two... 

Among the complications that can interfere with this conclusion is the possibility that the polymer becomes insoluble beyond a critical molecular weight or that the low molecular weight by-product molecules accumulate as the viscosity of the mixture increases and thereby shift some equilibrium to favor reactants. Note that we do not express reservations about the effect of increasing viscosity on the mobility of the polymer molecules themselves. Apparently it is not the migration of the center of mass of the molecule as a whole that determines the reactivity but, rather, the mobility of the chain ends which carry the reactive groups. 

Polymer melts are frequendy non-Newtonian. In this case the earlier expression given for the shear rate at the capillary wall does not hold. A correction factor (3n + 1)/4n, called the Rabinowitsch correction, must be appHed in such a way that equation 21 appHes, where 7 is the tme shear rate at the wall and nis 2l power law factor (eq. 22) determined from the slope of a log—log plot of the tme shear stress at the wad, T, vs 7. For a Newtonian hquid, n = 1. A tme apparent viscosity, Tj, can be calculated from equation 23. 

The strong interactions between the water molecules also become obvious from NMR measurements by Tsujii et al..57) 13C-NMR experiments were used for determining the microviscosity of water in reversed micelles of dodecylammonium-propionate with 13C glycine cosolubilized. It was found that the apparent viscosity of the water-pool corresponds to the viscosity of a 78 % aqueous glycerol solution, obviously as a consequence of the extended network formation by strong hydrogen bonding. 

The global rate of the process is r = rj + r2. Of all the authors who studied the whole reaction only Fang et al.15 took into account the changes in dielectric constant and in viscosity and the contribution of hydrolysis. Flory s results fit very well with the relation obtained by integration of the rate equation. However, this relation contains parameters of which apparently only 3 are determined experimentally independent of the kinetic study. The other parameters are adjusted in order to obtain a straight line. Such a method obviously makes the linearization easier. 

The shear history simulators operate at a single shear rate during an experiment and do not run shear ramps. For these Instruments, apparent viscosity at a single shear rate Is determined by the relationship of differential pressure (AP), capillary length (L) and radius (r), and volumetric flow rates (Q), as follows. 

One of the most popular applications of molecular rotors is the quantitative determination of solvent viscosity (for some examples, see references [18, 23-27] and Sect. 5). Viscosity refers to a bulk property, but molecular rotors change their behavior under the influence of the solvent on the molecular scale. Most commonly, the diffusivity of a fluorophore is related to bulk viscosity through the Debye-Stokes-Einstein relationship where the diffusion constant D is inversely proportional to bulk viscosity rj. Established techniques such as fluorescent recovery after photobleaching (FRAP) and fluorescence anisotropy build on the diffusivity of a fluorophore. However, the relationship between diffusivity on a molecular scale and bulk viscosity is always an approximation, because it does not consider molecular-scale effects such as size differences between fluorophore and solvent, electrostatic interactions, hydrogen bond formation, or a possible anisotropy of the environment. Nonetheless, approaches exist to resolve this conflict between bulk viscosity and apparent microviscosity at the molecular scale. Forster and Hoffmann examined some triphenylamine dyes with TICT characteristics. These dyes are characterized by radiationless relaxation from the TICT state. Forster and Hoffmann found a power-law relationship between quantum yield and solvent viscosity both analytically and experimentally [28]. For a quantitative derivation of the power-law relationship, Forster and Hoffmann define the solvent s microfriction k by applying the Debye-Stokes-Einstein diffusion model (2)... 

A coal slurry is to be transported by pipeline. It has been determined that the slurry may be described by the power law model, with a flow index of 0.4, an apparent viscosity of 50 cP at a shear rate of 100 s-1, and a density of 90 lbm/ft3. What horsepower would be required to pump the slurry at a rate of 900 gpm through an 8 in. sch 40 pipe that is 50 mi long ... 

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