Viscosity, calculation

Templeton obtained data of the following type for the rate of displacement of water in a 30-/im capillary by oil (n-cetane) (the capillary having previously been wet by water). The capillary was 10 cm long, and the driving pressure was 45 cm of water. When the meniscus was 2 cm from the oil end of the capillary, the velocity of motion of the meniscus was 3.6 x 10 cm/sec, and when the meniscus was 8 cm from the oil end, its velocity was 1 x 10 cm/sec. Water wet the capillary, and the water-oil interfacial tension was 30 dyn/cm. Calculate the apparent viscosities of the oil and the water. Assuming that both come out to be 0.9 of the actual bulk viscosities, calculate the thickness of the stagnant annular film of liquid in the capillary. 

Sato et al. " measured the viscosities of some binary and ternary alkali carbonates. Since melt creep must be prevented, a highly sintered alumina crucible was used instead of a gold-plated nickel crucible. Homogeneity of a mixture sample was achieved by gas bubbling. A laser beam is combined with a computer-assisted time counter to obtain the logarithmic decrement. Roscoe s equationi3i has been used for calculation of the viscosity, while it has been claimed by Abe et al. that the viscosities calculated from Roscoe s equation are 0.6-1.5% lower than those from more rigorous equations. 

The validity of a practical method of direct viscosity calculation from size exclusion chromatographic analysis is demonstrated. The method is convenient to use and is not limited by the availability of narrow MWD standards. It is possible to accurately measure polymer Mark-Houwink constants using the suggested broad standard SEC-[n] and SEC-MW calibration procedure. 

An analogy exists between mass transfer (which depends on the diffusion coefficient) and momentum transfer between the sliding hquid layers (which depends on the kinematic viscosity). Calculations show that the ratio of thicknesses of the diffnsion and boundary layer can be written as... 

Fig. 15. Comparison of the viscosities either directly measured or calculated from the spin-echo results for polyethylene melts at 509 K as a function of molecular mass ( experimental result o viscosities calculated on the basis of mode analysis). (Reprinted with permission from [52]. Copyright 1993 The American Physical Society, Maryland)...

Once a test 1s complete, another menu option provides the data analysis results 1n the form of a hard-copy report printed on the local line printer. The report Includes experiment identification Information and the apparent viscosities calculated for each data set. A subset of the data analysis program 1s scheduled automatically by the control programs while the experiment is 1n progress and provides immediate on-line analysis of apparent viscosities for each data set as It 1s collected. The results are viewed using the real-time data display program (Figure 5). 

The incorporation of non-Gaussian effects in the Rouse theory can only be accomplished in an approximate way. For instance, the optimized Rouse-Zimm local dynamics approach has been applied by Guenza et al. [55] for linear and star chains. They were able to obtain correlation times and results related to dynamic light scattering experiments as the dynamic structure factor and its first cumulant [88]. A similar approach has also been applied by Ganazzoli et al. [87] for viscosity calculations. They obtained the generalized ZK results for ratio g already discussed. 

Fig. 17. A log-log plot of expansion factor, (obtained from intrinsic viscosity calculations) vs reduced excluded volume, z, for MC data of 12 arms stars with N=25-109 units (symbols as in Fig. 11 ). The solid lines and figures represent slopes corresponding to the predicted asymptotic behaviors for the EV and sub-theta regimes. Reprinted with permission from [143]. Copyright (1992) American Chemical Society...

The numerical efficiency of the viscosity lower bound method has allowed calculations on considerably longer chains. The long chain Hmit results for 12-arm stars without intramolecular interactions and with EV (up to 325 beads) and in the theta region (up to 145 beads) [164] are close to the previous estimates with shorter chains (the extrapolated ratio g obtained in this study is also included in Table 4). The lower bound method has also served to characterize globule-coil transitions of 12-arm star chains from intrinsic viscosity calculations [143], though finite size effects are considerably more important than in the characterization of this transition from the radius of gyration data (see Fig. 17). This is due to the noticeable increase in the solvent permeabiHty associated with the chain expansion in better solvent conditions. However, the permeability effects are smaller in the more compact star chains than in their linear counterparts. 

Solutions to these equations yield the temperature distribution inside the mandrel and inside the composite as a function of time. Degree of cure or crystallinity and matrix viscosity in the composite as a function of time are also determined. This model is the building block for the other submodels. Viscosity calculations are input to the fiber motion submodel. Temperature and cure calculations are input to the stress submodel. Temperature data are also input to the void submodel. 

Table III. Viscosity Calculations Observations and Conversion Formulas...

Figure 18 shows the logarithm of the viscosity, calculated on the basis of Eqs. (43) and (45), as a function of the reciprocal absolute temperature. Figure 19 shows the same kind of plot, this time making use of the Eqs. (44) and (45). 

Assume that if Figure 15.8 is extrapolated to 200 °C, the viscosity of the lead-alkali glass is 1018 Pa s. Using this viscosity, calculate the strain that would occur in five centuries under a stress of 0.007 Pa. Assume that the stress is caused by the weight of a panel of glass 1/3 m high. Note that... 

Draining corrections have not been applied to any of the data for other cellulose derivatives, as they are in all cases smaller than for the nitrate. The results of the viscosity calculations for these substances arc... 

Another method to determine viscosity uses the falling-ball viscometer. Determine viscosity by noting the time it takes for a ball to fall through the distance between two marks on a tube filled with the unknown liquid (the tube is generally in a constant-temperature bath). Use balls of different weights to measure a wide range of viscosities. Calculate the viscosity by using manufacturer-supplied constants for the ball used. These instruments can be quite precise for Newtonian liquids, that is, liquids that do not have viscosities that vary with flow (more correctly, shear) rate. 

At a Reynolds number of 662, the viscosity power factor ]), is approximately 1.8. Applying this factor to the power number used in the apparent-viscosity calculation of step 2 enables the estimation of another apparent viscosity ... 

Laity and Treybal also measured power consumption with four baffles in the vessel, each baffle being % of the tank diameter in width. With single liquids, they found the same power number-Reynolds number correlation as given in Section III for normal baffled operations with the presence of an air-liquid interface at the surface. Again, with two-phase systems, the same relation correlated the data provided that an effective mean viscosity calculated as follows was used ... 

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