Variation with

Van Velzen s method provides an estimation of hydrocarbon viscosities and their variation with temperature ... 

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

As an example of the application of the method, Neumann and Tanner [54] followed the variation with time of the surface tension of aqueous sodium dode-cyl sulfate solutions. Their results are shown in Fig. 11-15, and it is seen that a slow but considerable change occurred. 

Fig. 11-15. Variation with time of aqueous sodium dodecyl sulfate solutions of various concentrations (from Ref. 54). See Ref. 56 for later data with highly purified materials.

Some studies have been made of W/O emulsions the droplets are now aqueous and positively charged [40,41 ]. Albers and Overbeek [40] carried out calculations of the interaction potential not just between two particles or droplets but between one and all nearest neighbors, thus obtaining the variation with particle density or . In their third paper, these authors also estimated the magnitude of the van der Waals long-range attraction from the shear gradient sufficient to detach flocculated droplets (see also Ref. 42). 

Statistical mechanics and kinetic theory, as we have seen, are typically concerned with the average behaviour of an ensemble of similarly prepared systems. One usually hopes, and occasionally can demonstrate, that the variations of these properties from one system to another in the ensemble, or that the variation with time of the properties of any... 

The remarkable stability and eontrollability of NMR speetrometers penults not only the preeise aeeiimulation of FIDs over several hours, but also the aequisition of long series of speetra differing only in some stepped variable sueh as an interpulse delay. A peak at any one ehemieal shift will typieally vary in intensity as this series is traversed. All the sinusoidal eomponents of this variation with time ean then be extraeted, by Fourier transfomiation of the variations. For example, suppose that the nomial ID NMR aequisition sequenee (relaxation delay, 90° pulse, eolleet FID) is replaeed by the 2D sequenee (relaxation delay, 90° pulse, delay i -90° pulse, eolleet FID) and that x is inereased linearly from a low value to ereate the seeond dimension. The polarization transfer proeess outlined in die previous seetion will then eause the peaks of one multiplet to be modulated in intensity, at the frequeneies of any other multiplet with whieh it shares a eoupling. 

Disadvantages. The magic angle must be extremely stable and accurately set. The spiiming speed must show good stability over the duration of the experiment. The probe needs to be accurately tuned and careful correction for irradiation and detection variations with frequency, and baseline effects are necessary. The gain... 

Small molecules in low viscosity solutions have, typically, rotational correlation times of a few tens of picoseconds, which means that the extreme narrowing conditions usually prevail. As a consequence, the interpretation of certain relaxation parameters, such as carbon-13 and NOE for proton-bearing carbons, is very simple. Basically, tlie DCC for a directly bonded CH pair can be assumed to be known and the experiments yield a value of the correlation time, t. One interesting application of the measurement of is to follow its variation with the site in the molecule (motional anisotropy), with temperature (the correlation... 

Although the proportion of nitric acid present as nitronium ions does not change between 90% and 100% sulphuric acid, the rate constants for nitration of most compounds decrease over this rai e. Fig. 2.1 illustrates the variation with acidity of the second-order rate constants of the nitration of a series of compounds of widely differing reactivities. Table 2.4 lists the results for nitration in 95% and 100% acid of a selection of less completely investigated compounds. 

Fig. 2.4, illustrates the variation with the concentration of sulphuric acid of the logarithm of the second-order rate coefficients for the nitration of a series of compounds for which the concentration of effective... 

Intensities of Raman transitions are proportional to R and therefore, from Equation (6.13), to (da/dx)g. Since a is a tensor property we cannot illustrate easily its variation with x instead we use the mean polarizability a, where... 

Those stmctural variables most important to the tensile properties are polymer composition, density, and cell shape. Variation with use temperature has also been characterized (157). Flexural strength and modulus of rigid foams both increase with increasing density in the same manner as the compressive and tensile properties. More specific data on particular foams are available from manufacturers Hterature and in References 22,59,60,131 and 156. Shear strength and modulus of rigid foams depend on the polymer composition and state, density, and cell shape. The shear properties increase with increasing density and with decreasing temperature (157). 

The mechanical piopeities of stmctuial foams and thek variation with polymer composition and density has been reviewed (103). The variation of stmctural foam mechanical properties with density as a function of polymer properties is extracted from stress—strain curves and, owkig to possible anisotropy of the foam, must be considered apparent data. These relations can provide valuable guidance toward arriving at an optimum stmctural foam, however. 

The prefactor M(T), also called a frequency factor, has units of inverse seconds. It may have a weak dependence on temperature. Some theoretical models predict a variation with, but such variation is frequently ignored and M is taken as constant over limited temperature ranges. The prefactor M is often... 

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. 

Fig. 8. Variation with percent Co binder content for cemented WC grades of (a) hardness, where the numbers represent carbide grain size in pm (b)...

Above 40 wt % hydrogen content at room temperature, zirconium hydride is brittle, ie, has no tensile ductiHty, and it becomes more friable with increasing hydrogen content. This behavior and the reversibiHty of the hydride reaction are utilized ki preparing zirconium alloy powders for powder metallurgy purposes by the hydride—dehydride process. The mechanical and physical properties of zirconium hydride, and thek variation with hydrogen content of the hydride, are reviewed in Reference 127. 

According to KirehhofPs law, the emissivity and absorptivity of a surface in surroundings at its own temperature are the same for both monochromatic and total radiation. When the temperatures of the surface and its surroundings differ, the total emissivity and absorptivity of the surface often are found to be different, but, because absorptivity is substantially independent of irradiation density, the monochromatic emissivity and absorptivity of surfaces are for all practical purposes the same. The difference between total emissivity and absorptivity depends on the variation, with wavelength, of Zx and on the difference between the emitter temperature and the effective source temperature. 

General Principles The underlying principle of an ideal area meter is the same as that of a head meter of the orifice type (see subsection Orifice Meters ). The stream to be measured is throttled by a constriction, but instead of observing the variation with flow of the differential head ac-ross an orifice of fixed size, the constriction of an area meter is so arranged that its size is varied to accommodate the flow while the differential head is held constant. 

Figure 12-41 7 indicates that the drying rate is subject to variation with time or moisture content. This variation is better ihustrated by... 

FIG. 12-88 CimeA shows surface variations with stone size, 100 percent active surfaces. Curv es in group B show the effect of irregular stone size. 

Such a control is good for machines that are required to operate at low speeds with a high accuracy. Now the phasor /, in terms of /, , is varied according to the speed required. Figure 6.2 now changes to Figure 6.8, which is a marked improvement on the earlier characteristics. The torque variation with speed is now almost constant, except at very low speeds. The reason for poor torque at low speeds is the method of speed variation which is. still based on Vlf. Now a motor s mathematical model is used... 

Figure 6.52 An approximate iliustration of p and loss variation, with change in speed in a variable-speed fluid coupling...

The method discussed above is a conventional one to achieve required speed variations. With the application of newer technologies, speed variations may be achieved more accurately and promptly with a single-speed motor, by the use of the following ... 

The governor can be set to make the machine run at a constant speed, even on load variations, with extremely quick and almost instantaneous speed control, and thus maintain a near-zero AN. In a parallel operation they can also control load sharing automatically and accurately. Power grids, receiving power from different sources, are extremely susceptible to frequency variations. Even a small Af of the order of 0.5 Hz, may cause the system to trip. A fast-actuating governor with low response time (as low as 0.5 second) can overcome such a situation by quickly regulating the speed of the PM. 

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