Phase Velocity Data

James Pouch (2002) showed intermediate period fundamental mode Rayleigh wave phase and group velocity data measured across the Kalahari Craton and a shear-wave velocity model from inversion of these data. They find evidence for a weak low-velocity zone below 120-130 km depth. The phase velocity data of James Pouch (2002) are not significantly different from the Rayleigh wave phase velocity measured by Priestley (1999). However, such intermediate period fundamental mode dispersion data do not provide stringent constraints on mantle velocities below c. 200 km depth. 

It is possible to investigate the flow structure in bubble column reactors by means of hot wire anemometers. The analysis of the liquid-phase velocity data results in consistent descriptive functions on the turbulent motion. The large-scale structures of these flows are determined by the column diameter, and a coherent circulation cell structure must be taken into account. Further measurements are required to establish quantitative relations between the flow structures and disperging properties of turbulent flows. 

As already mentioned, there are two so called "dead volumes" that are important in both theoretical studies and practical chromatographic measurements, namely, the kinetic dead volume and the thermodynamic dead volume. The kinetic dead volume is used to calculate linear mobUe phase velocities and capacity ratios in studies of peak variance. The thermodynamic dead volume is relevant in the collection of retention data and, in particular, data for constructing vant Hoff curves. 

Liquids have relatively low compressibility compared with gases and, thus, the mobile phase velocity is sensibly constant throughout the column. As a consequence, elution volumes measured at the column exit can be used to obtain retention volume data and, unless extreme accuracy is required for special applications, there is no need for the retention volume to be corrected for pressure effects. 

Thus, from equation (13) a value for (2X,dn) can obtained by plotting (H) against (1/Dm) for data that has been obtained at a constant linear mobile phase velocity... 

The separated flow models consider that each phase occupies a specified fraction of the flow cross section and account for possible differences in the phase velocities (i.e., slip). There are a variety of such models in the literature, and many of these have been compared against data for various horizontal flow regimes by Duckler et al. (1964a), and later by Ferguson and Spedding (1995). 

A mathematical model for solid entrainment into a permanent flamelike jet in a fluidized bed was proposed by Yang and Keaims (1982). The model was supplemented by particle velocity data obtained by following movies frame by frame in a motion analyzer. The experiments were performed at three nominal jet velocities (35, 48, and 63 m/s) and with solid loadings ranging from 0 to 2.75. The particle entrainment velocity into the jet was found to increase with increases in distance from the jet nozzle, to increase with increases in jet velocity, and to decrease with increases in solid loading in the gas-solid, two-phase jet. 

Maier (M2) has given quantitative data showing that the continuous-phase velocity results in a reduction in bubble size. During a study of bubble formation from vertical nozzles, Krishnamurthy et al. (K13) observed a decrease in the bubble volume resulting from an increase in buoyancy caused by the continuous-phase velocity. These authors developed equations based on drag considerations which can predict the bubble volume when the continuous phase has a velocity. But, in their study, the continuous-phase velocity is so directed as to decrease the bubble volume, and hence the results cannot be generalized. 

The Van Deemter equation remained the established equation for describing the peak dispersion that took place in a packed column until about 1961. However, when experimental data that was measured at high linear mobile phase velocities was fitted to the Van Deemter equation it was found that there was often very poor agreement. In retrospect, this poor agreement between theory and experiment was probably due more to the presence of experimental artifacts, such as those caused by extra column dispersion, large detector sensor and detector electronic time constants etc. than the inadequacies of th Van Deemter equation. Nevertheless, it was this poor agreement between theory and experiment, that provoked a number of workers in the field to develop alternative HETP equations in the hope that a more exact relationship between HETP and linear mobile phase velocity could be obtained that would be compatible with experimental data. 

Comparing equations (1) and (2) it is seen that there is a significant difference between them, in that, only the Van Deemter equations should provide an (A) term that is independent of both the linear mobile phase velocity and the solute diffusivity. The fit of the Van Deemter equation to the experimental data confirms the former condition and the plot of the (A) term against the solute diffusivity, data taken from tables (1) and (2) and shown in figure 2 confirms the latter. 

In summary, it can be said that all the dispersion equations give a good fit to experimental data but only the Van Deemter equation, the Gidciings equation and the Knox equation give positive and real values for the constants in the respective equations. The basically correct equation appears to be that of Giddings but, over the range of mobile phase velocities normally employed in LC, the Van Deemter equation is the simplest and most... 

In the preceding discussion, we presented experimental information on the singlephase air-water exchange velocities. Water vapor served as the test substance for the air-phase velocity v,a, while 02, C02 or other compounds yielded information on v,w. Now, we need to develop a model with which these data can be extrapolated to other chemicals which either belong also to the single-phase group or are intermediate cases in which both via and vlw affect the overall exchange velocity v,a/w (Eq. 20-3). 

Figure Cl. 1.2 shows a typical time course resulting from a continuous assay of product formation in an enzyme-catalyzed reaction. The hyperbolic nature of the curve illustrates that the reaction rate decreases as the reaction nears completion. The reaction rate, at any given time, is the slope of the line tangent to the curve at the point corresponding to the time of interest. Reaction rates decrease as reactions progress for several reasons, including substrate depletion, reactant concentrations approaching equilibrium values (i.e., the reverse reaction becomes relevant), product inhibition, enzyme inactivation, and/or a change in reaction conditions (e.g., pH as the reaction proceeds). With respect to each of these reasons, their effects will be at a minimum in the initial phase of the reaction—i.e., under conditions corresponding to initial velocity measurements. Hence, the interpretation of initial velocity data is relatively simple and thus widely used in enzyme-related assays.

For high data rate modulators, the dynamic behavior becomes an important issue. Today, a modulation rate of 100 GHz has become a realistic objective. For a better understanding of the modulator dynamics, we have to consider the phase velocity of the two interacting waves ... 

In this section, the UVP is applied to obtain the location of the gas-liquid interface of two-phase flow in a horizontal square channel. In this method, only the velocity data are used to obtain the position of the gas-liquid interface. 

Figure 6 UVP data (a) raw velocity data, (b) data using a Laplacian filter, (c) data using a forward differentiation filter, (d) data using a Sobel filter, (e) binarized Sobel data, and (f) gas-phase detected after the application of the Sobel filter.

The olivine spinel phase transition Experimental phase equilibrium studies have confirmed deductions from seismic velocity data that below 400 km, olivine and pyroxene, the major constituents of Upper Mantle rocks, are transformed to denser polymorphs with the garnet, y-phase (spinel) and P-phase (wadsleyite) structures (fig. 9.2). In transformations involving olivine to the P- or y-phases, transition pressures... 

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