Ideal Profile Analysis component

If we were to choose the ideal method for the analysis of any component of seawater, it would naturally be an in situ method. Where such a method is possible, the problems of sampling and sample handling are eliminated and in many cases we can obtain continuous profiles rather than limited number of discrete samples. In the absence of an in situ method, the next most acceptable alternative is analysis on board ship. A real-time analysis not only permits us to choose our next sampling station on the basis of the results of the last station, it also avoids the problem of the storage of samples until the return to a shore laboratory. 

We have developed several new measurement techniques ideally suited to such conditions. The first of these techniques is a High Pressure Sampling Mass Spectrometric method for the spatial and temporal analysis of flames containing inorganic additives (6, 7). The second method, known as Transpiration Mass Spectrometry (TMS) (8), allows for the analysis of bulk heterogeneous systems over a wide range of temperature, pressure and controlled gas composition. In addition, the now classical technique of Knudsen Effusion Mass Spectrometry (KMS) has been modified to allow external control of ambient gases in the reaction cell (9). Supplementary to these methods are the application, in our laboratory, of classical and novel optical spectroscopic methods for in situ measurement of temperature, flow and certain simple species concentration profiles (7). In combination, these measurement tools allow for a detailed fundamental examination of the vaporization and transport mechanisms of coal mineral components in a coal conversion or combustion environment. 

Furthermore, the theoretical analysis of the single-component problem in the ideal model provides some of the fimdamental concepts in nonlinear chromatography, such as the notions of the velocity associated with a concentration, of concentration shocks, and of diffuse bormdaries [1,2]. It also provides an understanding of the relationship between the thermod5mamics of phase equilibria, the shape of the isotherm (i.e., convex upward, linear, convex downward, or S-shaped) and the band profiles. Finally, it provides an explanation of the relative importance of the influences of the thermodynamics and the kinetics on the band profile. These concepts will provide a most useful framework for imderstanding the phenomena that occur in preparative chromatography. 

The appropriate SVD-derived spectral and temporal eigenvectors were selected and the temporal vectors were modeled. Ideally, the temporal vectors are the kinetic traces of individual components, each one being associated with a spectrum of a pure component Le., the spectral vector). Once the temporal vectors had been modeled the pure component spectra were reconstructed as a function of the pre-exponential multiplier obtained from the analysis, SVD determined spectral eigenvectors, and the corresponding eigenvalues. After the spectra of the component species were determined, the extinction profile was calculated and used along with the calculated decay times to construct a linear combination of the pure component species contributions to the observed... 

One should realize that these calculations are based on an expression for Vr which corresponds to potential flow past a stationary nonde-formable bubble, as seen by an observer in a stationary reference frame. However, this analysis rigorously requires the radial velocity profile for potential flow in the Uquid phase as a nondeformable bubble rises through an incompressible liquid that is stationary far from the bubble. When submerged objects are in motion, it is important to use liquid-phase velocity components that are referenced to the motion of the interface for boundary layer mass transfer analysis. This is accomplished best by solving the flow problem in a body-fixed reference frame which translates and, if necessary, rotates with the bubble such that the center of the bubble and the origin of the coordinate system are coincident. Now the problem is equivalent to one where an ideal fluid impinges on a stationary nondeformable gas bubble of radius R. As illustrated above, results for the latter problem have been employed to estimate the maximum error associated with the neglect of curvature in the radial term of the equation of continuity. 

The analysis can be extended to the multi-component case [43, 44, 51, 65, 66]. The number of the fronts is directly related to the number of components in the mixture. For ideal and moderately non-ideal mixtures the concentration and temperature profiles consist of n,. - 1 fronts connecting two pinch points. Again, constant pattern waves occur for ideal and moderately non-ideal mixtures. Addi-... 

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