Extractions, number

Equation 9 is plotted in Figure 2 for several values of the axial dispersion number, /mL,—i.e., the reciprocal of the above-mentioned axial Peclet number. E/uL approaches zero as piston-type or plug flow is approached, and approaches infinity as a completely mixed condition is approached. It is seen that axial dispersion has an increasingly detrimental effect on devolatilization as the extraction number, increases. The applicability of Equation 9 and the validity of some of the assumptions contained therein will be tested experimentally in the section on Results. 

This is a sizable discrepancy and definitely indicates a need for an additional cross-sectional bulk transport term in the original differential material balance, Equation 6. An approximate, but much simpler, way to take into account lack of cross-sectional mixing would be to multiply the extraction number, N xt (Figure 2) by an exponential correction term,, of the form ... 

Fig. 11.4.2. Analysis of chicory root extract. Numbers refer to length of saccharide chains. Chromatographic conditions column, Spherisorb S5 NH2 (250X4.6 mm) mobile phase, acetonitrile-water (60 40) flow rate, 2.0 ml/min detection, refractive index. Reproduced from Macrae (1982), with permission.

The extraction number is a measure of the overall devolatilization efficiency. The backmixing term disappears when the melt film thickness is zero. This is to be expected because the backmixing is caused by the transport in the melt film. If the film thickness is zero, there can be no transport in the melt film and consequently no backmixing. If the film stage efficiency X, = 1, the backmixing term will disappear as well. This is also easy to understand because In this case the concentration C (z) at which the melt film reenters the melt pool is known and will equal Cg. Thus, the Taylor s series expansion is no longer necessary and the first-order differential equation can be determined directly from the mass balance, Eq. 7.463. 

The second equality in the above equation is correct for single-flighted screws and negligible flight widths. Hence, backmixing increases with the degree of fill and decreasing values of (j). Ex is the extraction number, and it is a measure of the overall devolatilization efficiency. 

For chemical processes, some examples are the elimination of aromatics by sulfonation, the elimination of olefins by bromine addition on the double bond (bromine number), the elimination of conjugated diolefins as in the case of the maleic anhydride value (MAV), and the extraction of bases or acids by contact with aqueous acidic or basic solutions. 

The hydration of more inert ions has been studied by O labelling mass spectrometry. 0-emiched water is used, and an equilibrium between the solvent and the hydration around the central ion is first attained, after which the cation is extracted rapidly and analysed. The method essentially reveals the number of oxygen atoms that exchange slowly on the timescale of the extraction, and has been used to establish the existence of the stable [1 10304] cluster in aqueous solution. 

Enonnous numbers of chemical shifts have been recorded, particularly for FI and Many algoritlnns for the prediction of shifts have been extracted from these, so that the spectra of most organic componnds can be predicted at a useful level of accuracy, usmg data tables available in several convenient texts [12, F3,14 and 15]. Alternatively, computer programs are available that store data from 10 -10 spectra and then use direct... 

Wall M R and Neuhauser D 1995 Extraction, through filter-diagonalization, of general quantum eigenvalues or classical normal mode frequencies from a small number of residues or a short-time segment of a signal. 

Quantum chemical methods, exemplified by CASSCF and other MCSCF methods, have now evolved to an extent where it is possible to routinely treat accurately the excited electronic states of molecules containing a number of atoms. Mixed nuclear dynamics, such as swarm of trajectory based surface hopping or Ehrenfest dynamics, or the Gaussian wavepacket based multiple spawning method, use an approximate representation of the nuclear wavepacket based on classical trajectories. They are thus able to use the infoiination from quantum chemistry calculations required for the propagation of the nuclei in the form of forces. These methods seem able to reproduce, at least qualitatively, the dynamics of non-adiabatic systems. Test calculations have now been run using duect dynamics, and these show that even a small number of trajectories is able to produce useful mechanistic infomiation about the photochemistry of a system. In some cases it is even possible to extract some quantitative information. 

---