Schmidt plot

Fig. 4-23 Schmidt-plot conslruclion for four lime increments...

Fig. 4 24 Graphical technique of representing convection boundary condition with the Schmidt plot.

Fig- 4-25 Schmidt plot for four time increments, including convection boundary condition. 

Figure 25 shows the elugrams of the samples presented as Gram-Schmidt plots. The Gram-Schmidt plots are obtained from FTIR measurements by summarizing all peak intensities at all frequencies and compare well with the total concentration profile. Across the Gram-Schmidt plots the vinyl acetate (VA) contents are given as... 

Sherwood and Pigford(7) have shown that if the data of Gilliland and SHERWOOD<36) and others 35 38,395 are plotted with the Schmidt group raised to this power of 0.67. as shown in Figure 10.14, a reasonably good correlation is obtained. Although the points are rather more scattered than with heat transfer, it is reasonable to assume that both jd and 7/, are approximately equal to 0. Equations 10.224 and 10.226 apply in the absence of ripples which can be responsible for a very much increased rate of mass transfer. The constant of 0.023 in the equations will then have a higher value. 

SHERWOOD and Pigford(7) found that the effect of the Schmidt group was also influenced by the Reynolds group and that the available data were, fairly well correlated as shown in Figure 10.16, in which (hod )/D is plotted against Re Sc0-67. 

In Fig. 2, the normalized model scalar energy spectrum is plotted for a fixed Reynolds number (ReL = 104) and a range of Schmidt numbers. In Fig. 3, it is shown for Sc = 1000 and a range of Reynolds numbers. The reader interested in the meaning of the different slopes observed in the scalar spectrum can consult Fox (2003). By definition, the ratio of the time scales is equal to the area under the normalized scalar energy spectrum as follows ... 

In Fig. 9, the distribution of reactant C is shown in each environment. As cc is a linear combination of and Y2 (Eq. 78), we can distinguish features of both Fig. 7 and Fig. 8 in the plots in Fig. 9. In particular, because C is injected in the right-hand inlet stream, cC2 and 2 appear to be quite similar. Finally, as shown in Liu and Fox (2006), the CFD predictions for the outlet conversion X are in excellent agreement with the experimental data of Johnson and Prud homme (2003a). For this reactor, the local turbulent Reynolds number ReL is relatively small. The good agreement with experiment is thus only possible if the effects of the Reynolds and Schmidt numbers are accounted for using the correlation for R shown in Fig. 4. Further details on the simulations and analysis of the CFD results can be found in Liu and Fox (2006). 

The behavior of the scalar spectra for Schmidt numbers near Sc = 1 is distinctly different than the velocity spectrum. This can be most clearly seen by plotting compensated... 

In Fig. 3.14, the mechanical-to-scalar time-scale ratio computed from the model scalar energy spectrum is plotted as a function of the Schmidt number at various Reynolds numbers. Consistent with (3.15), p. 61, for 1 Sc the mechanical-to-scalar time-scale ratio decreases with increasing Schmidt number as ln(Sc). Likewise, the scalar integral scale can be computed from the model spectrum. The ratio L Lu is plotted in Fig. 3.15, where it can be seen that it approaches unity at high Reynolds numbers. 

In order to illustrate how the multi-variate SR model works, we consider a case with constant Re>. = 90 and Schmidt number pair Sc = (1, 1/8). If we assume that the scalar fields are initially uncorrelated (i.e., pup 0) = 0), then the model can be used to predict the transient behavior of the correlation coefficients (e.g., pap(i)). Plots of the correlation coefficients without (cb = 0) and with backscatter (Cb = 1) are shown in Figs. 4.14 and 4.15, respectively. As expected from (3.183), the scalar-gradient correlation coefficient gap(t) approaches l/yap = 0.629 for large t in both figures. On the other hand, the steady-state value of scalar correlation pap depends on the value of Cb. For the case with no backscatter, the effects of differential diffusion are confined to the small scales (i.e., (), / h and s)d) and, because these scales contain a relatively small amount of the scalar energy, the steady-state value of pap is close to unity. In contrast, for the case with backscatter, de-correlation is transported back to the large scales, resulting in a lower steady-state value for p p. 

Figure 13 Topographic plot of results from GC-DMS characterization of a mixture of explosives using a 2 m long capillary column with a fast temperature ramp. Source (A. Cagan, H. Schmidt, and G.A. Eiceman, NMSU, August 2005 unpublished results.)...

Figure 6.6 Magnetic moments of the odd-proton (A) and of the odd-neutron nuclei plotted as a function of the nuclear spin, j. The Schmidt limits are shown by the solid lines. The data generally fall inside the limits and are better reproduced as 60% of the limits.

Figure A1.3.4 Semi-log plot of Spin Echo amplitude with changing Hahn Echo experiment interval, x, for an oilseed containing excess moisture (therefore some is free) and oil. Extrapolation of the fitted lines (dashed) to x = 0 gives amplitudes for excess (free) moisture (Aw and oil A0 modified from Schmidt, 1991).

As might be expected, the dispersion coefficient for flow in a circular pipe is determined mainly by the Reynolds number Re. Figure 2.20 shows the dispersion coefficient plotted in the dimensionless form (Dl/ucI) versus the Reynolds number Re — pud/p(2Ai). In the turbulent region, the dispersion coefficient is affected also by the wall roughness while, in the laminar region, where molecular diffusion plays a part, particularly in the radial direction, the dispersion coefficient is dependent on the Schmidt number Sc(fi/pD), where D is the molecular diffusion coefficient. For the laminar flow region where the Taylor-Aris theory18,9,, 0) (Section 2.3.1) applies ... 

This relation is plotted in Fig. 2.20, the first term having only a small effect in the Reynolds number range shown, except at low Schmidt numbers. 

The diffusion constant, DCf has only recently been measured. Schmidt and Buck (37) observed the formation and decay of the transient conductivity during and following the pulse irradiation of dilute aqueous barium hydroxide, pH 9.5. These workers fitted the curve of the transient conductivity, plotted as a function of time, by means of a computer. Necessary for this calculation were ... 

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