Hodograph method

Figure 11.22 Comparison of experimental (symbols) and calculated individual elution profiles. 2-Phenylethanol and 3-phenylpropanol. Calculations made with the forward-backward scheme, the coefficients of the competitive isotherm Langmuir model derived from the hodograph method and the recorded injection profile (Solid line) or a rectangular injection profile (Dashed line) Same sample sizes as in Figure 11.21. (a) 1 1 mixture, (b) 1 3 mixture, (c) 3 1 mixture. Reproduced with permission from AM. Katti, M. Czok and G. Guiochon, ]. Chromatogr., 556 (1991) 205 (Fig. 6).

N.N. Bernshtein and M.L. Gerver (1980) Conditions for distinguishabihty of metrics by hodographs methods and algorithms for seismic data interpretation. Computational Seismology, vol. 13, Moscow, Nanka, 50-73. 

For a simple wave, apphcation of the method of characteristics (hodograph transformation) gives... 

There is a dearth of competitive adsorption data, in a large part because they are difficult to measme, but also because little interest has been devoted to them, as, until recently, there were few problems of importance whose solution depended on their understanding. Besides the static methods, which are extremely long and tedious and require a large amoimt of material, the main methods of measurement of competitive isotherms use column chromatography. Frontal analysis can be extended to competitive binary isotherms [14,73,93-99], as well as pulse techniques [100-104]. The hodograph transform is a powerful method that permits an approach similar to FACP for competitive binary isotherms [105,106]. 

Figure 4.31 Experimental determination of competitive isotherms by the method of the hodograph transform, (a) Individual elution profiles of the two components of a binary mixture, (b) Hodograph transform of the profiles in (a). Reproduced with permission from Z. Mfl and G. Guiochon,. Chromatogr. 603 (1992) 13 (Fig. 3).

There is an abimdant literature on the comparison between experimental and calculated band profiles for binary mixtures. The most popular methods used have been the forward-backward finite difference scheme and the OCFE method. The former lends itself readily to numerical calculations in many cases representative of the present preoccupations in preparative chromatography. We present first a comparison between the band profiles obtained with the ideal and the equilibrium-dispersive model to illustrate the dispersive influence of the column efficiency. Related to the comparison between these two models is the issue of the use of the hodograph transform of experimental results discussed in Section 11.2.2. Computer experiments are easy to carry out and most instructive because it is possible to show e effects of the change of a single parameter at a time. Some... 

FIGURE 4.22 Admittance hodographs in the electrical circuit at the different magnitudes of R( / Rj 1 0 2 0.1 5 1.0 4 10 and 5 100. (From Zhuiykov, S., In-situ diagnostics of solid electrolyte sensors measuring oxygen activity in melts by developed impedance method, Meas. Sci. Technol. 17 (2006) 1570-1578. With permission.)... 

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