Results Obtained with the Equilibrium Dispersive Model

4 Results Obtained with the Equilibrium Dispersive Model 

1 Comparison of Solutions of the Ideal and the Equilibrium-Dispersive Models 

The ideal model (Chapter 7) assiunes an infinite column efficiency. This makes the band profiles that it predicts unrealistically sharp, especially at low concentrations. This sharpness is explained by the fact that the ideal model propagates concentration discontinuities or shocks. For a hnear isotherm, the elution profile would be identical to the input profile, clearly an unacceptable conclusion. The effects of a nonideal column are significant in three parts of the band profile. The shock is replaced by a steep boimdary, the shock layer, whose thickness is related to the coefficients of the column HETP (axial dispersion and mass transfer resistance see Chapter 14). The top of the band profile is roimd, instead of being 

Golshan-Shirazi and Guiochon [27,66] have shown that the degree of agreement between the ideal and the equihbrirun-dispersive models depends on the value 

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The profiles of individual zones in displacement chromatography have also been calculated using the solid film linear driving force model [23]. Again, when the number of mass transfer units of the column is high, the results are very similar to those obtained with the equilibrium-dispersive model (Chapter 12). As an example. Figure 16.10 shows the displacement chromatogram calculated with kpi = kfg = = 50 s . The bands in the isotachic train are clearly formed... 

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... 

We discuss in this first part the formation of the isotachic train using the equilibrium-dispersive model and the influence of the various parameters that control the characteristics of this train the displacer concentration, the sample size, the column length, the concentration of the feed, and the column efficiency. The results differ from those reported in Chapter 9, which were obtained with the ideal model in which there is no dispersion. Because the differences observed consist essentially in the formation of mixed zones between the bands in the isotachic train, many results remain similar. We also discuss the behavior of trace components, either those contained in the sample or those contained in the displacer. 

It is important to differentiate between the two different types of sorption/ desorption tests (i. e.,batch and column-leaching), and the sorption characteristics determined from one should not be confused with the other. Sorption isotherms obtained with batch equilibrium tests are applied mainly to solid suspensions. The physical model, assumed with this situation, is one of a completely dispersed solid particle system, where all solid particle surfaces are exposed and available for interactions with the contaminants of concern. In contrast, column-leaching tests are performed with intact solid samples, and the sorption characteristics obtained from them are the results of contaminant interactions with a structured system where not all-solid particle surfaces are exposed or available for interactions with the contaminants. 

In a classic paper Lapidus and Amundson (1952) studied liquid chromatography for isothermal operation with linear, independent isotherms when mass transfer is very rapid, but axial dispersion is inportant. Although the two-porosity model can be used (Wankat, 1990), the solution was originally obtained for the single-porosity model. Starting with Eq. [18-551. we substitute in the equilibrium expression Eq. [18-6al to remove the variable q (solid and fluid are assumed to be in local equilibrium). Since the fluid density is essentially constant in liquid systems, the interstitial fluid velocity Vj ter can be assumed to be constant. The resulting equation for each solute is... 

The former two relationships (paragraphs (1) and (2) above) were focused on to access the distribution of quaternary cations. The equilibrium property cannot reveal when the total carbon number for various quaternary salts is the same. In paragraph 3, the Hildebrand parameter cannot be easily obtained for all quaternary salts. Hence, we took the results of paragraphs 1-3 and the concept of HLB for the surfactant to show that the dispersal efficiency of surfactant or emulsifier molecules is a function of the relative interactions of their polar, hydrophilic heads with the aqueous phase and of their nonpolar, lipophilic tails with the hydrocarbon phase [105,106]. We developed a new model as... 

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