Band Profiles of Single-Components with the Ideal Model

Band Profiles of Single-Components with the Ideal Model 

5 Time Needed for the Formation of a Shock on a Continuous Profile.359 

2 Comparison of Experimental and Calculated Elution Band Profiles..382 

For single-component systems, the theoretical solutions obtained are easy to compare to experimental profiles. They differ only by the smoothing effect due to axial dispersion and to the finite kinetics of mass transfers in actual columns. In many cases, because of the qualities of the stationary phases currently available, these effects appear to be secondary compared to the major role of thermodynamics in controlling the band proffles in overloaded elution. Admittedly, the influence of the finite coliunn efficiency on the band profiles prevents a successful quantitative comparison between theoretical and experimental band profiles. However, these profiles are similar enough at high concentrations and the solutions of the ideal model indicate which are the trends to be expected. 

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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. 

Chapter 10, which provides satisfactory accuracy and is the simplest and fastest calculation procedure. This method consists of neglecting the second-order term (RHS of Eq. 11.7) and calculating numerical solutions of the ideal model, using the numerical dispersion (which is equivalent to the introduction in Eq. 11.7 of a first-order error term) to replace the neglected axial dispersion term. Since we know that any finite difference method will result in truncation errors, the most effective procedure is to control them and to use them to simplify the calculation. The results obtained are excellent, as demonstrated by the agreement between experimental band profiles recorded with single-component samples and profiles calculated [2-7]. Thus, it appears reasonable to use the same method in the calculation of solutions of multicomponent problems. However, in the multicomponent case a new source of errors appears, besides the errors discussed in detail in Chapter 10 (Section 10.3.5). 

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