Band broadening nonlinear chromatography

The classical shift-invariant convolution permits a simple calculation of the combined effects of multiple sources of band broadening when the column efficiency is not very low. This approach gives correct results in linear chromatography but is incorrect in nonlinear chromatography [1]. The simplest model that takes axial dispersion and mass transfer kinetics into account is the equilibrium-dispersive model. This model permits, with a good approximation, the accurate prediction of the importance of the self-sharpening and dispersive phenomena due to thermodynamics and kinetics of phase equilibria. This, in turn, results in correct prediction of the band profiles and the achievement of often excellent... 

In nonlinear chromatography, most of band broadening is due to the thermodynamic contribution. As soon as is significant, the kinetic contribution becomes small compared to the thermod5mamic contribution and the difference between these two equations has little practical consequence. The contribution Hq is significant only when mass transfer kinetics is slow and the contribution of the mass transfer resistances to the band profile is greater than the contribution originating from the nonlinear behavior of the isotherm. 

Efficiency, N The column efficiency characterizes the combined effects of the sources of band broadening due to axial dispersion and mass transfer resistance. It is derived from the width of the elution peak observed as the response to the injection of a small, narrow pulse of a dilute solution of a compoimd. It is difficult to correct for the contribution of the extracolumn sources of band broadening which have to be kept small. In preparative and nonlinear chromatography, there is a correlation between the colmnn efficiency and both the steepness of the shock layer and the duration of the band beyond the retention time However, the column efficiency is essentially a concept of linear chromatography, and it is difficult to extend to and use in nonlinear chromatography, except through the shock layer thickness concept. 

Linear addition rule Rule stating that the contributions of axial dispersion and all the sources of mass transfer resistance to the band broadening are additive. This rule is valid in linear chromatography, but has limited applicability in nonlinear chromatography. 

Plate number (apparent) Derived from the ratio of the retention time and the width of a band, using equations valid in linear chromatography. The apparent plate number has no sense in nonlinear chromatography beside indicating the degree of band broadening due to thermod5mamics. 

The sharp concentration fronts shown in Fig. [4.1-2 and 14.1-3 never occur in practice. The zones are always diluted and broadened by mass transfer and dispersion for both linear and nonlinenr isotherms. The complete solution of (he equilibrium equations, mass balances, and mass transfer equations for nonlinear systems is a formidable task requiring numerical solutions. For I incur systems the task is much easier and very useful solutions have been developed. Even thongh large-scale chromatography often is operated in the u out inear range, the linear analyses are valnable siace they can provide a qualitative feel (quantitative for linear systems) for band broadening effects. 

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