Two-Component Band Profiles with the Equilibrium-Dispersive Model

Two-Component Band Profiles with the Equilibrium-Dispersive Model 

2 Finite Difference Methods. Errors in the Case of Two Components.534 

1 Comparison of Solutions of the Ideal and the Equilibrium-Dispersive Models. . 543 

5 Comparison of Calculated Band Profiles and Experimental Results.556 

Because we need to calculate numerical solutions to investigate systematically 

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We compare in Figure 11.7 the individual band profiles derived from the ideal model (solid lines) and those calculated with the equihbtium-dispersive model (dotted lines) in the case of two mixtures with relative compositions 1 3 and 3 1. The loading factors for the two components are Lf i = 1.2% and Lf i = 3.8%. The calculations with the equilibrium-dispersive model were made with efficiencies of 1000 (Figures 11.7a,c) and 5000 (Figure 11.7b,d). The apparent loading factors (m = N[k / 1+k see Eq. 10.115) for the two components range between 10 and 145. 

This value is in agreement with the one derived from band profiles calculated with the equilibrium-dispersive model [9]. The time given by Eq. 16.20 provides useful information regarding the specifications for the experimental conditions under which staircase binary frontal analysis must be carried out to give correct results in the determination of competitive isotherms. The concentration of the intermediate plateau is needed to calculate the integral mass balances of the two components, a critical step in the application of the method (Chapter 4). This does not apply to single-pulse frontal analysis in which series of wide rectangular pulses are injected into the column which is washed of solute between successive pulses. 

Prominent models for estimating peak profiles carry out a differentiation of the equilibrium isotherm with approximations for the mass transfer contribution. The equilibrium-dispersive model, above, assumes that all contributions due to nonequilibrium can be lumped into an apparent axial dispersion term. It further assumes that the apparent dispersion coefficient of the solutes remain constant, independent of the concentration of the sample components. For small particles, these approximations are reasonable for many applications. The ideal model assumes that the column efficiency is infinite. There is no axial diffusion, and the two phases are constantly at equilibrium. The band profiles obtained as solutions are in good agreement with experimental chromatograms for columns with N > 1000 having high loading factors. On the other... 

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