Linear nonideal chromatography

It is these two points of view which are used in the Chapter 2 to discuss the theory of gas chromatography. Linear, nonideal chromatography may be visualized by the relationships shown in Figures 1.12 and 1.13. 

Using these two sets of conditions, we can then describe four chromatographic systems (a) linear ideal chromatography, (b) linear nonideal chromatography, (c) nonlinear ideal chromatography, and (d) nonlinear nonideal chromatography. 

FIGURE 2.12 Linear nonideal chromatography = time at start of separation (point of sample injection) t = retention time of component A re = retention time of component B t = time for emergence of mobile phase from to. 

FIGURE 2.13 Isotherms for linear nonideal chromatography Cs = concentration at snr-face or in stationary phase Cq = concentration in solution (mobile phase) at equilibrium. 

The ideal model of chromatography, which has great importance in nonlinear chromatography, has little interest in linear chromatography. Along an infinitely efficient column, with a linear isotherm, the injection profile travels unaltered and the elution profile is the same as the injection profile. We also note here that, because of the profound difference in the formulation of the two models, the solutions of the mass balance equation of chromatography for the ideal, nonlinear model and the nonideal, linear model rely on entirely different mathematical techniques. 

There are simple algebraic solutions for the linear ideal model of chromatography for the two main coimter-current continuous separation processes. Simulated Moving Bed (SMB) and True Moving Bed (TMB) chromatography. Exphcit algebraic expressions are obtained for the concentration profiles of the raffinate and the extract in the columns and for their concentration histories in the two system effluents. The transition of the SMB process toward steady state can be studied in detail with these equations. A constant concentration pattern can be reached very early for both components in colimm III. In contrast, a periodic steady state can be reached only in an asymptotic sense in colunms II and IV and in the effluents. The algebraic solution allows the exact calculation of these limits. This result can be used to estimate a measure of the distance from steady state rmder nonideal conditions. 

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