Equilibrium proportionate-pattern case

B. Limiting Cases of Equilibrium Behavior 1. Proportionate-Pattern Case (Unfavorable Equilibrium)... 

The proportionate-pattern case is a classical one in the theory of chromatography, and was treated by DeVault (D2), Walter (Wl), Wilson (W7), and Weiss (W3). It is assumed that equilibrium is maintained everywhere in the column, that is, that N approaches infinity, due to high mass-transfer rates or to long residence times. 

In the case of an unfavorable isotherm (or equally for desorption with a favorable isotherm) a different type of behavior is observed. The concentration front or mass transfer zone, as it is sometimes called, broadens continuously as it progresses through the column, and in a sufficiently long column the spread of the profile becomes directly proportional to column length (proportionate pattern behavior). The difference between these two limiting types of behavior can be understood in terms of the relative positions of the gas, solid, and equilibrium profiles for favorable and unfavorable isotherms (Fig. 7). 

The attention of many workers has been given to the equilibrium-limited case (proportionate-pattern) of multiple adsorption (D2, Wl, W3, W7, among others). In the constant-pattern case, Fujita s work has already been discussed (Section III, B, 2b). Also, using the theoretical-plate approximation to a packed column, plate-by-plate calculations can be carried out in the constant-pattern case exactly as for continuous (countercurrent) distillation this treatment is suggested from work on chromatographic and displacement problems by Mair (M2), Spedding (S6), and Glueckauf (G3). Moreover the linear-equilibrium result can be extended, in a nearly trivial fashion, to any number of components. 

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