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LONGITUDINAL DIFFUSION AND RESISTANCE TO MASS TRANSFER AS CAUSES OF NONIDEALITY IN CHROMATOGRAPHY
J. J. V A N D E E M T E R , F. J. Z U I D E R W E G Koninklijke/Shell-Laboratorium, Amsterdam (N.V. De Bataafsche Petroleum Maatschappij) and A. K L I N K E N B E R G N. V. De Bataafsche Petroleum Maatschappij, The Hague

(Received 1 February 1956)
Al~tract--The mechanisms of band broadening inlinear, nonideal chromatography are examined. A development is presented of a rate theory for this process, wherein nonideality is caused by axial molecular diffusion; axial eddy diffusion; finiteness of transfer coefficient. The correspondence with the plate theory is given, so that the results can also be expressed in heights equivalent to a theoretical plate. The plate theory has been extendedto the case of a finite volume of feed; the requirement for this feed volume to be negligible has been examined and a method is presented for evaluating concentration profiles obtained with a larger volume of feed. An analysis is given of experimental results, whereby the relative contributions to band broadening for various cooperating mechanisms could be ascertained. R ~ n m ~ - U n e 6tude a 6t6faite des m6canismes de l'61argissement des bandes dans la chromatographie lin6aire non-id/~ale. On a d6velopp6 une th6orie sur la vitesse de ce processus, selon laquelle la non-id6alit6 est caus6e par: la diffusion mol6culaire axiale; la diffusion turbulente axiale; le fait que le coefficient de transfert aune valeur finie. La correspondance &ablie entre cette thgorie et celle des plateauxpermet d'exprimer les r6sultats obtenus aussi en termes de la hauteur de colonne 6quivalente ~ un 6tage th~orique. La th6orie des plateaux a 6t6 rendue applicable sur le ces d'un 6chantillon de volume fini; les conditions dans lesquelles le volume de cet 6chantillon est n6giigeable ont 6t6 6tudi6es et on pr6sente une m6thode pour interpreter les profiles de concentration obtenus avec des 6chantillonsplus grands. Une analyse des r6sultats exp&imentaux a permis de d6terminer les contributions relatives des diff6rents m6canismes en question ~. l'61argissement des bandes.

1. INTRODUCTION F o r the design of efficient chromatographic columns it is desirable to have a background of theory, in order to know how various factors influence the sharpness of separation. In the theories ofchromatography simplifying assumptions are introduced in order to make the basic differential equations accessible to mathematical treatment. As the nature of the assumption depends on the type of chromatography adopted, a survey of the possible assumptions should first be made. These are: 1. The equilibrium concentrations in the two phases are proportional ("linear chromatography"). 2. The exchange process isthermodynamically reversible, i.e. the equilibrium between particle and fluid is i m m e d i a t e - - t h e mass transfer coefficient is infinitely h i g h - - a n d longitudinal diffusion and other processes having a similar effect can be ignored. Such a process is commonly called "ideal chromatography".

By making these assumptions or not in the two cases, respectively, one arrives at thefollowing four possibilities:

Ideal Nonideal chromatography chromatography Linear isotherm Nonlinear isotherm I II III IV

Reprinted from Chem. Engng Sci. 5, 271-289, 1956.

Case I covers the simplest theory still possessing the essential features of chromatography. The retardation of solute with regard to solvent depends on the product of the distribution (partition) coefficient between thephases and the ratio of the amounts of those phases present in the column, but not on concentrations. The shape of a band, during its movement, thus remains unchanged. Furthermore, different solutes behave independently [1]. If a band of mixed solutes is introduced in a column, it is a matter of simple arithmetic to find the requirement for the individual bands to become separated; this point...
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