Nature of the eddy dispersion in packed beds

Abstract

Relationships describing the dependence of the height equivalent to a theoretical plate (HETP) on the linear velocity u contain a term that is traditionally called the eddy dispersion term. In some theories, this term is independent of velocity, in others it results in a curved relationship with velocity. Both have been obsrved experimentally. In this paper, we advocate a theory which is capable of explaining both. This theory is based on the mass-transfer between sections of the mobile phase that move at different velocities. The equation obtained is formally identical to the equation derived by Giddings. However, the meaning of the coefficients in both theories is different. In our approach, the coefficients are related to structural parameters of the packed bed and can be assessed quantitatively. This is helpful in the interpretation of eddy dispersion terms obtained in column packing experiments. The mathematical approach used here allows the calculation of all moments of the peak and therefore a prediction of the peak-shape. Although a relationship exists between structural parameters of the packed bed and the experimental observations of peak width and peak symmetry, this relationship can only be expressed in the form of the product of velocity difference with a characteristic distance. This term cannot be deconvoluted further. Thus, large velocity differences over small distances result in the same peak-width and -shape as small velocity differences over large distances.