Chromatography in a Bed of Spheres

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Abstract
A computationally efficient method is presented for calculating the combined effects of intraparticle diffusion, interphase mass-transfer resistance, and fluid-phase axial dispersion for chromatography in a column of uniform regularly packed spheres. The method uses an extension of the generalized Sturm-Liouville theory of Ramkrishna and Amundson to adapt the Taylor-Gill-Subramanian dispersion analysis to two-phase systems. The primary utility of the analysis is to determine the importance of diffusional transients and to obtain asymptotic limiting behavior for very long columns. Simple closed-form solutions are given for this limiting condition. Our analysis suggests that the transients neglected in presently used lumped-parameter analyses are in fact often small, especially for small packing diameter and low flow rates. In addition, the Glueckauf and Coates approximation for internal diffusional resistance is found to be a valid asymptotic limit. However, conditions do arise in practice where transients should be considered.