I carry out separations of rare earths, amino acids, and other inorganic and organic materials that are not isolated easily by the older chemical procedures. The present paper will outline a quantitative calculation method for interpreting and predicting the performance of fixed-bed separation columns under the limiting condition of low relative concentration-i.e., under "trace" conditions. The proposed method is based upon a kinetic or diffusional approach and reduces under specified restrictions to a result given also by the equilibrium plate theory of Mayer and Tompkins (86).The relation of an ion exchange separation to a bulk saturation of ion exchange resin will be of interest to the general reader. As shown in the upper diagram of Figure 1, an ordinary bulk saturation operation as performed on a process liquor involves a large extent of displacement of an innocuous ion from the resin by an undesirable ion (adsorbate ion) from the feed liquor. When the column is saturated t o the extent that breakthrough of the undesirable ion occurs, the flow is interrupted and the column is then eluted or regenerated by passing through it an excess of solution of the innocuous ion. Saturation operations will be considered here only to the extent needed for deriving the theory of trace separations.The lower diagram of Figure 1 depicts an elution separation of the chromatogaphie type. In this operation only a small amount of solution containing the components to be separated is admitted to the column. These components are then washed through (eluted) by an electrolyte solution (the elutant) that initially is free of them. The components travel through the column as bands or zones a t slightly different velocities. If the column is of sufficient length the zones will draw apart completely from one another and may be recovered in the effluent as separate solutions of each individual component in carrier electrolyte. Movement of a zone through the resin occurs by the following mechanism: Liquid on the upstream (trailing) side of a zone is 1 Present address, Stanford Research Institute, Stanford, Calif. undersaturated with respect to the adsorbed component and continually takes it into solution. Passing beyond the peak of the zone to the downstream (leading) side, the same liquid is supersaturated relative to coexisting resin and hence gradually redeposits the solute component.
OPERATING VARIABLESThe elution separation just described is a function of a large number of chemical and physical factors, which will be shown in this paper to be amenable to mathematical interpretations. DISTRIBUTION RATIO. This is the dimensionless ratio. DA q;Pb/CAfE which is given in Equation 4, of solute concentrations in the solid and liquid phases. The distribution ratio affects directly the rate of linear advance ( U A ) of a zone; the ratio ( R~) A of zone movement to fluid movement (I;) is given h5-In order to carry out a separation, it iF; obviously necerisary for the values DA, DB, etc., of the components undergoing elution to differ substanti...