Shrinking-core modeling of binary chromatographic breakthrough

Most chromatographic processes involve separation of two or more species, so development of a simple, accurate multicomponent chromatographic model can be valuable for improving process efficiency and yield. We consider the case of breakthrough chromatography, which has been considered in great depth for single-component modeling but to a much more limited degree for multicomponent breakthrough. We use the shrinking core model, which provides a reasonable approximation of particle uptake for proteins under strong binding conditions. Analytical column solutions for single-component systems are extended here to predict binary breakthrough chromatographic behavior for conditions under which the external transport resistance is negligible. Analytical results for the location and profile of displacement effects and expected breakthrough curves are derived for limiting cases. More generally, straightforward numerical results have also been obtained through simultaneous solution of a set of simple ordinary differential equations. Exploration of the model parameter space yields results consistent with theoretical expectations. Additionally, both analytical and numerical predictions compare favorably with experimental column breakthrough data for lysozyme–cytochrome c mixtures on the strong cation exchanger SP Sepharose FF. Especially significant is the ability of the model to predict experimentally observed displacement profiles of the more weakly adsorbed species (in this case cytochrome c). The ability to model displacement behavior using simple analytical and numerical techniques is a significant improvement over current methods.