Mathematical analysis of frontal affinity chromatography in particle and membrane configurations

The scaleup and optimization of large-scale affinity-chromatographic operations in the recovery, separation and purification of biochemical components is of major industrial importance. The development of mathematical models to describe affinity-chromatographic processes, and the use of these models in computer programs to predict column performance is an engineering approach that can help to attain these bioprocess engineering tasks successfully. Most affinity-chromatographic separations are operated in the frontal mode, using fixed-bed columns. Purely diffusive and perfusion particles and membrane-based affinity chromatography are among the main commercially available technologies for these separations. For a particular application, a basic understanding of the main similarities and differences between particle and membrane frontal affinity chromatography and how these characteristics are reflected in the transport models is of fundamental relevance. This review presents the basic theoretical considerations used in the development of particle and membrane affinity chromatography models that can be applied in the design and operation of large-scale affinity separations in fixed-bed columns. A transport model for column affinity chromatography that considers column dispersion, particle internal convection, external film resistance, finite kinetic rate, plus macropore and micropore resistances is analyzed as a framework for exploring further the mathematical analysis. Such models provide a general realistic description of almost all practical systems. Specific mathematical models that take into account geometric considerations and transport effects have been developed for both particle and membrane affinity chromatography systems. Some of the most common simplified models, based on linear driving-force (LDF) and equilibrium assumptions, are emphasized. Analytical solutions of the corresponding simplified dimensionless affinity models are presented. Particular methods for estimating the parameters that characterize the mass-transfer and adsorption mechanisms in affinity systems are described.