Modeling of protein breakthrough performance in cryogel columns by taking into account the overall axial dispersion

A model considering the overall axial dispersion for describing protein adsorption and breakthrough in monolithic cryogel beds has been developed. The microstructure of cryogels was characterized by tortuous capillaries with a normal diameter distribution but a constant pore wall thickness. The axial dispersion within cryogel columns was described by using the overall axial dispersion coefficient, which can be easily obtained by matching the experimental breakthrough curves without adsorption or measuring residence time distributions (RTDs). Experimental breakthrough curves of lysozyme within a metal-chelated affinity cryogel by Persson et al. (Biotechnol. Bioeng. 2004, 88, 224-236) and a cation-exchange cryogel by Yao et al. (J. Chromatogr. A 2007, 1157, 246-251) were employed as examples to test the model. The results showed that by using the axial dispersion coefficient and assuming uniform radial concentration profile at a given cross-section of the cryogel along the bed height, the model can describe the detailed behaviors of the in-bed overall axial dispersion, the in-pore mass transfer, as well as the protein adsorption and breakthrough. For a known overall axial dispersion coefficient, the lumped parameter of the mass transfer coefficient between the bulk liquid and the capillary wall can be determined by fitting the protein breakthrough curve at a known chromatographic condition. Once this parameter is determined, the model can be used to predict the protein breakthrough profiles under different conditions based on the basic physical parameters of the cryogel bed and the properties of the fluid and protein. The effective capillary diameters employed in the model are close to the actual pore sizes observed from the images by SEM. The model predictions of lysozyme breakthrough profiles at various flow rates are also in good agreement with the experimental data in both the metal-chelated affinity and cation-exchange cryogel columns.