A MATHEMATICAL-ANALYSIS OF AFFINITY MEMBRANE BIOSEPARATIONS

A mathematical model including convection, diffusion and Langmuir adsorption is formulated to analyze the design and operation of affinity membrane bioseparations. A key prediction from the analysis is that the flow velocity through affinity membranes may be limited not by pressure drop, but rather by association kinetics between soluble protein and immobilized ligand. Furthermore, for thin membranes with Peclet numbers less than 40, slow association kinetics may limit the flow velocity to an extent where diffusion axial to flow undesirably becomes a dominant mechanism for transport of protein through the membrane. Lastly, even relatively small thickness variations of 3% and porosity variations of 1% may severely degrade membrane performance. Practical consequences of these results are presented, e.g. constructing thicker membranes from stacks of thinner membranes will tend to reduce the effect of thickness and porosity variations, sharpen breakthrough curves, raise allowable flow velocities and increase loading capacities.