Development of modified stokes expression to model the behavior of expanded beds containing polydisperse resins for protein adsorption

Expanded bed behavior was modeled by using the Richardson-Zaki correlation between the superficial velocity of the feed stream and the void fraction of the bed. A polydisperse material, Chelating excellose® (70-210 Μm in diameter, 1.21 g/cm³ in density), which has Ni²⁺ ions for the selective binding of histidine-tagged proteins, was used as the resin. A method to modify the Stokes expression to express the terminal settling velocity of the resins by introducing two empirical parameters, the effective diameter of the resins and an exponent for(ρ _p -ρ)/Μ term, was developed. Combined use of the Richardson-Zaki correlation and the modified Stokes expression was successful in modeling the bed expansion by incorporating physical properties of feed streams and the resins.