Particle-size distribution effects in batch adsorption

Mathematical models for pore-diffusion-controlled batch adsorption that take an arbitrary distribution of particle sizes into account are developed and solved for two extreme cases: the linear isotherm case and the irreversible isotherm case. Numerical calculations based on these solutions show that the effects of the particle-size distribution (PSD) are significant, even for relatively narrow and symmetrical PSDs. The uptake rate is faster initially and slower as equilibrium is approached than is predicted using the volume-average particle radius. These results are confirmed by comparing model predictions with experimental results obtained for the batch uptake of the protein alpha-chymotrypsinogen on SP-Sepharose-FF. Although the PSD of this commonly used commercial medium for preparative protein chromatography is fairly narrow, significant effects are observed in both shallow-bed and stirred batch-uptake experiments. As a result, the PSD needs to be taken into account when precise predictions are desired, such as when batch-uptake experiments are used for diffusivity measurements. The PSD also affects the shape of the breakthrough curve in packed beds. The effects are somewhat less pronounced, but still quite significant for the irreversible isotherm case.