A method for prediction of the gel concentration in macromolecular ultrafiltration

A method is proposed for a priori estimation of the important ‘gel’ concentration in macromolecular ultrafiltration, which, historically, has always been calculated by fitting a mathematical model to experimental ultrafiltration data. The method based on the lattice-fluid-hydrogen-bond (LFHB) theory for phase behavior is shown to predict the same qualitative behavior of the variation of poly-ethylene-glycol (PEG) osmotic pressure with molecular weight of PEG and its concentration as the experimentally measured trend reported in the literature. The solubility limit (lower branch of the binodal envelope) for PEG (6000 kDa) is predicted to be ∼340 kg/m3. The corresponding high polymer concentration branch of the binodal is predicted to be at a polymer volume fraction of 0.84 which is the predicted ‘gel’ concentration for PEG.