A membrane fouling model based on pore adsorption

To fit complex experimental membrane fouling data, a model was derived that assumes foulant adsorption occurs due to a reaction between foulants and membrane pore surface area, reducing pore radius and increasing membrane resistance. The decline in pore radius was described by a reaction rate law involving a rate constant, pore area, and foulant concentration. The dependence of pore radius on time was inserted into the Hagen-Poiseuille law for flux to obtain explicit equations to predict flux, resistance, or volume versus time for different values of reaction orders with respect to pore area or foulant concentration. The model was extended to the case of multiple pore radii. Surprisingly, the new model can be reduced to the four classical fouling models, but adds the capability to fit a non-linear dependence on foulant concentration. The model was applied to flux versus time data from the literature using a range of BSA concentrations with hydrophobic and hydrophilic PVDF membranes, or PEG with hydrophilic PVDF membrane. The new model demonstrated the ability to fit a wider range of data than the four classical models using only two to four fitted parameters. This included data with a negative fouling index and data with a non-linear dependence on foulant concentration.