A mathematical model for co-surfactant enhanced removal of PFAS by foam fractionation

Due to the affinity of many per- and polyfluoroalkyl substances (PFAS) for the air-water interface, foam fractionation has emerged as a cost-effective method to treat PFAS-impacted water. Co-surfactants are often needed to enhance the removal of short-chain PFAS due to their lower surface activity, however, models are not currently available to describe this process. The goal of this research was to develop and validate a mathematical model for PFAS removal in a foam fractionation system with and without the addition of a co-surfactant. The model framework allows for (i) competitive Langmuir adsorption among PFAS and co-surfactants, (ii) liquid-side mass transfer with energy barrier limitations, (iii) a mean-bubble interfacial area with concentration-dependent bubble radius, and (iv) cationic surfactant binding (complexation). A limited set of input parameters are needed for predictions of time-resolved bulk concentrations, species complexation, and PFAS removal rates. The model accurately captures experimental measurements of long- and short-chain PFAS removal in the absence of co-surfactant, with non-ionic or cationic co-surfactants at various dosing rates, achieving low root means square error (RMSE) values. The model provides a tool that can be used to select operating parameters for foam fractionation systems and predict PFAS removal for each species and co-surfactant concentration.