Predicting the Solubilization of Hydrocarbons in Aqueous Surfactant Solutions

Surfactants are widely employed across numerous applications due to their amphiphilic nature, which drives aggregate formation and enables the solubilization of hydrophobic compounds in aqueous solutions once the critical micelle concentration (CMC) is exceeded. In this work, we present a holistic modeling approach that considers both aggregation equilibria as well as phase equilibria in ternary systems of water, hydrophobic solutes (“oil”), and surfactants. For that purpose, PC-SAFT is incorporated into a novel mixed-aggregate formation model. Micellar solubilization effects are described by accounting for the formation of mixed oil-surfactant aggregates. Consequently, our model is based on a continuous distribution along all possible compositions and sizes of the mixed aggregates while calculating their equilibrium geometries. Our approach, for the first time, enables quasi-quantitative predictions of liquid–liquid equilibria in water–oil–surfactant systems. It accurately captures the sharp increase in oil solubility at surfactant concentrations just above the CMC and captures the influence of surfactant polarity on the maximum solubilization capacity for various hydrophobic solutes in very good agreement with experiments. Our methodology is validated for polyethoxylated alkyl ethers (CiEj) as surfactants and for alkanes and alkenes as example oil components, with the predicted binodal curves closely matching experimental LLE data.