A unified surface tension model for multi-component salt, organic, and surfactant solutions

Despite the fact that the surface tension of liquid mixtures is of great importance in numerous fields and applications, there are no accurate models for calculating the surface tension of solutions containing water, salts, organic, and amphiphilic substances in a mixture. This study presents such a model and demonstrates its capabilities by modelling surface tension data from the literature. The presented equations not only allow to model solutions with ideal mixing behaviour but also non-idealities and synergistic effects can be identified and largely reproduced. In total, 22 ternary systems comprising 1842 data points could be modelled with an overall root mean squared error (RMSE) of 3.09 mN m⁻¹. In addition, based on the modelling of ternary systems, the surface tension of two quaternary systems could be well predicted with RMSEs of 1.66 mN m⁻¹ and 3.44 mN m⁻¹. Besides its ability to accurately fit and predict multi-component surface tension data, the model also allows to analyze the nature and magnitude of bulk and surface non-idealities, helping to improve our understanding of the physicochemical mechanisms that influence surface tension.