Prediction of Interfacial Tension using the van der Waals-711 Equation of State

The classical van der Waals equation of state is primarily regarded as a pedagogical model with limited predictive power. A lesser-known modification, the van der Waals-711 equation, extends its applicability by introducing an additional parameter that accounts for thermodynamic temperature and the acentric factor. In this study, we compare its performance with both the classical van der Waals and the more popular cubic equation of state (Peng-Robinson). The equation is applied within an interfacial model based on the Density Gradient Theory (DGT), enabling predictions of interfacial tension using only critical thermodynamic data as input, free of parameter estimation from experimental data. As a kind of numerical relaxation scheme, the time-dependent Cahn-Hilliard equation is solved to obtain equilibrium density profiles. Comparative analysis for a group of selected hydrocarbons shows that van der Waals-711 yields comparable accuracy as Peng-Robinson equation for interfacial tension prediction across all investigated temperatures. The developed model is supplemented with global sensitivity analysis, indicating susceptibility of the predicted interfacial tension values to the variations in model input parameters.