Surface tension of binary liquid–vapor mixtures: A comparison of mean-field and scaling theories

We use two different methods to estimate surface tension of binary liquid–vapor mixtures of CO2 and a hydrocarbon near a critical point. The first method is based on the gradient theory, which is essentially a mean-field approximation to the problem that reduces the determination of the interface’s structure and the surface tension to a boundary value problem. The theory’s input is an equation of state of homogeneous fluid and the influence parameters of inhomogeneous fluid. The Peng–Robinson equation and a modification of it are used as the equation of state of homogeneous fluid. The second method is based on the concept of two-scale-factor universality which can predict the surface tension from the singularity in the thermodynamic properties of the bulk fluid. The inputs of the method are an equation of state and certain universal amplitude ratios near the critical point. As the equation of state, we use a modification of a model first proposed by Leung and Griffiths, and further developed by Moldover, Rainwater, and co-workers. We use the two models to examine in detail CO2+n -butane and CO2+n -decane mixtures. While both models provide accurate estimates of surface tension of CO2+n -butane mixtures, only the gradient theory can predict accurately surface tension of CO2+n -decane mixtures. Moreover, while the gradient theory and the Peng–Robinson equation of state use very few adjustable parameters (at most three parameters), calculation of surface tension based on two-scale-factor universality and the corresponding equation of state requires many adjustable parameters whose number has to be increased dramatically as the fluid mixture becomes more complex. We then use the gradient theory to predict surface tension of binary liquid–vapor mixtures of CO2 and benzene, cyclohexane, and n-hexadecane. In all cases, the predictions of the gradient theory are in good agreement with the available experimental data.