Dependence of the Equation of State in Surface Tension Prediction by the Theory of Capillarity

Abstract

The theory of capillarity was originally developed by J. D. van der Waals to provide a means of predicting interfacial (surface) tension data using saturation pressure and liquid-vapor density data. This theory was recently extended to the Redlich-Kwong, Soave-Redlich-Kwong, and Peng-Robinson fluid models. The latter two equations of state are more advanced than the Redlich-Kwong model in that they use an acentric factor to predict saturated vapor pressure values more in agreement with experimental data. However, the agreement in the predicted interfacial tension values is worse for the latter two models compared to the Redlich-Kwong model. This study features a sensitivity analysis to show that the predicted interfacial tension values are more sensitive to vapor density than liquid density and vapor pressure, and that increasing the vapor density reduces the corresponding predicted interfacial tension value. Furthermore, all three fluid models tend to overpredict interfacial tension when experimental data are applied in their predictive equations. This study finds that the reason why the simpler Redlich-Kwong model predicts better interfacial tension values than the two advanced models is because the former overpredicts vapor density moreso than the two advanced cubic fluid models, and this in turn reduces the prediction of interfacial tension to make its value more comparable to experimental data.