Abstract

The influence of the droplet geometry on the interfacial tension of liquid-liquid mixtures of aliphatic hydrocarbons + water is studied through the use of the square gradient theory of van der Waals in cylindrical and spherical geometries. Under a lower limit or critical radius of the droplet, the density profiles fail to converge to the equilibrium values at the bulk limit corresponding to the outside of the droplet, giving a more steep and irregular curve. To avoid this, calculations are conducted in a consistent range between a lower critical value and an upper value from which the radius dependency of the interfacial tension is negligible. Since the determination of the radius of tension is still a controversial topic, a zeroth-order approximation is used for choosing the dividing surface, corresponding to the Gibbs dividing surface. The theoretical results are qualitatively compared to the available molecular dynamics calculations of similar systems to validate the trend predicted by the model.