ABSTRACT: Thermodynamic analysis of droplets and their interfaces grants insight into coalescence phenomena. Using classical Density Functional Theory (DFT), a native thermodynamic approach presents itself to problems including, but not limited to, nucleation, coalescence and structure analysis of fluids. DFT is a powerful tool for analysis of interfacial phenomena and prediction of interfacial properties. Helmholtz energy functionals of the PC-SAFT equation of state  are used, allowing for the calculation of single droplets without usage of interfacial-specific parameters.
Relaxation of the equilibrium assumption yields Dynamic Density Functional Theory (DDFT), which is suitable for the prediction of dynamic density distributions of vapor-liquid systems .
This contribution presents predictions from one- & two-dimensional DDFT in Cartesian coordinates applied to droplet coalescence, utilizing a Discontinuous Galerkin Spectral Elements Method adjusted for integral equations. This enables application of efficient methods for solving the balance equations from DDFT in one or more dimensions and can be used for the analysis of interface phenomena during droplet coalescence.
 Joachim Gross: A density functional theory for vapor-liquid interfaces using the PCP-SAFT equation of state, J. Chem. Phys. 131 (2009), 204705
 Andrew J. Archer: Dynamical density functional theory for molecular and colloidal fluids: A microscopic approach to fluid mechanics, J. Chem. Phys. 130 (2009), 014509