Abstract
Density gradient theory describes the evolution of diffuse interfaces in both mixtures and pure substances by minimization of the total free energy, which consists of a non-convex bulk part and an interfacial part. Minimization of the bulk free energy causes phase separation while building up the interfacial free energy (proportional to the square of gradients of the species' densities) and it results in the equilibrium shape of the interface.
However, direct minimization of the free energy is numerically unstable and the coefficients in the interfacial part of the free energy are often estimated from experimental data (not determined from the underlying physics). In this paper we develop a robust physics-based numerical approach that leads to the interface density profiles for both pure substances and mixtures.
The model is free of fitting parameters and validated by available experimental data.