Three-dimensional density functional study of heterogeneous nucleation of droplets on solid surfaces

We present a three-dimensional density functional approach to investigate heterogeneous nucleation behaviors of Lennard-Jones fluid on solid walls. In the theoretical calculation, fast Fourier transforms to compute the convolutions of Euler-Lagrange equation enables a high-efficient algorithm in three-dimensional space. The density distributions of a growing nucleus are presented to account for the nucleation process. Accordingly, the structures of nucleated droplet and surrounding supersaturated vapor on different walls are analyzed, and the corresponding free energy barriers and the critical radii are obtained to evaluate the difficulty of droplet formation. Since the theoretical approach is strictly constructed in three-dimensional space, and the liquid-solid, vapor-solid, and vapor-liquid interfacial tensions as well as the vapor-liquid-solid line tension are entirely integrated into the excess free energy expression, the present approach provides a flexible and efficient tool for studying heterogeneous nucleation.