Spreading Equilibria Under Mildly Singular Potentials: Pancakes Versus Droplets

We study global minimizers of a functional modeling the free energy thin liquid layers over solid substrate under combined effect surface, gravitational, and intermolecular potentials. When latter ones have mild repulsive singularity at short ranges, are compactly supported display microscopic contact angle $\pi/2$. Depending on form potential, macroscopic shape can either be droplet-like or pancake-like, with transition profile between two zero spreading coefficient. These results generalize, complete, give mathematical rigor to de Gennes' formal discussion equilibria. Uniqueness non-uniqueness phenomena also discussed.