Equilibrium of a liquid in a spherical shell caused by gravity, surface tension, and van der Waals forces

A rigorous proof is presented which shows that the classical Young-Laplace equation cannot predict a continuous liquid layer inside a spherical-shell container. An augmented Young-Laplace equation is in turn derived to describe the equilibrium profiles of a continuous liquid hydrogen layer inside a spherical-shell inertial fusion target. The augmentation is achieved by adding to the total free energy a term originating from the attractive intermolecular forces of the van der Waals type.