On the stability of planar fluid interfaces under van der Waals surface forces

This paper concerns an analysis of the stability of infinite planar interfaces between two immiscible fluids. The interface is subjected to a two-dimensional stress arising from the van der Waals interaction with a solid, infinite plate of finite thickness, positioned edge-on to the interface. The physical problem models the setup of a Wilhelmy plate experiment just prior to plate immersion through a fluid interface and three-phase contact line formation. The van der Waals surface force is attractive, causing the fluid interface to deform. We investigate the stability of the fluid interface and establish an analytical condition which is sufficient to ensure a stable interface as well as a condition for which the interface will not be stable to arbitrary disturbances. Both conditions focus on a sole, key function of the equilibrium profile, the latter a solution of the Euler-Lagrange equation for the system