Stability of a Liquid Drop Trapped Between Two Parallel Planes

Abstract

We consider a connected drop of prescribed volume between and contacting two planes. The liquid–air interface is a free surface and the boundaries of the wetted regions in the planes are also free. The drop is shown to be rotationally symmetric. Necessary and sufficient stability criteria are derived for general contact angles, and are applied to the special case of contact angles equal to $\pi/2$. The instability of the cylinder in this special case is related to Rayleigh instability.