Stability of a liquid bridge under vibration

We examine the stability of a vertical liquid bridge between two vertically vibrating, coaxial disks. Assuming that the vibration amplitude and period are much smaller than the mean distance between the disks and the global timescale, respectively, we employ the method of multiple scales to derive a set of asymptotic equations. The set is then used to examine the stability of a bridge of an almost cylindrical shape. It is shown that, if acting alone, gravity is a destabilizing influence, whereas vibration can weaken it or even eliminate altogether. Thus, counter-intuitively, vibration can stabilize an otherwise unstable capillary structure.