Stabilization of axisymmetric liquid bridges through vibration-induced pressure fields

Previous theoretical studies have indicated that liquid bridges close to the Plateau-Rayleigh instability limit can be stabilized when the upper supporting disk vibrates at a very high frequency and with a very small amplitude. The major effect of the vibration-induced pressure field is to straighten the liquid bridge free surface to compensate for the deformation caused by gravity. As a consequence, the apparent Bond number decreases and the maximum liquid bridge length increases. In this paper, we show experimentally that this procedure can be used to stabilize millimeter liquid bridges in air under normal gravity conditions. The breakup of vibrated liquid bridges is examined experimentally and compared with that produced in absence of vibration. In addition, we analyze numerically the dynamics of axisymmetric liquid bridges far from the Plateau-Rayleigh instability limit by solving the Navier-Stokes equations. We calculate the eigenfrequencies characterizing the linear oscillation modes of vibrated liquid bridges, and determine their stability limits. The breakup process of a vibrated liquid bridge at that stability limit is simulated too. We find qualitative agreement between the numerical predictions for both the stability limits and the breakup process and their experimental counterparts. Finally, we show the applicability of our technique to control the amount of liquid transferred between two solid surfaces.