Oscillations of a liquid bridge resulting from the coalescence of two droplets
The inertial oscillations of a bridge of liquid maintained between two disks are studied under condition of negligible gravity. Both experimental and theoretical results are reported. In the experiment, the bridge is formed by the coalescence of two droplets so that its static equilibrium shape is either concave or convex depending on its length. After coalescence, the bridge performs weakly damped oscillations until it reaches its equilibrium shape. Four modes of oscillations are extracted from digital processing of images recorded by means of a high-speed camera. Their frequency and damping rate are determined and found to be independent of the initial conditions that fix the amplitudes of each mode. Concurrently, the eigen modes of oscillations of a non-cylindrical bridge have been computed by assuming inviscid flow and small amplitude oscillations. The agreement between theoretical and measured frequencies confirms that the experimental modes correspond to the eigenmodes of the linear inviscid theory. Their characteristics turn out to be significantly different from that of a cylindrical bridge. In particular, the eigenfrequencies scale as root gamma/rho R-m(3), where gamma is the surface tension, rho the liquid density, and R-m the radius at the middle of the bridge, which characterizes the shrunk/swollen character of the mean shape.