Influence of the Outer Bath on the Eigenfrequencies of Rotating Axisymmetric Liquid Bridges

In experiments with liquid bridges, the neutral buoyancy technique has frequently been used to simulate microgravity conditions. In this technique the liquid bridge is surrounded by an outer liquid with similar density to compensate partially for the effect of the hydrostatic pressure over the interface. The outer bath is expected to play a relevant role not only in the static problem, but also in the dynamical behaviour of this fluid configuration. In the present contribution the eigenfrequencies characterizing the oscillation modes of a rotating axisymmetric liquid bridge are calculated. The analysis focuses on the influence of the outer bath and the liquid bridge equilibrium shape on those quantities. The results are obtained numerically by solving the inviscid two-dimensional model by means of a finite difference scheme. The method provides accurate results as is shown by comparison with the analytical solution for the cylindrical configuration. The comparison between the theoretical predictions for the first eigenfrequency and the experimental data obtained by Perales and Meseguer (1992) shows the capability of the model to describe the dynamics of real liquid bridges.