Stability of Liquid Bridges Between Coaxial Equidimensional Disks to Axisymmetric Finite Perturbations: A Review

Abstract

This paper reviews the dynamics of breaking or oscillating axisymmetric liquid bridges, and estimates of the energy which is needed to break a liquid bridge. We consider a liquid bridge spanning two coaxial equal disks with sharp edges and held by surface-tension forces. The liquid volume is assumed to be conserved under perturbations, and the contact lines are pinned to the disk edges. The perturbations are finite and axisymmetric. An analysis is based on the one-dimensional models previously used in capillary jet theory and last several decades for study a liquid bridge dynamics. According to the scientific project JEREMI (Japanese and European Research Experiment on Marangoni Instabilities), the first stage of the space experiment on ISS will involve an isothermal liquid bridge with a gas blowing parallel to the axial direction of the bridge. The geometry corresponds to a cylindrical volume liquid bridge coaxially placed into an outer cylinder with solid walls. The gas enters the annular duct bounded by the outer cylinder and the internal system consisting of supporting vertical rods and the liquid bridge. Considering that the bridge is small (the rod’s radii are 3 mm) and the gas velocity is typically (0.25 ÷ 0.37) m/s, the perturbations cannot be considered small. Thus, one may assume that the amplitude of the liquid bridge perturbations is sufficiently large that departures from linearity must be considered.