Natural Axisymmetric Frequencies of Cylindrical Liquid Column with Anchored Free Surface

Abstract

A liquid is placed between two concentric parallel discs in a zero-gravity environment. Its circular cylindrical free surface is held together by surface tension, which may act in the case of a disturbance as the restoring force of the oscillation. Therefore the natural axisymmetric frequencies of a cylindrical liquid column and an annular liquid layer between two discs and anchored liquid edges (stuck-edges) have been determined. It was found that with increasing aspect ratio of the liquid system the natural frequencies decrease. If the liquid column was placed between two parallel plates with no edge effects, i.e. freely slipping liquid edges, the natural frequencies exhibit much lower values. It may also be seen, that the liquid with free edges becomes unstable for aspect ratios h/a≥π, while those with anchored edges exhibits instability for h/a≥2π, a being the radius of the column