The transient behaviour of a large bubble in a vertical tube

Abstract

Novel experimental results are presented of the transient motion of a large spherical-cap bubble and of the displaced liquid motion in a closed cylindrical vertical tube of finite length. This is a fundamental fluid mechanics problem and has direct application to Space flight where liquids in fuel tanks are exposed to large changes in acceleration. The initial spherical cap shape is produced by a thin membrane which can be considered equivalent to a large surface tension. The bubble is released by puncturing the membrane which, subsequently, retracts in a time of order 1 ms. Apart from the generation of shear instabilities of very short wavelength, the membrane withdrawal has a negligible effect on the bubble and liquid motions and can thus be considered instantaneous. The displacements of the bubble, the annular liquid sheet and the geyser front were determined from high-speed video images from which velocities and accelerations were calculated. The results are compared with a theoretical model of the unsteady bubble and sheet velocities.