On the rise of an ellipsoidal bubble in water: oscillatory paths and liquid-induced velocity

This work is an experimental study of the rise of an air bubble in still wa ter. For the bubble diameter considered, path oscillations develop in the a bsence of shape oscillations and the effect of surfactants is shown to be n egligible. Both the three-dimensional motion of the bubble and the velocity induced in the liquid are investigated. After the initial acceleration sta ge, the bubble shape remains constant and similar to an oblate ellipsoid wi th its symmetry axis parallel to the bubble-centre velocity, and with const ant velocity magnitude. The bubble motion combines path oscillations with s low trajectory displacements. (These displacements, which consist of horizo ntal drift and rotation about a vertical axis, are shown to have no influen ce on the oscillations). The bubble dynamics involve two unstable modes whi ch have the same frequency and are pi /2 out of phase. The primary mode dev elops first, leading to a plane zigzag trajectory. The secondary mode then grows, causing the trajectory to progressively change into a circular helix . Liquid-velocity measurements are taken up to 150 radii behind the bubble. The nature of the liquid flow field is analysed from systematic comparison s with potential theory and direct numerical simulations. The flow is poten tial in front of the bubble and a long wake develops behind. The wake struc ture is controlled by two mechanisms: the development of a quasi-steady wak e that spreads around the non-rectilinear bubble trajectory; and the wake i nstability that generates unsteady vortices at the bubble rear. The velocit ies induced by the wake vortices are small compared to the bubble velocity and, except in the near wake, the flow is controlled by the quasi-steady wa ke.