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 water. For the bubble diameter considered, path oscillations develop in the absence of shape oscillations and the effect of surfactants is shown to be negligible. Both the three-dimensional motion of the bubble and the velocity induced in the liquid are investigated. After the initial acceleration stage, the bubble shape remains constant and similar to an oblate ellipsoid with its symmetry axis parallel to the bubble-centre velocity, and with constant velocity magnitude. The bubble motion combines path oscillations with slow trajectory displacements. (These displacements, which consist of horizontal drift and rotation about a vertical axis, are shown to have no influence on the oscillations). The bubble dynamics involve two unstable modes which have the same frequency and are π/2 out of phase. The primary mode develops 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 comparisons with potential theory and direct numerical simulations. The flow is potential in front of the bubble and a long wake develops behind. The wake structure is controlled by two mechanisms: the development of a quasi-steady wake that spreads around the non-rectilinear bubble trajectory; and the wake instability that generates unsteady vortices at the bubble rear. The velocities 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 wake.