Wake-induced relative motion of bubbles rising in line

The motion of nearly spherical air bubbles rising in a column in stagnant water is measured at Reynolds numbers ranging from Re-D = 0.2 to 35. The relative velocity is found to be dependent on the distance between bubbles and on their diameter. For the larger bubbles, the relative velocities increased with decreasing distance, reaching maximum values just prior to contact. For the smaller bubbles, the relative velocity decreased prior to coalescence. For the entire range of Reynolds numbers considered, the wake-induced relative motion results in collisions between bubbles. These collisions culminate in coalescence at the present levels of water purity and surface tension. In order to understand the basic features of the measured relative motion, a simple model is developed. It is based on the known flow field and viscous-wake structure around a single bubble, and examines how other bubbles move within this field. Oseen flow for Re much less than 1 and potential flow with a thin wake for Re much greater than 1 are assumed. The approximations involved limit the validity of the model to distances larger than a few bubble diameters. The general agreement between the predictions and experimental results suggest that the model contains the most relevant mechanisms that govern the interaction, within its range of validity. Prior analyses for non-deformable bubbles that predicted an equilibrium distance due to balance between pressure gradients and wake-induced motion, are contradicted by the observed coalescence. A possible cause for the discrepancy is bubble deformation.