In-Line Motion of a Pair of Bubbles in a Viscous Liquid

We study the motion of a pair of bubbles rising in the vertical line, at intermediate Reynolds number (5<Re<150), both numerically and experimentally. It has been predicted, by analytical and numerical studies, that there exists a stable equilibrium distance between a pair of bubbles due to the balance between the potential repulsive and viscous atractive forces. However, no experimental results have ever confirmed the existence of an equilibrium distance between bubbles rising in a vertical line. Most experimental results indicated that a pair of bubbles collided. We solve this paradox and answer the question: "Is there an equilibrium distance?" by presenting both experimental evidence of an existence of the equilibrium distance and the detailed numerical results of a deforming-spatial-domain/space-time finite element method, taking bubble surface deformation effects into account.