Near-wall rising behaviour of a deformable bubble at high Reynolds number

Abstract

The dynamics of a large deformable bubble ($\mathit{Re}\sim \mathit{O}(10^{3})$) rising near a vertical wall in quiescent water is experimentally investigated. The reference (without the wall) rising path of the considered bubble is a two-dimensional zigzag. For a range of wall configurations (i.e. initial wall distance and boundary condition), using high-speed shadowgraphy, various rising behaviours such as periodic bouncing, sliding, migrating away, and non-periodic oscillation without collisions are measured and analysed. Unlike low-Reynolds- and Weber-number bubbles, the contribution of the surface deformation to the transport between the energy components becomes significant during the bubble’s rise. In particular, across the bubble–wall collision, the excess surface energy compensates the deficit of kinetic energy. This enables a large deformable bubble to maintain a relatively constant bouncing kinematics, despite the obvious wall-induced energy dissipation. The wall effect, predominantly appearing as energy loss, is found to decrease as the initial distance from the bubble centre to the wall increases. Compared to the regular (no-slip) wall, a hydrophobic surface enhances or reduces the wall effect depending on the wall distance, whereas a porous surface reduces the energy loss due to the wall, regardless of the initial distance from the wall. Furthermore, the bubble–wall collision behaviour is assessed in terms of a restitution coefficient and modified impact Stokes number (ratio of the inertia to viscous forces), which shows a good correlation, the trends of which agree well with the variations in the energy components. The dependence of near-wall bubble motion on the wall distance and boundary condition may suggest a way of predicting or controlling the near-wall gas void-fraction distribution in gas–liquid flow systems.