Bubble drag in electrolytically generated microbubble swarms with bubble-vortex interactions

Abstract

Air bubbles entrained in ocean breaking waves play various roles in air–sea gas transfer, wave energy dissipation, and surface layer mixing. While sub-mm bubbles dominate the distribution of sizes observed in bubble plumes created by breaking waves, the dynamics of such microbubbles in a swarm are poorly understood, and most previous experimental and computational studies have focused on the behavior of homogeneous swarms of larger mm-scale bubbles for industrial applications. Here, we propose novel probabilistic empirical models of rise velocity and bubble drag for a microbubble swarm incorporating bubble–vortex interactions. These are based on image measurements of the motion of electrolytically generated microbubbles. We found that convective interactions between bubbles and vortex-induced flows, that is, Rayleigh–Taylor instability caused by density difference near the electrodes, induce counter-rotating vortices that accelerate bubbles and align them along paths in the flow induced between them, resulting in an increase in rise velocity and its variance in the statistical equilibrium state. We describe the statistical features of bubble rise in such swarms in our proposed empirical model and deduce its optimal parameters. We anticipate our findings being a starting point for understanding behaviors of oceanic bubbles possessing an analogous size distribution to the present electrolytically generated microbubbles.