The transient buoyancy driven motion of bubbles across a two-dimensional quiescent domain

The transient buoyancy driven motion of two-dimensional bubbles across a domain bounded by two horizontal walls is studied by direct numerical simulations. The bubbles are initially released next to the lower wall and as they rise, they disperse. Eventually all the bubbles collect at the top wall. The goal of the study is to examine how a simple one-dimensional model for the averaged void fraction captures the unsteady bubble motion. By using void fraction dependent velocities, where the exact dependency is obtained from simulations of homogeneous bubbly flows, the overall dispersion of the bubbles is predicted. Significant differences remain, however. We suggest that bubble dispersion by the bubble induced liquid velocity must be included, and by using a simple model for the bubble dispersion we show improved agreement.