Free-surface air entrainment into bubbles by a Rushton-type impeller in unbaffled stirred tank

While the bubbles generated through the free-surface air entrainment in an unbaffled stirred tank affect the dynamics of fluid mixing and gas exchange, their detailed mechanism and characteristics have not been investigated so far. In this study, we focus on analyzing the spatial distribution and the Sauter mean diameter of entrained bubbles by a Rushton-type impeller inside the tank, using high-speed shadowgraphy while varying the impeller rotation speed and geometrical parameters. It was mainly found that the air entrainment mechanism and evolution of entrained bubbles depend on the flow structure, which was identified by particle image velocimetry. Following the change from double- to single-loop vortical structures as the distance between the free-surface and impeller decreases, the role of free-surface instability becomes dominant in bubble entrainment. The impeller rotation speed also has a greater impact on the Sauter mean diameter of entrained bubbles compared to the double-loop regime. Based on the above, we classified the regimes and drew scaling relations for the Sauter mean diameter of entrained bubbles in terms of the geometrical and flow parameters, including the Weber number. Furthermore, it is shown that the turbulent kinetic energy is the primary contributor to the fragmentation of entrained bubbles inside the tank, following the theory of classical Kolmogorov-Hinze framework.