Advective diffusion of air bubbles in turbulent water flows
Air bubble entrainment is defined as the exchange of air between the atmosphere and flowing water. Also called self-aeration, the continuous exchange between air and water is most important for the biological and chemical equilibrium on our planet. Air bubble entrainment is observed in chemical, coastal, hydraulic, mechanical and nuclear engineering applications as well as in the natural environment such as waterfalls, mountain streams and river rapids, and breaking waves on the ocean surface. The resulting “white waters” provide some spectacular effects. The entrainment of air bubbles may be localised at a flow discontinuity or continuous along an air-water free-surface: i.e., singular and interfacial aeration respectively. At a flow singularity, the air bubbles are entrained locally at the impinging perimeter and advected in a region of high turbulent shear stresses. The interfacial aeration is the air bubble entrainment process along an air-water interface which is parallel to the flow direction. The onset of air bubble entrainment may be expressed in terms of the tangential Reynolds stress and the fluid properties. Once self-aeration takes place, the distributions of void fraction may be modelled by some analytical solutions of the advective diffusion equation for air bubbles. The microscopic structure of turbulent bubbly flows is complex and a number of examples are discussed. The results reveal the turbulent nature of the complex two-phase flows and the complicated interactions between entrained air bubbles and turbulence.