Quantifying bubble degassing in entraining free-surface turbulence

Understanding the volume and size distribution of bubbles due to air entrainment by strong free-surface turbulence is important to a variety of natural and engineering applications. In these free-surface flows, the balance between the creation of bubbles by entrainment and subsequent degassing is critical to the volume, as well as the size distribution, of bubbles. Previous work on strong free-surface turbulence has been limited to measuring the net effect of entrainment and degassing. In this work, we utilize Eulerian label advection bubble tracking (Gaylo et al., J. Compt. Phys., vol. 470, 2022) to separately measure entrainment and degassing. We study the period of active entrainment in direct numerical simulations of the canonical strong free-surface turbulence driven by an underlying shear flow. We find that the volume flux of bubbles due to degassing is similar in magnitude to the volume flux due to entrainment, showing that degassing plays an important role in determining the bubble population during active entrainment. Studying the size-distribution of degassing bubbles, we highlight the importance of the bubble Froude number, Fr_b, characterizing the relationship between bubble buoyancy and the surrounding turbulence. For small Fr_b (large bubbles), we observe that the degassing rate scales roughly with bubble radius squared, consistent with the terminal velocity of a creeping bubble in quiescent flow. For large Fr_b (small bubbles), we show that the effects of turbulence lead to a weaker dependence of degassing rate on bubble radius.