Effect of degassing on bubble populations in air-entraining free-surface turbulent flows

We investigate air-entraining flows where degassing, rather than fragmentation, plays a significant role. Of interest is the power-law slope beta of the bulk bubble size distribution N(a) during the air-generating period, when the total volume of bubbles is increasing. We study a canonical air-entraining flow created by strong underlying free-surface turbulence. We perform analysis using the population balance equation (PBE) and computations using direct numerical simulations (DNS) with bubble tracking. We quantify the importance of degassing by the ratio of degassing flux (QD) to entrainment flux (QI),D=QD/QI, and the ratio of degassing rate (Lambda(a)) to fragmentation rate (Omega(a)) for a bubble of radius a, Lambda(a)/Omega(a). For a broad range of large Froude numbers Fr=U/root Lg, DNS give D=O(1) (independent of Fr), showing that degassing is relevant,and Lambda(a)>>Omega(a), showing that the bubble population is degassing-dominated. In contrast to fragmentation-dominated populations, such as those due to wave breaking, where beta=-10/3, degassing-dominated populations have qualitatively different N(a)during air entrainment. Analysis using the PBE shows that degassing-dominated beta is a function of Lambda(a), which has a turbulence-driven regime (a<a Lambda) and a buoyancy-driven regime(a>a(Lambda)). Here, a Lambda is the bubble radius where terminal buoyant rise velocity equals u(rms). Consequently, N(a)exhibits a split power with beta (a< a(Lambda))=-4.<(3)over bar> and beta(a>a Lambda)=-5.8 (3) over bar for moderate bubble Reynolds numbers Re-b. For large Re-b, beta(a>a(Lambda))=-4.8 (3) over bar .TheDNS strongly confirm these findings for moderate Reb. By identifying and describing degassing-dominated bubble populations, this work contributes to the understanding and interpretation of broad types of air-entraining problems where degassing plays a relevant role.