Bubble-mediated transfer of dilute gas in turbulence

Bubble-mediated gas exchange in turbulent flow is critical in bubble column chemical reactors as well as for ocean-atmosphere gas exchange related to air entrained by breaking waves. Understanding the transfer rate from a single bubble in turbulence at large Peclet numbers (defined as the ratio between the rate of advection and diffusion of gas) is important as it can be used for improving models on a larger scale. We characterize the mass transfer of dilute gases from a single bubble in a homogeneous isotropic turbulent flow in the limit of negligible bubble volume variations. We show that the mass transfer occurs within a thin diffusive boundary layer at the bubble-liquid interface, whose thickness decreases with an increase in turbulent Peclet number, (Pe) over tilde. We propose a suitable time scale theta for Higbie (Trans. AIChE, vol. 31, 1935, pp. 365-389) penetration theory, theta = d(0)/(u) over tilde, based on d(0) the bubble diameter and (u) over tilde a characteristic turbulent velocity, here (u) over tilde = root 3 u(rms), where u(rms) is the large-scale turbulence fluctuations. This leads to a non-dimensional transfer rate Sh = 2(3)(1/4) root(Pe) over tilde/pi from the bubble in the isotropic turbulent flow. The theoretical prediction is verified by direct numerical simulations of mass transfer of dilute gas from a bubble in homogeneous and isotropic turbulence, and very good agreement is observed as long as the thin boundary layer is properly resolved.