Direct numerical simulations of bubble-mediated gas transfer and dissolution in the quiescent and turbulent flow

Mass transfer of gases at the ocean-atmosphere interface is significantly enhanced by air entrainment by breaking waves. The bubbles formed are subjected to highly turbulent flow are critical to the mass transfer of gases as the molecular diffusivity of atmospheric gases is very low (Sc ≈ 600). We develop a numerical method for gas transfer in two-phase flows, including volume change effects. We investigate the bubble rising in quiescent flow and suspended in homogeneous and isotropic turbulent (HIT) flow. We show the dissolution of a single component bubble rising in quiescent flow can be described by the classic Levich formula (Levich, 1962). We show that for the bubble suspended in homogeneous and isotropic turbulent (HIT) flow, the mass transfer coefficient k_L is governed by the smallest scales in the flow, the Kolmogorov η and Batchelor η_B microscales, and is independent from the bubble size. We present a model for mass transfer coefficient as a function of Reynolds and Schmidt numbers and is verified in the range of 50 < Pe < 5 x 10⁴.