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

We perform direct numerical simulations of a gas bubble dissolving in a surrounding liquid. The bubble volume is reduced due to dissolution of the gas, with the numerical implementation of an immersed boundary method, coupling the gas diffusion and the Navier-Stokes equations. The methods are validated against planar and spherical geometries' analytical moving boundary problems, including the classic Epstein-Plesset problem. Considering a bubble rising in a quiescent liquid, we show that the mass transfer coefficient kL can be described by the classic Levich formula kL = (2/root pi)root Dl U(t)/d(t), with d(t) and U(t) the time-varying bubble size and rise velocity, and Dlthe gas diffusivity in the liquid. Next, we investigate the dissolution and gas transfer of a bubble in homogeneous and isotropic turbulence flow, extending Farsoiya et al. (J. Fluid Mech., vol. 920, 2021, A34). We show that with a bubble size initially within the turbulent inertial subrange, the mass transfer coefficient in turbulence kL is controlled by the smallest scales of the flow, the Kolmogorov eta and Batchelor eta B microscales, and is independent of the bubble size. This leads to the non-dimensional transfer rate Sh = kLL*/Dl scaling as Sh/Sc-1/2 proportional to Re-3/4, where Re is the macroscale Reynolds number Re = urmsL*/nu l, with urms the velocity fluctuations, L* the integral length scale, nu l the liquid viscosity, and Sc = nu l/Dl the Schmidt number. This scaling can be expressed in terms of the turbulence dissipation rate E as kL proportional to Sc-(1/2)(is an element of nu l)(1/4), in agreement with the model proposed by Lamont & Scott (AIChE J., vol. 16, issue 4, 1970, pp. 513-519) and corresponding to the high Re regime from Theofanous et al. (Intl J. Heat Mass Transfer, vol. 19, issue 6, 1976, pp. 613-624).