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).

Automated summary

This study performs direct numerical simulations to investigate the dissolution of a gas bubble in a surrounding liquid. The methods used are validated against analytical moving boundary problems and show good agreement. The results suggest that the mass transfer coefficient kL can be described by the classic Levich formula and that in turbulent flow, the coefficient is controlled by the smallest scales of the flow and is independent of the bubble size.