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 $k_L$ can be described by the classic Levich formula $k_L = (2/\sqrt {{\rm \pi} })\sqrt {\mathscr {D}_l\,U(t)/d(t)}$ , with $d(t)$ and $U(t)$ the timevarying bubble size and rise velocity, and $\mathscr {D}_l$ the 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 $k_L$ 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 nondimensional transfer rate ${Sh}=k_L L^\star /\mathscr {D}_l$ scaling asmore »
The effect of nonlinear drag on the rise velocity of bubbles in turbulence
We investigate how turbulence in liquid affects the rising speed of gas bubbles within the inertial range. Experimentally, we employ stereoscopic tracking of bubbles rising through water turbulence created by the convergence of turbulent jets and characterized with particle image velocimetry performed throughout the measurement volume. We use the spatially varying, timeaveraged mean water velocity field to consider the physically relevant bubble slip velocity relative to the mean flow. Over a range of bubble sizes within the inertial range, we find that the bubble mean rise velocity $\left \langle v_z \right \rangle$ decreases with the intensity of the turbulence as characterized by its rootmeansquare fluctuation velocity, $u'$ . Nondimensionalized by the quiescent rise velocity $v_{q}$ , the average rise speed follows $\left \langle v_z \right \rangle /v_{q}\propto 1/{\textit {Fr}}$ at high ${\textit {Fr}}$ , where ${\textit {Fr}}=u'/\sqrt {dg}$ is a Froude number comparing the intensity of the turbulence to the bubble buoyancy, with $d$ the bubble diameter and $g$ the acceleration due to gravity. We complement these results by performing numerical integration of the Maxey–Riley equation for a point bubble experiencing nonlinear drag in threedimensional, homogeneous and isotropic turbulence. These simulations reproduce the slowdown observed experimentally, and show that the more »
 Award ID(s):
 1844932
 Publication Date:
 NSFPAR ID:
 10308644
 Journal Name:
 Journal of Fluid Mechanics
 Volume:
 924
 ISSN:
 00221120
 Sponsoring Org:
 National Science Foundation
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