Abstract
We investigate the growth of gas bubbles in a water solution at rest with a supersaturation level that is generally associated with diffusive mass transfer. For $\text{CO}_{2}$ bubbles, it has been previously observed that, after some time of growing in a diffusive regime, a density-driven convective flow enhances the mass transfer rate into the bubble. This is due to the lower density of the gas-depleted liquid which surrounds the bubble. In this work, we report on experiments with different supersaturation values, measuring the time $t_{conv}$ it takes for convection to dominate over the diffusion-driven growth. We demonstrate that by considering buoyancy and drag forces on the depleted liquid around the bubble, we can satisfactorily predict the transition time. In fact, our analysis shows that this onset does not only depend on the supersaturation, but also on the absolute pressure, which we corroborate in experiments. Subsequently, we study how the depletion caused by the growth of successive single bubbles influences the onset of convection. Finally, we study the convection onset around diffusively growing nitrogen $\text{N}_{2}$ bubbles. As $\text{N}_{2}$ is much less soluble in water, the growth takes much longer. However, after waiting long enough and consistent with our theory, convection still occurs as for any gas–liquid combination, provided that the density of the solution sufficiently changes with the gas concentration.
Highlights
The physics of bubble growth in mildly supersaturated solutions is potentially relevant to several processes associated with energy production and consumption, e.g. increased production rate in oil generation (Pooladi-Darvish & Firoozabadi1999; Akin & Kovscek 2002)
CO2 bubble formation is an undesired event in carbon sequestration, where CO2 is injected at high pressures into reservoirs of saline water trapped in porous rocks at depth (Neufeld et al 2010; Tsai, Riesing & Stone 2013; Bolster 2014)
In previous experimental studies of single CO2 bubbles growing on a silicon substrate in very mildly supersaturated solutions with ζ ∼ 0.1–0.3 (Enríquez et al 2014; Moreno Soto et al 2017), significant differences were observed with respect to a purely diffusive growth
Summary
The physics of bubble growth in mildly supersaturated solutions is potentially relevant to several processes associated with energy production and consumption, e.g. increased production rate in oil generation C0 is the concentration in the bulk liquid at the initial saturation pressure P0, cs is the supersaturated concentration at the ambient pressure Ps during the experiments, ρg is the gas density and D is the diffusion coefficient of the dissolved gas in the liquid Such time evolution of the bubble radius has been confirmed in several experimental works, with supersaturations ζ = (c0 − cs)/cs comparable to that of carbonated beverages (ζ ∼ 1–3) It has been shown that buoyancy-driven convection is the cause of higher dissolution rates of sessile droplets in a less dense liquid (Dietrich et al 2016) and during droplet evaporation (Shahidzadeh-Bonn et al 2006) Both situations are physically analogous to growing bubbles and customarily treated as purely diffusion-driven phenomena Two different gases in solution (CO2 and N2) are contrasted, revealing a unique behavioural change in the mass transfer rate at the predicted time tconv due to the different gas properties
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