Slug bubble growth and dissolution by solute exchange

In many environmental and industrial applications, the mass transfer of gases in liquid solvents is a fundamental process during the generation of bubbles for specific purposes or, vice versa, the removal of entrapped bubbles. We address the growth dynamics of a trapped slug bubble in a vertical glass cylinder under a water barrier. In the studied process, the ambient air atmosphere is replaced by a CO$_2$ atmosphere at the same or higher pressure. The asymmetric exchange of the gaseous solutes between the CO$_2$-rich water barrier and the air-rich bubble always results in net bubble growth. We refer to this process as solute exchange. The dominant transport of CO$_2$ across the water barrier is driven by a combination of diffusion and convective dissolution. The experimental results are compared to and explained with a simple numerical model, with which the underlying mass transport processes are quantified. Analytical solutions that accurately predict the bubble growth dynamics are subsequently derived. The effect of convective dissolution across the water layer is treated as a reduction of the effective diffusion length, in accordance with the mass transfer scaling observed in laminar or natural convection. Finally, the binary water-bubble system is extended to a ternary water-bubble-alkane system. It is found that the alkane (n-hexadecane) layer bestows a buffering (hindering) effect on bubble growth and dissolution. The resulting growth dynamics and underlying fluxes are characterised theoretically.