  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.
