  We derive mathematical models of the elementary process of dissolution/growth
of bubbles in a liquid under pressure control. The modeling starts with a fully
compressible version, both for the liquid and the gas phase so that the entropy
principle can be easily evaluated. This yields a full PDE system for a
compressible two-phase fluid with mass transfer of the gaseous species. Then
the passage to an incompressible solvent in the liquid phase is discussed,
where a carefully chosen equation of state for the liquid mixture pressure
allows for a limit in which the solvent density is constant. We finally provide
a simplification of the PDE system in case of a dilute solution.
