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Thermodynamically consistent modeling for dissolution/growth of bubbles in an incompressible solvent

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.