Again assumptions. There are plenty of assumptions, but then is better to know what kind of assumptions we are making.
We assume that the dry air is of single species, and then we will use the Henry's law for equilibrium of this dissolved air.
Then we assume thermal equilibrium between phases, which means that the three phases are at the same temperature. They are in equilibrium.
Then the vapour concentration is again in equilibrium with the liquid phase.
And we will use the psychometric law to express its concentration.
The state variables are: solid displacement, liquid pressure, gas pressure and temperature.
The balance of momentum as a whole is reduced to the equation of stress equilibrium together with a mechanical constitutive model to relate stresses with strains.