You have two parts to this problem. Flow in the domain strips moisture from the rock at a rate that's determined by what is available & air conditions (temperature, speed & humidity). On the rock side you have diffusion of moisture which is a function of what's in the rock (moisture, porosity & permeability) and moisture concentration on the surface.
Modelling the whole lot isn't going to be easy, and you almost certainly won't know about the cave geology.
Fixing a moisture fraction at the wall may be easier for you to model. But that then depends on exactly what you're trying to prove.
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