OK, I think you want the wet particles that are used in the combustion models. They're designed so you can boil/evaporate off the volatiles to leave a char which is then burnt. In your case you want to lose the volatile but retain the solid.
For the wall contact, there isn't a model to then build up a mass of material. However, the accretion model will give you an idea of what hits where.
But.....
If you explain what phenomena you're trying to model (pictures are good) there may be alternatives. I need to be a little careful about my answers there as I'm not permitted to give "engineering advice" need to limit answers to public domain information but you may want to be looking at a slightly different modelling approach.
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