I haven't done furfural desorption from biochar, but I have done furfural desorption from metals. Here are some thoughts off the top of my head.
Regarding your question of furfural adsorption. I would be concerned about the adsorption selectivity of furfural (a fairly "mid sized" molecule) from bio-oil. My expectation is that it's not that good since bio-oil has so many different components. Then, you may have to deal with recovery losses from the biochar adsorbent.
The biochar also presents two other issues, namely:
1. Properties (pore size etc) may not be very consistent between biochar from different feedstocks (switchgrass etc)
2. Biochar particle attrition if it occurs during the adsorption may hinder (i.e. clog) further downstream bio-oil refining processes if not dealt with.
Edit:
As to the mechanism oh boy. I don't think anyone really knows. Here's a guess. Diffusion into pores, then furfural is likely physisorbed (VdW interactions) on carbon substrate (the biochar). I'd really really really (did I say really!) doubt chemisorption, but I could be wrong. Then, desorption should also be easy followed by diffusion back out the pore (assuming pore size and shape were large enough and right shape). Pretty standard. Check out some kinetics textbook like Fogler or read up on how molecular sieves work if you aren't familiar.