It very much depends on the media that the adsorbent needs to operate in. ( whether it is going to be gas or liquid). In case of wastewater treatment, for example, there are good natural adsorbents but given their weak mechanical properties, they can not stand the physiochemical stress of the media. having the weak structure they swell, breakdown or rotten due to mechanical or pH stress. in addition, the adsorbent has to have proper physical robustness for handling/transport. in case of the adsorbent for oil, for example, the definition of stability might be different. a natural wool based oil adsorbent is soft, fluffy which can float on the water but not necessarily mechanically strong as such.