Recollements and stratifying ideals

Surjective homological epimorphisms with stratifying kernel can be used to construct recollements of derived module categories. These 'stratifying' recollements are derived from recollements of module categories. Can every recollement be put in this form, up to equivalence? A negative answer will be given after providing a characterisation of recollements equivalent to stratifying ones. Moreover, criteria for a ring epimorphism to be 'stratifying' will be presented as well as constructions of such epimorphisms.