A biological or chemical reactor (2) has an inner vessel (4) disposed within an outer vessel (6) and an annular space (16) defined therebetween in which fluid is to be contained. The fluid comprises reactants of a biological or chemical reaction. A reaction support (10a) is disposed in an opening in a wall of one of the vessels and is designed to support a structure such as a scaffold that receives fluid under pressure from the annular space. The reactor generates hydrodynamic pressure and shear stress in the fluid within the annular space, upon relative rotational movement between the vessels so as to drive the fluid through intersticies in the scaffold.