Apparatus for removing substances from blood is disclosed. The apparatus includes concentric cylinders defining an annulus therebetween with the inner cylinder adapted for rotation with respect to the outer cylinder. At least one of the cylinders includes a porous membrane covered portion forming a compartment containing an immobilized active species. The active species is adapted to break down or remove the substance. Plasma in blood flowing in the annulus passes through the porous membrane and interacts with the active species either by reaction or binding. Red and white blood cells do not pass through the membrane. In this way, a substance is removed from plasma without exposing blood cells to the active species.