In embodiments of the invention, there is provided a dialyzer or filter comprising hollow fibers, in which blood flows on the exterior of the hollow fibers, and dialysate or filtrate may flow on the inside. The external surfaces of the hollow fibers may have properties of smoothness and hemocompatibility. The fiber bundle may have appropriate packing fraction and may have wavy fibers. Optimum shear rates and blood velocities are identified. Geometric features of the cartridge, such as pertaining to flow distribution of the blood, may be different for different ends of the cartridge. Air bleed and emboli traps may be provided. Lengthened service life may be achieved by combinations of these features, which may permit additional therapies and applications or better economics.