A risk of thrombogenesis is minimized in a tubular fiber membrane filter by flowing blood or other fluid through a header manifold that ensures a minimum shear rate on the wetted surfaces without flow reversal, stagnation volumes, or a shear rate that is too high. In an embodiment, fluid is conveyed into a header space and into a manifold face at a perimeter of the header space. The header space has a progressively decreasing clearance that is minimal to provide for substantial shear rate and decreasing toward a minimum clearance in a region that is remote from the perimeter and vented by openings to the microtubular membrane fibers. Other features and embodiments are described.