Sharpening the cut: physical origins of rejection-curve broadening and routes to precision ultrafiltration.

Sectors that require precise separation between solutes of comparable size often rely on ultrafiltration (UF) and loose nanofiltration (LNF) for a low-cost, scalable, selective separation. However, solute separations in this regime have stubbornly exhibited broad rejection curves where solutes with dimensions substantially smaller than the nominal pore size are rejected. The widened profile of these curves results from three distinct mechanisms. Pore-size heterogeneity convolves the single-pore response with a broad size distribution, and because Hagen-Poiseuille flow scales as the fourth power of radius, the largest pores dominate the permeate and disproportionately leak oversized solutes. Confined (hindered) transport leads to intrapore hydrodynamics, slowing a solute relative to the background solvent velocity and effectively rejecting solutes that would intuitively pass through based on size exclusion alone. Finally, the pore array presents only a limited open area to an approaching solute; under single-pass operation, a solute that does not encounter a pore mouth is recorded as rejected regardless of its size. Despite these challenges in achieving sharp separations, no fundamental phenomena preclude much narrower rejection curves in principle. Advancing toward an ideal "step function" rejection profile requires a systematic dissection of each broadening mechanism and a scaffolded approach where geometric, intrapore, and process architecture might collectively enable unprecedented precision in practical size-selective separations.