Negative differential flow resistance in reverse osmosis

Reverse osmosis (RO) is an efficient desalination approach, but the widely used solution-diffusion model was challenged for failing to explain field-dependent permeabilities, particularly when the continuum theory may break down in Ångström scale. Here we developed a non-equilibrium statistical theory, supported by molecular dynamics simulations that captures the field-dependent water and ion permeabilities through a single Ångström-scale channel. Surprisingly, our simulation reveals a counterintuitive negative differential flow resistance (NDFR) effect, where the flow velocity decreases with increasing pressure. This phenomenon arises from ion trapping at the nanotube entrance, caused by dielectric and dehydration barriers and hydrodynamic friction. The NDFR effect significantly reduces water permeability and may be a predominant factor constraining the selectivity-permeability trade-off in RO. Our statistical theory is based on a bidirectional escape framework that predicts the pressure- and size-dependent permeabilities and explains the NDFR effect. Our findings offer molecular-level insights into RO and can be extended to broader transport phenomena in confined systems.