Nuclear pore complexes (NPCs) regulate all cargo traffic across the nuclear envelope. The transport conduit of NPCs is highly enriched in disordered phenylalanine/glycine-rich nucleoporins (FG-Nups), which form a permeability barrier of still elusive and highly debated molecular structure. Here we present a microfluidic device that triggered liquid-to-liquid phase separation of FG-Nups, which yielded droplets that showed typical properties of a liquid state. On the microfluidic chip, droplets were perfused with different transport-competent or -incompetent cargo complexes, and then the permeability barrier properties of the droplets were optically interrogated. We show that the liquid state mimics permeability barrier properties of the physiological nuclear transport pathway in intact NPCs in cells: that is, inert cargoes ranging from small proteins to large capsids were excluded from liquid FG-Nup droplets, but functional import complexes underwent facilitated import into droplets. Collectively, these data provide an experimental model of how NPCs can facilitate fast passage of cargoes across an order of magnitude in cargo size.