Simulations and measurements have established that water moves through carbon nanotubes with exceptionally high rates due to nearly frictionless interfaces1–4. These observations have stimulated interest in nanotube-based membranes for applications that range from desalination to nano-filtration and energy harvesting5–10, yet the exact water transport mechanisms inside the nanotubes and at the water-carbon interface continue to be controversially discussed11,12 because existing theories fail to provide a satisfying explanation for the limited number of experimental results available to date13. This is because even though controlled and systematic studies have explored transport through individual nanotubes8,9,14–7, none has met the considerable technical challenge of unambiguously measuring the permeability of a single nanotube11. Here we show that the pressure-driven flow rate across individual nanotubes can be determined with unprecedented sensitivity and without dyes from the hydrodynamics of water jets as they emerge from single nanotubes into a surrounding fluid. Our measurements reveal unexpectedly large and radius-dependent surface slippage in carbon nanotubes (CNT), and no slippage in boron-nitride nanotubes (BNNT) that are crystallographically similar to CNTs but differ electronically. This pronounced contrast between the two systems must originate from subtle differences in atomic-scale details of their solid-liquid interfaces, strikingly illustrating that nanofluidics is the frontier where the continuum picture of fluid mechanics confronts the atomic nature of matter.

Osmosis is a universal phenomenon occurring in a broad variety of processes and fields. It is the archetype of entropic forces, both trivial in its fundamental expression -the van 't Hoff perfect gas law -and highly subtle in its physical roots. While osmosis is intimately linked with transport across membranes, it also manifests itself as an interfacial transport phenomenon: the so-called diffusio-osmosis and -phoresis, whose consequences are presently actively explored for example for the manipulation of colloidal suspensions or the development of active colloidal swimmers. Here we give a global and unifying view of the phenomenon of osmosis and its consequences with a multi-disciplinary perspective. Pushing the fundamental understanding of osmosis allows one to propose new perspectives for different fields and we highlight a number of examples along these lines, for example introducing the concepts of osmotic diodes, active separation and far from equilibrium osmosis, raising in turn fundamental questions in the thermodynamics of separation. The applications of osmosis are also obviously considerable and span very diverse fields. Here we discuss a selection of phenomena and applications where osmosis shows great promises: osmotic phenomena in membrane science (with recent developments in separation, desalination, reverse osmosis for water purification thanks in particular to the emergence of new nanomaterials); applications in biology and health (in particular discussing the kidney filtration process); osmosis and energy harvesting (in particular, osmotic power and blue energy as well as capacitive mixing); applications in detergency and cleaning, as well as for oil recovery in porous media.to counteract the flow: the applied pressure is then equal to the osmotic pressure. solute semi-permeable membrane hydrostatic pressure drop relaxation Fig. 1 : Key manifestation of osmosis. A semi-permeable membrane allows transport of water upon a solute concentration difference (in red). The flow of water is directed from the fresh water reservoir to the concentrated reservoir.Osmosis is therefore extremely simple in its expression. Yet it is one of the most subtle physics phenomenon in its roots -it resulted in many debates over years 1,2 . Osmosis also implies subtle J o u r n a l N a me , [ y e a r ] , [ v o l . ] , 1-43 | 1 arXiv:1902.06219v2 [cond-mat.soft] 6 May 2019 2 | 1-43 J o u r n a l N a me , [ y e a r ] , [ v o l . ] , .Noting then that for small pressure drops, µ w (T, p (r) , 0)0) the molec-J o u r n a l N a me , [ y e a r ] , [ v o l . ] , 1-43 | 3where L hyd = κ hyd A /(ηL) is the solvent permeance through the 4 | 1-43 J o u r n a l N a me , [ y e a r ] , [ v o l . ] , 6 | 1-43 J o u r n a l N a me , [ y e a r ] , [ v o l . ] ,