Transport of liquid mixtures through porous membranes is central to processes such as desalination, chemical separations and energy harvesting, with ultrathin membranes made from novel 2D nanomaterials showing exceptional promise. Here we derive, for the first time, general equations for the solution and solute fluxes through a circular pore in an ultrathin planar membrane induced by a solute concentration gradient. We show that the equations accurately capture the fluid fluxes measured in finite-element numerical simulations for weak solute-membrane interactions. We also derive scaling laws for these fluxes as a function of the pore size and the strength and range of solute-membrane interactions. These scaling relationships differ markedly from those for concentration-gradient-driven flow through a long cylindrical pore or for flow induced by a pressure gradient or electric field through a pore in an ultrathin membrane. These results have broad implications for transport of liquid mixtures through membranes with a thickness on the order of the characteristic pore size.

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 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.

Despite extensive investigations of dissipation and deformation processes in micro- and nano-sized metallic samples1,2,3,4,5,6,7, the mechanisms at play during the deformation of systems with ultimate (molecular) size remain unknown. Although metallic nanojunctions, which are obtained by stretching metallic wires down to the atomic level, are typically used to explore atomic-scale contacts5,8,9,10,11, it has not been possible until now to determine the full equilibrium and non-equilibrium rheological flow properties of matter at such scales. Here, by using an atomic-force microscope equipped with a quartz tuning fork, we combine electrical and rheological measurements on ångström-size gold junctions to study the non-linear rheology of this model atomic system. By subjecting the junction to increasing subnanometric deformations we observe a transition from a purely elastic regime to a plastic one, and eventually to a viscous-like fluidized regime, similar to the rheology of soft yielding materials12,13,14, although orders of magnitude different in length scale. The fluidized state furthermore exhibits capillary attraction, as expected for liquid capillary bridges. This shear fluidization cannot be captured by classical models of friction between atomic planes15,16 and points to an unexpected dissipative behaviour of defect-free metallic junctions at ultimate scales. Atomic rheology is therefore a powerful tool that can be used to probe the structural reorganization of atomic contacts.

Recent advances in nanofluidics have allowed the exploration of ion transport down to molecular-scale confinement, yet artificial porins are still far from reaching the advanced functionalities of biological ion machinery. Achieving single ion transport that is tunable by an external gate—the ionic analogue of electronic Coulomb blockade—would open new avenues in this quest. However, an understanding of ionic Coulomb blockade beyond the electronic analogy is still lacking. Here, we show that the many-body dynamics of ions in a charged nanochannel result in quantized and strongly nonlinear ionic transport, in full agreement with molecular simulations. We find that ionic Coulomb blockade occurs when, upon sufficient confinement, oppositely charged ions form ‘Bjerrum pairs’, and the conduction proceeds through a mechanism reminiscent of Onsager’s Wien effect. Our findings open the way to novel nanofluidic functionalities, such as an ion pump based on ionic Coulomb blockade, inspired by its electronic counterpart.

Over the past decade, the ability to reduce the dimensions of fluidic devices to the nanometre scale (by using nanotubes1–5 or nanopores6–11, for example) has led to the discovery of unexpected water- and ion-transport phenomena12–14. More recently, van der Waals assembly of two-dimensional materials¹⁵ has allowed the creation of artificial channels with ångström-scale precision¹⁶. Such channels push fluid confinement to the molecular scale, wherein the limits of continuum transport equations¹⁷ are challenged. Water films on this scale can rearrange into one or two layers with strongly suppressed dielectric permittivity18,19 or form a room-temperature ice phase²⁰. Ionic motion in such confined channels²¹ is affected by direct interactions between the channel walls and the hydration shells of the ions, and water transport becomes strongly dependent on the channel wall material²². We explore how water and ionic transport are coupled in such confinement. Here we report measurements of ionic fluid transport through molecular-sized slit-like channels. The transport, driven by pressure and by an applied electric field, reveals a transistor-like electrohydrodynamic effect. An applied bias of a fraction of a volt increases the measured pressure-driven ionic transport (characterized by streaming mobilities) by up to 20 times. This gating effect is observed in both graphite and hexagonal boron nitride channels but exhibits marked material-dependent differences. We use a modified continuum framework accounting for the material-dependent frictional interaction of water molecules, ions and the confining surfaces to explain the differences observed between channels made of graphene and hexagonal boron nitride. This highly nonlinear gating of fluid transport under molecular-scale confinement may offer new routes to control molecular and ion transport, and to explore electromechanical couplings that may have a role in recently discovered mechanosensitive ionic channels²³.

Traditionally, ion selectivity in nanopores and nanoporous membranes is understood to be a consequence of Debye overlap, in which the Debye screening length is comparable to the nanopore radius somewhere along the length of the nanopore(s). This criterion sets a significant limitation on the size of ion-selective nanopores, as the Debye length is on the order of 1–10 nm for typical ionic concentrations. However, the analytical results we present here demonstrate that surface conductance generates a dynamical selectivity in ion transport, and this selectivity is controlled by so-called Dukhin, rather than Debye, overlap. The Dukhin length, defined as the ratio of surface to bulk conductance, reaches values of hundreds of nanometers for typical surface charge densities and ionic concentrations, suggesting the possibility of designing large-nanopore (10–100 nm), high-conductance membranes exhibiting significant ion selectivity. Such membranes would have potentially dramatic implications for the efficiency of osmotic energy conversion and separation techniques. Furthermore, we demonstrate that this mechanism of dynamic selectivity leads ultimately to the rectification of ionic current, rationalizing previous studies, showing that Debye overlap is not a necessary condition for the occurrence of rectifying behavior in nanopores.

Ionic current measurements through solid-state nanopores consistently show a power spectral density that scales as 1/f α at low frequency f, with an exponent α ∼ 0.5–1.5, but strikingly, the physical origin of this behavior remains elusive. Here, we perform simulations of particles reversibly adsorbing at the surface of a nanopore and show that the fluctuations in the number of adsorbed particles exhibit low-frequency pink noise. We furthermore propose theoretical modeling for the time-dependent adsorption of particles on the nanopore surface for various geometries, which predicts a frequency spectrum in very good agreement with the simulation results. Altogether, our results highlight that the low-frequency noise takes its origin in the reversible adsorption of ions at the pore surface combined with the long-lasting excursions of the ions in the reservoirs. The scaling regime of the power spectrum extends down to a cutoff frequency which is far smaller than simple diffusion estimates. Using realistic values for the pore dimensions and the adsorption–desorption kinetics, this predicts the observation of pink noise for frequencies down to the hertz for a typical solid-state nanopore, in good agreement with experiments.

Most spindle-shaped cells (including smooth muscles and sarcomas) organize in vivo into well-aligned ‘nematic’ domains1, 2, 3, creating intrinsic topological defects that may be used to probe the behaviour of these active nematic systems. Active non-cellular nematics have been shown to be dominated by activity, yielding complex chaotic flows4, 5. However, the regime in which live spindle-shaped cells operate, and the importance of cell–substrate friction in particular, remains largely unexplored. Using in vitro experiments, we show that these active cellular nematics operate in a regime in which activity is effectively damped by friction, and that the interaction between defects is controlled by the system’s elastic nematic energy. Due to the activity of the cells, these defects behave as self-propelled particles and pairwise annihilate until all displacements freeze as cell crowding increases6, 7. When confined in mesoscopic circular domains, the system evolves towards two identical +1/2 disclinations facing each other. The most likely reduced positions of these defects are independent of the size of the disk, the cells’ activity or even the cell type, but are well described by equilibrium liquid crystal theory. These cell-based systems thus operate in a regime more stable than other active nematics, which may be necessary for their biological function.

Cytoskeletal filaments assemble into dense parallel, antiparallel, or disordered networks, providing a complex environment for active cargo transport and positioning by molecular motors. The interplay between the network architecture and intrinsic motor properties clearly affects transport properties but remains poorly understood. Here, by using surface micropatterns of actin polymerization, we investigate stochastic transport properties of colloidal beads in antiparallel networks of overlapping actin filaments. We found that 200-nm beads coated with myosin Va motors displayed directed movements toward positions where the net polarity of the actin network vanished, accumulating there. The bead distribution was dictated by the spatial profiles of local bead velocity and diffusion coefficient, indicating that a diffusion-drift process was at work. Remarkably, beads coated with heavy-mero-myosin II motors showed a similar behavior. However, although velocity gradients were steeper with myosin II, the much larger bead diffusion observed with this motor resulted in less precise positioning. Our observations are well described by a 3-state model, in which active beads locally sense the net polarity of the network by frequently detaching from and reattaching to the filaments. A stochastic sequence of processive runs and diffusive searches results in a biased random walk. The precision of bead positioning is set by the gradient of net actin polarity in the network and by the run length of the cargo in an attached state. Our results unveiled physical rules for cargo transport and positioning in networks of mixed polarity.

Frequency analysis of sound by the cochlea relies on sharp frequency tuning of mechanosensory hair cells along a tonotopic axis. To clarify the underlying biophysical mechanism, we have investigated the micromechanical properties of the hair cell’s mechanoreceptive hair bundle in the rat cochlea. We studied both inner and outer hair cells, which send nervous signals to the brain and amplify cochlear vibrations, respectively. We find that tonotopy is associated with gradients of stiffness and resting mechanical tension, with steeper gradients for outer hair cells, emphasizing the division of labor between the two hair-cell types. We demonstrate that tension in the tip links that convey force to the mechano-electrical transduction channels increases at reduced Ca2+. Finally, we reveal tonotopic gradients in stiffness and tension at the level of a single tip link. We conclude that mechanical gradients of the tip-link complex may help specify the characteristic frequency of the hair cell.

SIGNIFICANCE STATEMENT The tip-link complex of the hair cell is mechanically tuned along the tonotopic axis of the cochlea.