The field of nanofluidics has shown considerable progress over the past decade thanks to key instrumental advances, leading to the discovery of a number of exotic transport phenomena for fluids and ions under extreme confinement. Recently, van der Waals assembly of 2D materials 1 allowed fabrication of artificial channels with ångström-scale precision 2 . This ultimate confinement to the true molecular scale revealed unforeseen behaviour for both mass 2 and ionic 3 transport. In this work, we explore pressure-driven streaming in such molecular-size slits and report a new electro-hydrodynamic effect under coupled pressure and electric force. It takes the form of a transistor-like response of the pressure induced ionic streaming: an applied bias of a fraction of a volt results in an enhancement of the streaming mobility by up to 20 times. The gating effect is observed with both graphite and boron nitride channels but exhibits marked materialdependent features. Our observations are rationalized by a theoretical framework for the flow dynamics, including the frictional interaction of water, ions and the confining surfaces as a key ingredient. The material dependence of the voltage modulation can be traced back to a contrasting molecular friction on graphene and boron nitride. The highly nonlinear transport under molecular-scale confinement offers new routes to actively control molecular and ion transport and design elementary building blocks for artificial ionic machinery, such as ion pumps. Furthermore, it provides a versatile platform to explore electro-mechanical couplings potentially at play in recently discovered mechanosensitive ionic channels 4 .

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.

Ion transporters in Nature exhibit a wealth of complex transport properties such as voltage gating, activation, and mechanosensitive behavior. When combined, such processes result in advanced ionic machines achieving active ion transport, high selectivity, or signal processing. On the artificial side, there has been much recent progress in the design and study of transport in ionic channels, but mimicking the advanced functionalities of ion transporters remains as yet out of reach. A prerequisite is the development of ionic responses sensitive to external stimuli. In the present work, we report a counterintuitive and highly nonlinear coupling between electric and pressure-driven transport in a conical nanopore, manifesting as a strong pressure dependence of the ionic conductance. This result is at odds with standard linear response theory and is akin to a mechanical transistor functionality. We fully rationalize this behavior on the basis of the coupled electrohydrodynamics in the conical pore by extending the Poisson-Nernst-Planck-Stokes framework. The model is shown to capture the subtle mechanical balance occurring within an extended spatially charged zone in the nanopore. The pronounced sensitivity to mechanical forcing offers leads in tuning ion transport by mechanical stimuli. The results presented here provide a promising avenue for the design of tailored membrane functionalities.

Despite essentially identical crystallography and equilibrium structuring of water, nanoscopic channels composed of hexagonal boron nitride and graphite exhibit an order-ofmagnitude difference in fluid slip. We investigate this difference using molecular dynamics simulations, demonstrating that its origin is in the distinct chemistries of the two materials. In particular, the presence of polar bonds in hexagonal boron nitride, absent in graphite, leads to Coulombic interactions between the polar water molecules and the wall. We demonstrate that this interaction is manifested in a large typical lateral force experienced by a layer of oriented hydrogen atoms in the vicinity of the wall, leading to the enhanced friction in hexagonal boron nitride. The fluid adhesion to the wall is dominated by dispersive forces in both materials, leading to similar wettabilities. Our results rationalize recent observations that the difference in frictional characteristics of graphite and hexagonal boron nitride cannot be explained on the basis of the minor differences in their wettabilities.

Liftoff is the hydraulically forced detachment of buoyant freshwater from the channel bottom or seabed that occurs as river water discharges into the coastal ocean. It is a key feature of strongly stratified systems, occurring well upstream in the channel or seaward of the river mouth under sufficiently strong forcing. We present a two-layer hydraulic solution for the river–ocean interface that considers the river, estuary and near-field river plume as a single interlinked system, extending previous work that considered them separately. This unified approach provides a prediction of the liftoff location and free-surface profile for a wide range of forcing conditions, which are characterized in terms of the freshwater Froude number $F_{f}\equiv Q/b_{0}\sqrt{g_{0}^{\prime }h_{0}^{3}}$. Here, $Q$ is the river discharge, $b_{0}$ is the channel width, $g_{0}^{\prime }\equiv (\unicode[STIX]{x0394}\unicode[STIX]{x1D70C}_{0}/\unicode[STIX]{x1D70C}_{2})g$ is the reduced gravitational acceleration, $\unicode[STIX]{x0394}\unicode[STIX]{x1D70C}_{0}$ is the density contrast between fresh and ocean water and $h_{0}$ is the total water depth at the river mouth. The solution is validated with laboratory experiments using an experimental apparatus consisting of a long, sloping river channel that discharges into a deep, wide saltwater basin. The experiments simulate the full range of hydraulic behaviours predicted by the model, from saltwater intrusion to offshore liftoff. For $F_{f}<1$, liftoff occurs in the estuary channel and our results show that the relationship between intrusion length and $F_{f}$ depends on the channel slope. For $F_{f}>1$, corresponding to flood conditions in many natural systems, liftoff is forced outside the river mouth and the hydraulic coupling between the channel and shelf becomes more important. For these conditions and for intermediate to steeply sloped shelves, the offshore liftoff distance varies linearly with $F_{f}-1$, a particularly simple scaling given the nonlinearity and relative complexity of the governing equations. The model and experimental results support a conceptual description of the river–ocean interface that relates the liftoff location, free-surface elevation and the spreading rate of the buoyant river plume.

The water surface expression of liftoff and its dependence on discharge are examined using numerical simulations with the Regional Ocean Modeling System (ROMS). Liftoff is the process by which buoyant river water separates from the bed and flows over denser saltwater. During low‐discharge conditions liftoff occurs in the river and is accompanied by a change in the surface slope. During high‐discharge conditions liftoff occurs outside the mouth and generates a ridge on the water surface. The location and height of the ridge can be described by analytical equations in terms of discharge, shelf slope, and river mouth aspect ratio. The offshore distance and height of the ridge are proportional to the river discharge and vary inversely with river mouth aspect ratio. For steep shelf slopes liftoff occurs close to the river mouth and generates a large ridge. The ridge is modified, but not eliminated, by the presence of tides. The water surface slope change at the ridge peak is large enough to be detected by the upcoming Surface Water and Ocean Topography (SWOT) altimeter and can be used to identify the liftoff location during high discharge. However, during low discharge the water surface slope change at the liftoff location is too small to be detected by SWOT. These results indicate that remote measurements of the presence or absence of the ridge may be useful to distinguish between low and high flows, and remote measurements of the ridge location or height could be used to estimate freshwater discharge.

The authors develop a two-layer hydraulic model to determine the saline intrusion length in sloped and converging salt wedge estuaries. They find that the nondimensional intrusion length = CiL/hS depends significantly on the channel bottom slope and the rate and magnitude of landward width convergence, in addition to the freshwater Froude number. In the definition of , Ci is a quadratic interfacial drag coefficient, L is the salt wedge intrusion length, and hS is the depth at the mouth of the estuary. Bottom slope is found to limit the saline intrusion length, and this limitation accounts for the deviation of the observed exponent n in a scaling relationship with the river discharge of the form L ~ Q−n from the canonical value of 2 to 2.5 predicted by the theory of Schijf and Schönfeld for a flat, prismatic estuary. The authors find that estuary convergence is important only when the ratio of the slope-limited intrusion length to the convergence length is greater than one, and that the effects of convergence are less significant than those of slope limitation. They compare this model to field and validated numerical data and find that the solution predicts the intrusion length with good accuracy, improving on the flat, prismatic solution by orders of magnitude. While this model has good predictive capability, it is sensitive to Ci and the location of the hydraulic control point, both difficult to determine a priori.

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