During the past century, significant progress has been made in expanding our atomistic understanding of systems in equilibrium. However, to understand life and much of the technology that sustains life, we need to be able to understand and control non-equilibrium processes. The past two decades have witnessed a paradigm shift away from studying equilibrium behaviour to the study of spatial and temporal organisation far from equilibrium. This development is not just driven by scientific curiosity but by the realisation that a sustainable society is one that minimises waste in the form of heat and materials. To achieve these goals, we need to understand how living organisms combine robustness with selectivity and energy efficiency and have to learn how to transpose the underlying biological design principles to processes with inanimate, nano-scale building blocks.                        

Recent developments in the design of nano-pores have demonstrated that very large gains in the separation efficiency are possible by an appropriate nano-scale functionalization of the channels through which transport takes place.  Transport through nano-pores is almost always coupled transport, i.e., it couples fluxes (e.g., electrical, material or heat transport) that would be independent in bulk materials. Consequently, externally applied thermodynamic gradients (thermal, mechanical, electrical, osmotic...) that cannot lead to bulk flow, induce a coupled charge-mass response, which is more efficient than bare hydrodynamic mass transport. Such phoretic effects stem from the forces acting within the first few nanometres from the confining surfaces. The ability to control their action opens a way to synthetic mimicry of the efficient transport in Nature leading to development of novel nanodevices with unprecedented efficiencies.                                                         

Exploiting the predominance of surfaces at the nanoscale, new fluidic functionalities can be developed for nanofluidic or angstrofluidic devices. Nanoscale water is the frontier where continuum of fluid dynamics meets atomic, and even quantum nature of matter. Due to discrete molecular effects and molecular interactions with surfaces, confined water has very different structural and dynamic properties compared to bulk water. The field of nanoscale transport has considerably developed over the last 10 years  thanks to the emergence of new experimental tools (e.g. nanotubes, van der Waals assembly) and theoretical/modelling instruments (quantum simulations boosted by machine learning, etc). A whole cabinet of curiosities has been unveiled, with frictionless flows, quantum drag effects, superionic states at mild conditions, dielectric anomalies, neuromorphic effects, where it is noted that most of these phenomena still lack a proper understanding. Therefore, atomic-level understanding of confined water structure and its link to the properties of charge and mass flow in nanoconfinement is of key importance not only for improving the knowledge of biological processes, but also for a variety of applications such as water desalination, osmotic energy, nanofluidics, voltage generation, flow sensing, and water conservation.                                  

The transition to studying nanoscale systems is not simply a matter of scaling down the approaches and methods that work for microscopic counterparts: at the nanoscale, new physics emerges due to the enhanced fluctuations, prevalence of surfaces and granularity of the matter at this scale. Therefore, the atomistic description becomes crucial to enhance the fundamental understanding of the non-equilibrium phenomena at the nanoscale. Novel simulation and experimental tools are being developed, which couple quantum-level and force-field molecular simulations to mesoscale modelling based on continuum hydrodynamics, and to experiments that can probe such nanoscale effects. Such methods can probe the crucial aspects of non-equilibrium physics in nanoconfinement:

- Fluid flow: effects of confinement on mass transport, fluid viscosity, surface friction, phoretic flows.

=Charge flow: dynamics of free/polarisation charges in confinement, effect of externally applied static and oscillating electric fields, linear and non-linear dielectric properties, ionic/polarisation currents.

=Reactivity: surface effects, chemical reactions, activation, confinement-specific bond formation/dissociation.

There is vast potential for applications exploiting these processes in nano-confined water. Exploiting the predominance of surfaces, new fluidic functionalities can be developed, such as nanofluidic transistors and diodes. However, progress in this direction strongly depends on a fundamental understanding of water and ion transport through nanoscale pores. Several discoveries over the recent years have highlighted the great potential of nanofluidics and membranes made of novel nanomaterials, such as carbon (CNT) or boron-nitride (BNT) nanotubes, graphene, or related materials. BNTs allow harvesting the energy contained in salinity gradients with an exceptional efficiency suggesting that they could be used as highly competitive membranes to harvest the chemical energy contained in the difference of salinity between sea and river water, the so-called osmotic power or ‘blue energy’. Recent experiments revealed colossal flow permeability of CNTs, which was related to molecular superlubrication of the water-carbon interface. Another new technology to fabricate atomically smooth angstrom-scale capillaries using 2D materials such as graphite, hexagonal boron nitride (h-BN), and MoS₂ has transformed the study of ‘unusual Physics’ in ultra-confinement: selective ion/molecular transport, voltage gated molecular streaming, low dielectric constant of water and fast flow of water using these capillaries. Reproducing such behaviour in bio-mimetic membranes is a great challenge and would represent a major technological progress, with applications in a broad range of domains, e.g., molecular level drug delivery, energy-efficient nanofiltration, and chemical detection. A key challenge is to understand the observed phenomena theoretically. Pioneering classical molecular dynamics (MD) simulations showed that diffusion of water in sub-nm tubes occurs through a burst-like mechanism, stemming from the presence of single-file water chains capable of moving with little resistance. Since then, atomic-level simulations have been extended to larger-size, different types of CNTs, quantum and machine-learning approaches. While there is now compelling evidence that liquid flow enhancement does indeed occur in nanoconfinement, the quantitative measure of the flow enhancement and the origin of this phenomenon is subject to lively debate. The current state of the art highlights the inherent difficulties in probing the properties of confined water and the dependence of simulation results on parameterization of classical molecular dynamics force fields, or on the details of the underlying electronic structure theory.

Experimental visualization of motion of water and particles in sub-nanometre structures and devices is highly challenging due to small amount of probed water. Experimental techniques that visualize particles and fluid flow are severely limited by light diffraction: Particles smaller than about 100 nm cannot be tracked by direct visualisation with microscopy. To indirectly determine nanoparticle volumes, one usually measures the electric polarizability, which can also provide some information on the shape of the anisotropic particles. Elastic properties can be deduced from microrheological experiments, as well as from single-molecule manipulation used to probe elastic properties of DNA molecules. Recently, fluidic nano-slits were used to trap single charged nanoscale objects and to determine their charge. Within our consortium, we have developed fluorescence-based assays for characterizing the flow in extreme confinement. While ionic currents can be measured in single sub-nanometric channels, quantifying fluid transport in confinement down to ~1 nm is out of reach with present instrumentation. This requires sensitivity down to femtoliter per second or below (L/s), which is still not achieved by state-of-the-art methods. A promising direction are novel techniques based on fluorescent calcium-sensitive dye and our previous nanojet approach for nanotubes extended to 2D channels. Similarly, the label-free detection and identification of single molecules in aqueous environments remains a challenging goal. 

The behaviour of charged particles at charged interfaces is a central yet elusive problem in the out-of-equilibrium statistical mechanics of Coulomb fluids. Despite huge progress in understanding strongly coupled charged colloidal suspensions, the dynamical behaviour of the electrical double-layers is far less understood. The question is discussed following the recent emergence of electrochemical energy storage technologies exploiting confinement of ionic liquids into nanoscopic carbon pores and carbon networks in particular supercapacitors, which store energy through charging and discharging of electrochemical double layers. From the experimental perspective, the most useful approaches have been atomic force microscopy (AFM) and surface force apparatus (SFA), which confine the electrolyte to films of 0 – 100 nm between two macroscopic curved surfaces. While much research has focused on the equilibrium structure of such highly confined electrolytes, the dynamics have not been much explored. Yet, the ion translation into and out of pores, or towards/away from electrodes, is critical for the power output of devices. The electrophoretic mobility is exploited in electroosmosis generating fluid flow near a solid surface (in nanofluidic devices^]) and in experimental techniques like phase shift electrophoresis and electro-acoustic methods. Multiscale modelling of electrophoresis is challenging due to the coexisting length- and timescales and materials heterogeneity at the nanoscale, which requires flexibility in dealing with boundary conditions. All-atom simulations provide a proper model for electrostatics and electrokinetics of electrolytes, and have determined the surface capacitance of water, which is a prerequisite for a correct treatment of the electrokinetic effect. In larger-scale problems (e.g., porous flow), the computational cost of atomistic simulations is prohibitive and coarse-grained continuum methods (Lattice Boltzmann, MPCD) are used. 

Probing the chemical reactivity of water and ions at solid surfaces is essential to complete the accurate vision of the confined fluids. Is the solid entirely inert in mild liquid conditions or does it modify its surface composition by forming different kinds of chemical bonds such as hydrogen, ionic or covalent bonds? To answer this delicate question, simulations capturing electronic level details (ab initio methodology) of interfacial interactions are required, combined with experimental spectroscopic insights into the state of water and ions at interfaces. Such computations are presently possible on dedicated supercomputers.  How this chemistry at work (including quantum friction) influences the transport of fluids, and how such electronic structure properties allow quantum engineering of hydrodynamic flows is a question of utmost importance in nanodevices.

The range of expertise and skills required to implement these approaches and tackle the exiting fundamental questions and technological challenges are rarely attainable in regular PhD programs. A well-organized training school can equip young scientists with a unique set of skills needed to work in this rapidly developing field and with the state-of-the-art knowledge and experience, which will be crucial for their future careers. We will bring together top international speakers who will cover the fundamental physics of nanoscale transport, experimental, theoretical and computational methods, and conduct in-depth discussions of the open challenges in the field.