to appear in Chem. Soc. Rev. (2009) Nanofluidics, from bulk to interfaces Lyd´ericBocquet∗ and Elisabeth Charlaix Laboratoire de Physique de la Mati`ere Condens´eeet des Nanostructures; Universit´eLyon 1 and CNRS, UMR 5586, 43 Bvd. du 11 Nov. 1918, 69622 Villeurbanne Cedex, France (Dated: October 22, 2018) Nanofluidics has emerged recently in the footsteps of microfluidics, following the quest of scale reduction inherent to nanotechnologies. By definition, nanofluidics explores transport phenomena of fluids at the nanometer scales. Why is the nanometer scale specific ? What fluid properties are probed at nanometric scales ? In other words, why 'nanofluidics’ deserves its own brand name ? In this critical review, we will explore the vast manifold of length scales emerging for the fluid behavior at the nanoscales, as well as the associated mechanisms and corresponding applications. We will in particular explore the interplay between bulk and interface phenomena. The limit of validity of the continuum approaches will be discussed, as well as the numerous surface induced effects occuring at these scales, from hydrodynamic slippage to the various electro-kinetic phenomena originating from the couplings between hydrodynamics and electrostatics. An enlightening analogy between ion transport in nanochannels and transport in doped semi-conductors will be discussed. I. NANOFLUIDICS, SURROUNDING THE There is indeed a lot of room for improvements at these FRAME smallest scales: the example of aquaporins (AQP) is in- teresting in this context. Aquaporins channels are a key component of many biological processes [10] and play the Nanofluidics, the study of fluidic transport at nanome- role of water filters across biological membranes. These ter scales, has emerged quite recently in the footsteps of channels fullfill the conflicting tasks of being both ex- microfluidics. Pushing further the limits of fluidic down- tremely permeable to water, while extremely selective for sizing is an attracting stream, in the spirit of scale re- other species [8]. To give an order of magnitude, the per- duction inherent to all micro- and nano- technologies. meability of the water channel is typically 3 orders of Various reasons may be seen as to motivate these novel magnitude larger than what would be expected on the developments. First, from the point of view of biotech- basis of the classical fluid framework for the same pore nological (\lab on a chip") applications, decreasing the size [11, 12]. A potential answer is that AQP, although scales considerably increases the sensitivity of analytic a filter for water, is mainly hydrophobic, i.e. water re- techniques, with the ultimate goal of isolating and study- pellent ! Of course some hydrophilic polar nodes are dis- ing individual macromolecules [1, 2]. But also, from the tributed along the pore, so as to keep water in the mainly point of view of fluidic operations, nanometric scales al- hydrophobic environment. Quoting the terms of Sui et low to develop new fluidic functionalities, taking explicit al. in Ref. [8], \the availability of water-binding sites at benefit of the predominance of surfaces. Typical exam- these nodes reduces the energy barrier to water transport ples involve preconcentration phenomena [3], the devel- across this predominantly hydrophobic pathway, while the opment of nanofluidic transistors [4, 5] or the recently relatively low number of such sites keeps the degree of proposed nano-fluidic diodes [6, 7]. But the analogy to solute-pore interaction to a minimum. In balancing these micro-electronics is somewhat limited: fluid molecules opposing factors the aquaporins are able to transport wa- are not electrons and the notion of large scale integration ter selectively while optimizing permeability." Beyond for fluidic devices, i.e. nanofluidics as a way of increasing this elementary picture, understanding how AQP fullfills the density of fluidic operations on a chip even further, its challenging properties would definitely be a source of is probably not a pertinent goal to reach for fluidic oper- inspiration and open new perspectives for technological ations. breakthrough in filtration, desalination, power conver- arXiv:0909.0628v1 [cond-mat.soft] 3 Sep 2009 But from a different perspective, nanofluidics also car- sion, ... However reproducing such a delicate composite ries the hope that new properties will emerge by taking (patched) architecture in bio-mimetic membranes is a benefit of the specific phenomena occurring at the small- great challenge, which requires breakthrough in the con- est scales: new solutions may be obtained from the scales ception of its elementary constituents. But it points out where the behavior of matter departs from the common that surfaces and their chemical engineering are a key expectations. The great efficiency of biological nanopores actor to optimize fluid properties at nano-scale. (in terms of permeability or selectivity) is definitely a However, in its roots, nanofluidics is not a new field: as great motivation to foster research in this direction [8, 9]. judiciously recalled by Eijkel and van den Berg in their pioneering review on the subject [1], many 'old' fields of physics, chemistry and biology already involves the be- havior of fluids at the nanoscale. Like Monsieur Jourdain ∗Electronic address: [email protected] in \Le bourgeois gentilhomme" by Moli`ere,one has done 2 ’nanofluidics’ for more than forty years without know- new questions, open new directions and attract people in ing it [151]. One may cite for example the domains of this fascinating domain. electro-kinetics (electro-osmosis or -phoresis, ...) with applications in chemistry and soil science, membrane sci- ence (ultra-filtration, reverse osmosis, fuel cells, ...), col- II. LIMITS OF VALIDITY OF CONTINUUM loid chemistry, and of course physiology and the study of DESCRIPTIONS AND NANOFLUIDIC LENGTH biological channels [1]. An interesting question is accord- SCALES ingly wether { on the basis of the novel ’nanofluidic’ point of view { one may go beyond the traditional knowledge The introduction of the terminology “nanofluidics” in those 'old' fields and obtain unforeseen results, e.g. al- (furthermore to define a specific scientific field) suggests lowing for better optimization of existing technologies ? that something special should occur for the transport of a Our belief is that the answer to this question is already fluid when it is confined in a channel of nanometric size. positive and this is one of the key aspects that we shall This leads to an immediate question: why should the discuss in this review. nanometer length scale have anything specific for fluidic Finally it is also important to note that nanofluidics transport ? Nanofluidics \probe" the properties of fluids has emerged recently as a scientific field (i.e. naming a at the nanoscale: so, what does one probe specifically in field as ”nanofluidics”) also because of the considerable the nanometer range ? progress made over the last two decades in developping Actually one may separate two different origins for nano-fabrication technologies, now allowing to fabricate finite-size effects associated with nanometer scales: bulk specifically designed nanofluidic devices, as well as the and surface finite-size effects. The former, bulk effects great development of new instruments and tools which are intimately associated with the question of validity give the possibility to investigate fluid behavior at the of the classical continuum framework, in particular the nanometer scale. One may cite for example: new electri- Navier-Stokes equations of hydrodynamics: when do such cal detection techniques, Surface Force Apparatus (SFA), descriptions breakdown ? Can one then expect 'exotic' Atomic Force Microscopy (AFM), nano-Particle Image fluid effects associated with the molecular nature of the Velocimetry (nano-PIV) coupling PIV to TIRF set-up fluid ? On the other hand, surface effects play an in- (Total Internal Reflection Fluorescence), as well as the creasingly important role as the \surface to volume ra- considerable progress made in computational techniques, tio" increases (i.e. as the confinement increases). We like Molecular Dynamics simulations. It is now possible already pointed out the importance of such effects on the to control/design what is occuring at these scales, and example of AQP water channels. As we show below, the observe/measure its effects. This is the novelty of the surface effects occur at much larger scales than the 'bulk' field, and the reason why nanofluidics now deserves its deviations from continuum expectations. own terminology. The discussion on the length scales at play, to be ex- The paper is organized as follows: In the second sec- plored in this section, is summarized in Fig. 1. tion we will replace nanofluidics in the perspective of the various length scales at play in fluid dynamics. We shall in particular discuss the limits of validity of continuum (e.g. hydrodynamic) descriptions. In the third section we discuss the dynamics of fluid at interfaces and the nanofluidic tools which have been developped recently to investigate it. In the fourth section we will explore var- ious transport phenomena occuring in diffuse layers. In the fifth section we raise the question of thermal noise in nanofluidic transport. Finally we will conclude by explor- ing some general consideration and expectations about nanofluidics, especially in terms of energy conversion and desalination. As a final remark, this review, like any review, is our FIG. 1: Various length scales at play in nanofluidics. subjective and personal view of the field of nanofluidics and the perspectives one may foresee. We organized our exploration around the length scales underlying fluid dy- namics at the nanometric scales and how nanofluidics A. Validity of bulk hydrodynamics allows to probe the corresponding mechanisms. Accord- ingly, our aim is not to explore exhaustively the { al- We first start with a short discussion on the validity of ready large { litterature of the domain, but merely to bulk hydrodynamics. In practice, this raises the question: disentangle the various effects and length scales under- when do the Navier-Stokes (NS) equations break down ? lying the behavior of fluids at the nanometer scales.