Xiaoyu Hu,Diannan Lu*

State Key Laboratory of Chemical Engineering,Key Lab of Industrial Biocatalysis,Ministry of Education,China Department of Chemical Engineering,Tsinghua University,Beijing 100084,China

Keywords:Nanofluidics Nanostructured channel Molecular simulation Chemical separation engineering

A B S T R A C T With the development of manufacturing technology on the nanoscale,the precision of nano-devices is rapidly increasing with lower cost. Different from macroscale or microscale fluids, many specific phenomena and advantages are observed in nanofluidics.Devices and process involving and utilizing these phenomena play an important role in many fields in chemical engineering including separation,chemical analysis and transmission.In this article,we summarize the state-of-the-art progress in theoretical studies and manufacturing technologies on nanofluidics.Then we discuss practical applications of nanofluidics in many chemical engineering fields,especially in separation and encountering problems.Finally,we are looking forward to the future of nanofluidics and believe it will be more important in the separation process and the modern chemical industry.

1.Introduction

In recent twenty years,the development in nanofluidics field is brought into focus. With the maturity of manufacture of nanodevices,theories on this field have been verified and developed and become more general and precise.Generally,nanofluidics is defined as studying the flow pass or through a structure,which has at least one dimension between 1 and 100 nm.Ions,particles and fluids show specific phenomena and properties in the nanoscale, receiving a lot of attentions and general interests[1].On this scale,many specific phenomena and properties have an important influence on fluids in or near nanostructures,like the overlap of double electric layers,high specific surface areas,surface charges and entropy effects.This is because the length scale of these forces is close to the scale of the characteristic size of nano-devices.

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New research tools, like atomic force microscopy (AFM) and scanning tunneling microscopy(STM),provide powerful techniques on probing and fabricating nanostructures.Etching methods,like electron beam(e-beam),X-ray,ion beam and soft etching and bottom-toup assemblies, represent the micro-manufacture technology; all these new methods are of fundamental importance for research and applications of nanofluidics [2]. In recent years, review articles on nanofluidics are published gradually [2-7], focusing on the whole nanofluidics field[2],manufacture technologies[1,4,5]and electrokinetic problems in nanofluidics[6,7].

Because of the generality and importance of nanofluidics phenomena,many classical and emerging disciplines are involved in this field,as shown in Fig. 1. For example, in biology, the foundation layer of creatures,a cell works under a system of nanofluidics.Creatures under natural selection have been using nanofluidics to evolve,which deserve more careful research[2].Like the Brownian motion,creatures have found a way to harness nanofluidics [2], not only on the molecule scale,but also on larger scales[2].

We find better motivation in other variants, such as a Norwegian version of the tale, Lord Peter. In this tale, the cat is an enchanted Princess. She helps the son and then asks him to cut off her head. When he finally agrees to do so, he breaks the enchantment and marries her. Another famous cat story with an enchanted princess is The White Cat, a French tale, by Madame la Comtesse d Aulnoy.Return to place in story.

This review begins with theories on the nanofluidics to explain specific phenomena and reasons underneath.Then we focus on manufacture and applications of nano-devices,especially on the separation process.Finally,we discuss about unresolved issues and give our perspective on nanofluidics in the future.

2.Theoretical Studies

2.1.Main forces on the nanoscale

On the nanoscale, many forces exert influences, including forces from walls on particles or solvent molecules or other walls and forces between particles and solvent molecules.All these forces determine the behavior of molecules or particles inside nanostructures,and they lead to equilibrium phenomena(like distribution of ions)and dynamics phenomena(like viscosity on the macroscale).Forces are classified into different types as shown in Fig.2.It should be emphasized here that the classification of these forces is only for the convenience of our research.As we know,these forces are actually electric interactions,which have a variety of forms for practical utilization in research and applications.Because the characteristic lengths of electrostatic force,van der Waals and hydrophobic interaction are 1-100 nm,2 nm and 10 nm,respectively, these forces are significantly interfered by the system size under nanoscale.

With the increase of the specific surface area,the conductivity of the wall(i.e.the conductivity of the electrical double layer)becomes more important. When two electrical double layers overlap as shown in Fig. 3, the streaming potential decreases and the conductivity of the aperture increases.Besides,ions with the same charge as the wall are expelled from the channels,and those with the opposite charge gather inside the channels.The Donnan equilibrium is established between the solution inside the nanochannels and reservoirs connected to them.In the kidney,the basement membranes prevent the serum protein with the negative charge from flowing into primary urine[23].The result of the research shows that in addition to the size effect,the electrical repulsion from the basement membranes with the negative charge is of great importance.These semipermeable membranes play an important role in many separation processes,for example, in the desalination field.

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2.2.Specific phenomena

As the result of the effect of the size and these forces,specific phenomena happen on the nanoscale,which also provide the foundation for its potential applications. In nature, many functions in cells are accomplished by these specific phenomena.

Because of the system size,the discrete nature of fluid molecules is evident,but it is still possible to calculate the properties of the system by continuum and mean-field theory if the specific size is larger than 10 nm,with different behavior limited to the few layers of molecules closest to the wall[15].The transport phenomena rely on three factors including the external forces like hydraulic pressure, electric field or concentration gradient,various colloidal forces and friction between the wall and fluid[16].

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First, the effect of the wall is quite important in the nanofluidics as the result of the large specific surface area.Experiments conducted on capillaries made with atomic-scale precision show that the gas and water flux inside these capillaries are much larger compared with traditional channels [17]. For example, negative pressure has been observed in the experiments as the result of capillary effect in twophase flows inside a nanochannel [14]. Well-known slip effect can happen on the atomic-scale flat surface[18]and a rough hydrophobic surface [19,20]. The liquid-solid contact angle is influenced by the material and roughness of the wall. On the nanoscale, a near 180°contact angle can be achieved on the wall with slight hydrophobicity if it is a rough surface[19].In the nonequilibrium state,even a rough hydrophilic surface can exert strong hydrophobic interactions [21].For drops with small contact angles, this effect can give it superhydrophobicity or ‘lotus effect’, which is found in natural lotuses to clean themselves[22].

In last century,researchers built the whole system of forces on the nanoscale gradually. In the 1940s, Derjaguin, Verwey, Landau and Overbeek proposed the DLVO theory,which considered two main forces on the nanoscale,i.e.the electrostatic force and the van der Waals force[8].The scope of the electrostatic force is in the double electrical layer(usually 1-100 nm),and the attraction or repulsion of the force depends on the species of the electrolytes.The scope of the van der Waals force is in 2 nm and the force is always attractive.In 1999,Lyklema et al.developed the DLVO theory in dynamics and related it with electrokinetic phenomena[9].In 1954,Derjaguin designed a surface force apparatus(SFA),which is able to measure the electrostatic force and the van der Waals force directly[9,10].The utilization of SFA plays an import role in the research of forces on the nanoscale.Nowadays,the atomic force microscope(AFM)becomes an excellent method to measure the surface forces gradually,and can study opaque materials,but it is less sensitive than SFA[11].

Fig.2.Typical forces involved in the nanofluidics.(a)Electrostatic force,(b)van der Waals force,(c)Hydrophobic interaction.

Corresponding steric effect is brought into the nanofluidics as the result of the scale effect.Steric exclusion effect makes some molecules with specific configuration hard to pass the nanochannels, which is quite useful for separation especially in biological and pharmaceutical industries. In nature, the aquaporin and potassium channels exhibit their selectivity by combination of steric effect and electrostatic interactions[24].

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In the meantime the willow tree near the drawbridge had grown upinto a splendid tree, and stood there, free, and was never clipped. It is our genealogical tree, said the old people to theirchildren, and therefore it must be honoured.

Because of the simplicity of the PB equations,the ignorance of the excluded volume effect and interactions between ions make it unreliable

Fig. 3. Overlap of electrical double layers (EDLs) in the nanochannel. Ψ(z) is the distribution of the electrical potential along the z direction.The solid line represents the overlap phenomena. The dashed line represents the EDL potentials without the presence of the opposite wall.

2.3.Theoretical model

As a flow,nanofluidics displays specific fluid dynamics.The fundamental objective of the theory is to describe the velocity distribution of the flow passing through or by a nano-structure. In nanofluidics,the pervasiveness of the surface charge influences the distribution of ion concentration significantly.The distribution of solute concentration is important for the separation and energy conversion processes.Therefore, it is quite important to provide a precise profile of the solute molecules to predict the efficiency of the energy conversion and the selectivity of the separation process. Normally, the method we use here is MD simulation and continuum models. For example,Reshadi and Saidi study the effect of the ion partitioning from the inclusion of EDL overlap and steric effects on electrokinetic transport by the modified Poisson-Boltzmann (MBP) equation [25]. Amani and Movahed also developed a hybrid continuum-atomic approach to describe the behavior inside the nanochannels for predicting electrokinetics in complicated geometries and provide more details[26].All these two types of theoretical models are divided into two parts,the main equations describe the behavior of the flow and the boundary conditions describe the effect of the wall.

The critical boundary between the continuous and discrete flows is Kn= 1, where the characteristic size of the device is about 3 nm.For liquid,the λ reflects the interaction of liquid molecules with each other,and ten molecule lengths are chosen as a rule of thumb.Based on results from molecular simulations and experiments for Newtonian fluids,the Navier-Stokes equation is still fair if the characteristic size is larger than 10 nm. On this condition, the typical version of the Navier-Stokes equation for incompressible flow with external field is where the terms from left to right are for variation,convection,diffusion and conservative field, respectively. The common external field in the nanofluidics is the hydraulic field(pressure)and the electric field(electrical potential),which is also called electro-osmosis.

To achieve a more precise boundary between continuity and discreteness,a dimensionless number is introduced,the famous Knudsen number Kn. For gas, the Knudsen number is defined as the ratio of molecule free path λ to the feature size of the device L,

First,we discuss on the models that describe the velocity profile of the flow. Traditionally, the conservation of mass, which is universal under our consideration,and Newton's laws of motion are combined to the famous Navier-Stokes equations,which are widely used on the macroscale and the microscale to obtain the velocity distribution.The foundation of the Navier-Stokes equations is the continuity of the flow, which means that inside a relatively infinitesimal point there are plenty of liquid molecules. This assumption is not applicable to the nanofluidics.Liquid water at room temperature,for example,has about 30 molecules in 1 nm[3].The discreteness of nanofluidics exists in the nanofluidics and its influence cannot be ignored and reflected by the traditional Navier-Stokes equations[28].However,we should emphasize that the difference of the continuous model and the discrete one is at the several outermost layers of molecules for the liquid flow[27]. If the time consumption of the computers is not a considerable restraint,the most precise and elaborate model is the molecular simulation, which considers the van der Waals forces and the electrostatic interactions and is first developed by pioneering work from Alder and Wainwright et al.[29].

When the characteristic size of the device is less than 10 nm,the effect of interactions and discreteness of individual molecules should be considered seriously.We can achieve this by discretizing important parameters in continuous models,like giving every layer of molecules its own viscosity,which should be a predefined distribution.If the surface absorption and slip effect are dismissed and the surface is perfectly plain, Zhang et al. use the nonlocal linear hydrodynamic constitute model to evaluate the effect of viscosity and discreteness[30].The results show that for the nanochannels with width less than 5 molecule length,the variation of the viscosity dominates the flow,especially for the Poiseuille flow.Besides,experiments with SFA suggest the variation of the surface force between two mica and KCl solution,which means the existence of the discrete water layer[30-32].Although continuous models are not able to provide precise results all the time, they are applicable to estimate the magnitude of different physical processes with different types of nanofluidics.

In addition to the forces in the static state,the difference of the shear force between the nanoscale and the macroscale is verified by phenomena discovered by experiments,for example,lubrication of polyelectrolytes and hydrated ions[12].It is observed that when the liquid flows through the walls on the nanoscale,the resistance is much lower than that on the macroscale.Therefore the traditional boundary condition that assumes that the velocity of the flow at the wall is zero is not applicable to nanofluidics,and slip length is introduced by some theories[13,14].Compared with these forces,forces which are traditionally important on the macroscale like the gravity and the inertia force,are much less important on the nanoscale.

Because of the nanoconfinement effect,the density distribution on the nanoscale is different from that on the macroscale. The pioneer work was conducted by Somers and Davis [33] and they found that the fluid atoms are ordered symmetrically in layers.After that,Monte Carlo[34]and MD simulations[35,36]are also widely used for analyzing the density profiles. Giannakopoulos et al. [37] developed a quasicontinuum multi-scale theory to predict density profiles inside the nanochannel,which requires MD result as the fluid parameters in the theoretical equations.

As for the boundary condition,the difference between the nanoscale and the microscale or the macroscale is quite large and has a significant effect on the behavior of the nanofluidics,which is usually generated as the result of the surface properties.The famous one is the slip effect[14,38]as shown in Fig.4,which means the velocity of the layer of molecules close to the surface is not zero,or v(0)=0 is not applicable to nanofluidics with some surfaces.Huang et al.analyze two concepts of the friction coefficient and provide an enlightening way to analyze flow resistance of nano-confined fluids from nano-lubrication in their review[39].This phenomenon is usually the result of the hydrophobicity and roughness of the surface [14,40,43], which has been verified by many experiments, and can improve the electro-osmosis greatly[41,42].For the hydrophobic surface,the increase of the roughness can improve this effect significantly, because the roughness causes gas trap as studied by Cottin-Bizonne et al. [41]. This effect is important for nanofluidics because it can reduce the pressure on the flow significantly.The functional devices with carbon nanotubes and nanochannels which utilize this effect are reviewed by Whitby and Quirke[40].The slip length is a parameter describing the effect of slip by assuming the velocity at the slip length is zero, i.e. v(-b) = 0, where b is the slip length, and the Navier-Stokes equation is applied from -b. For example, for the flow inside two infinite parallel plates, the average velocity is

Fig.4.Three boundary conditions on slip effect.(a)No slip,(b)slip length b is larger than zero but not infinite,(c)slip length is infinite.

where dp/dx is the hydraulic field,η is the viscosity and h is the width of the nanochannel.The effect of surface properties on the slip length can be studied by non-equilibrium MD simulation(NEMD).The wettability,tube flexibility,pore size and its distribution have a significant influence on the water flux.For flexible CNTs,the enhancement of water flux is about 20%larger than the corresponding rigid one[44].Zhao et al.[45]used NEMD with cDFT to study the effect wettability of surfaces on the flux of LJ benzene quantitatively.Moreover,the roughness of the surface has an effect on the diffusion mechanism of water as reported by Cao et al.[46].

But if he could overcome and kill these two giants he should have his only daughter for a wife, and half his kingdom into the bargain; he might have a hundred horsemen, too, to back him up

Another important aspect is the distribution of charged particles inside the nanostructures with charged surface. This phenomenon is studied thoroughly on the microscale from the simple Helmholtz model to the common Poisson-Boltzmann equation. Two typical models are compared as shown in Fig.5.For microfluidics,by combining the traditional Poisson equation,which relates the charge density to the electric potential,and the Boltzmann distribution based on the electric energy,we get this equation

where ciis the concentration of ion i,ziis the charge number of ion i,and Ψ is the electric potential.For low electric potential(i.e.assuming zieΨ ?kT),the characteristic length of the EDL is defined as the Debye length λD,which is the length where the electric potential decreases to exp(-1)

When the overlap of the EDL is ignorable(λD?h/8),the result of differential equations[4]for two infinite parallel plates can be treated as the sum of potential generated by each individual plate.It is called the Gouy-Chapman equation [7]. When the EDLs highly overlap, by linearize Eq.(4),the analytical result can be achieved for the surface with a lower charge density,which is the famous Debye-Hückel equation[7].

You will be a long time in getting to it, if ever you get to it at all; but you shall have the loan of my horse,51 and then you can ride on it to an old woman who is a neighbor of mine: perhaps she can tell you about him

There was great joy and gladness between them all that night, but the next day, when the wedding was to take place, the Prince said, I must see what my bride can do

Fig.5.Comparison of two typical charge density distribution model of the electrical double layer.a)Schematic of two models,b)charge density distribution of two models.

on the description of ion distribution when the specific size of the channel is comparable to that of the ion. The non-monotonic profile and charge inversion phenomena happening in the multivalent ions cannot be deduced from these equations[47-49],but these phenomena are observed in the fabricated devices today[50,51]and important for output and efficiency of the power generation and the separation process[52].Based on the ideas similar to DFT in the quantum field,classical density functional theory (cDFT) assumes that the grand potential of an inhomogeneous fluid can be described by a functional of a onebody density profile ρ(r)minimized to achieve the result of ρ(r)profile[53-55]. Based on these ideas, cDFT has been applied to describe the property of the charge distribution for aqueous ionic systems[56]and ionic liquid[57]in the nanofluidics.The ion density provided by cDFT is

where ρiband μiexare the bulk density and the excess chemical potential of the ion species i,respectively,Δμiexis the deviation of the local excess chemical potential from the bulk, and Viexis the confining potential due to the slit wall.If the ion is described as a hard sphere of radius Ri,Viexin a slit nanochannel of height h is

The deviation of the local excess chemical potential Δμiexis the cDFT theoretical detail to reflect the influence of interactions between ions and walls within the coarse-grained model.The electrostatic correlations are described by a quadratic expansion of the excess Helmholtz energy with respect to the bulk [58], and excluded volume effects are described by the modified fundamental measure theory(MFMT)[59]. The theory and calculation detail can be found in our previous work[60].

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where CDand CIare the capacitance of the diffuse layer and the inner layer.By setting p=0 or 1,we can recover the constant potential or the constant charge boundary conditions.

For the separation process,the key trade-off is between permeability and selectivity.Generally,the increase of the permeability will result in the decrease of the selectivity and vice versa.For gas separation with the membrane, the well-known trend was studied by Robeson with an empirical upper bound for different gas pairs,which represents the most favorable combinations of polymer membranes and described by:where αA/Bis the selectivity,PAis the permeability,and βA/Band λA/Bare the empirical parameters for different A/B gas pairs[67,68].Based on this empirical upper bound relation,the influence of temperature[69]and solubility[70]on the ability of the membrane separation has been studied thoroughly.

3.Manufacture of Nano-devices

The primary artificial nano-devices have been made up in membrane science for separation.Although these nano-devices are workable in the lab,they are not applicable to examine the theory on nanofluidics and hard to replicate in the industry.With the development in the manufacture technology in recent two years,more precise and replicable nano-devices are available. For example,Esfandiar et al. successfully fabricated angstrom-scale nanoslits by effectively removing a single atomic plane from bulk crystal[71].This angstrom-scale nanoslit can help the verification of theoretical models.Nowadays,the fabrication of devices with many individual precise nanostructures is one of the hot and promising topics in nanotechnology.Here,we focused on manufacture of two main nanostructures,which are widely used in separation processes,i.e.,the nanochannel and the nanopanel.

Because of reactions on the surface or the physical electric field,the surface itself can be charged.There are three types of boundary conditions for charged surface,constant electric potential models,constant electric density models and models based on the surface reaction[58].For example, if the surface is made of glass (Si, SiOH), the charge of the surface is influenced by pH as the result of protonation and deprotonation from chemical reactions,which can be described by the sitebinding model and the site-dissociation model [61]. As the result of these reactions,anomalous pH-dependent nanofluidic salinity gradient power(NSGP)can be harvested with ion-selective nanopores[62].The reactions between ions and walls modify the surface charge and diffuse layer potential,and the results depend on solution composition[63,64].This phenomenon is called charge regulation,as it regulates the electrical property of the wall[65,88].In order to qualify this effect,a parameter p is defined as[66]

Toward the end of the year Tony was killed in some argument over gambling8, and Tony s widow9 left Harry in complete charge of the magazine stand. And when she got married again some time later, Harry bought the stand from her. He borrowed money and installed10 a soda11 fountain and pretty soon he had a very nice little business.，。。，。，，。

The nanochannel can be divided into two categories for its degree of freedom,one dimension and two dimensions.The nanochannel with one dimension is usually easier to fabricate using traditional methods like lithography and wet chemical etching.These methods have been discussed thoroughly[5,72].Three major nanofabrications are nanolithography, MEMS based nanofabrication [73] and methods using various nanomaterials like ion selective polymer[74,75],nanoparticle crystal[76],nanowire[77]and nanotube[78].For nano-lithography,electron beam lithography(EBL)fabricates nanochannels by emitting a beam of electrons on a surface covered with a thin film [79,80].Focused ion beam (FIB) is another nano-lithography technique that uses a focused beam of ions instead of electrons to implement swelling,milling or etching to fabricate one dimension nano-devices [81,82].In recent years, nanoimprint lithography (NIL) as another popular nano-lithography technique is widely used to fabricate 1-D and 2-D nano-devices by mechanically pressing molds into an imprint resist[83,84].

But for nanochannels with two dimensions,more advanced technologies like the electron beaming lithography and the focused ion beam etching are recently developed.In the electron beaming lithography(EBL),an electron beam is used to etch the required pattern on the surface covered by one thin electron-sensitive resistant layer.The focused ion beam etching usually uses gallium ion to build the nanochannels on the substrate by projecting ions through raster with specially made pattern[85].Many other manufacture technologies are developing to decrease the cost and increase the output capacity, like the stacked graphene oxide and the nanoimprint lithography(NIL),which makes an expensive master mask to produce more nanochannels swiftly and inexpensively by mechanical pressing. These methods can also be used to make other nano-apertures. For example, the focused ion beam etching can make nano-apertures on a thin membrane by using the gallium ion beam to make an aperture with tens of nanometers.Moreover, the atomic layer deposition can be used to decrease the diameter of the aperture. As a result, an aperture with the diameter less than 6 nm can be achieved[86].This type of manufacture is still being developed. For example, the aperture with the diameter less than 4 nm is produced by helium ion beam, and even the aperture with 1-2 nm diameter can be made if the energy of the beam is low[87].Electron beam lithography can make apertures with several diameters after the aperture made by high-energy electron beam.The ion track etching on a thin membrane is another method to make nanoapertures but lose the inside detail of the aperture.Many technologies are being developed to make nano-apertures, too. For example,traditional lithography and wet chemical etching are still used.Metal nanoparticle assisted plasma etching on the silicon substrate is also applicable to make nano-apertures with small diameters.

The time that I ve wasted is my biggest regretSpent in these places I will never forget.Just sitting and thinking about the things that I ve doneThe crying, the laughing, the hurt and the fun.

4.Applications

Because of many specific phenomena occurring only in the nanofluidics,it has lots of potential value in many fields.In biological and pharmaceutical industries,the size of typical biological macromolecules like DNA and proteins is close to the characteristic size of nanodevices,which help to analyze and manipulate biological macromolecules more precisely and efficiently.These technologies are promising to achieve the project 1000 USD genome’ by inventing inexpensive nano-chips based on nanofluidics.Nowadays,with the development of nano-devices, the analysis of one single macromolecule becomes achievable. By the fluorescence correlation spectrum (FCS), Foquet et al.make it possible to count DNAs and measure its length directly[89].With FCS with high resolution,Wang et al.study the interactions between the DNA and proteins,which are connected to the DNA and further counted directly[90].For medicines,it is import to control its leak into the live body. Some medicines require devices which can leak them slowly and controllably,which can be achieved by devising specific nano-apertures with a precise size and structure[90].

With charged surface, many special electrical phenomena can happen in the nanofluidics,which make it possible to use nanofluidics in the electrical and electronic industry. As the result of the overlap of the electrical double layer, the coions are repulsed from the nanochannels,but the counterions accumulate inside the nanochannels,which generates the streaming current and the streaming potential if additional driving forces are added into the system like the difference of the pressure or concentration[91-93].The usage of the latter one is called blue energy, which transfers the difference of concentration into electric energy [50,94,95]. The increase of the length in the slip effect of the water flow inside the nanochannels can augment the efficiency of this process [96]. In the traditional electronic industry,the n-type diode uses electron as its charge carries, and the p-type diode uses holes as its charge carries.Accordingly,in the nanofluidics,the surface charge can be used to manipulate the ions inside the nanochannel, which generates an idea to make a nanofluidics diode or transistor.And the external electrical field[97,98]and chemical modification of the surface[99,100]correspond to the doping operation.However,this kind of nano-devices is not used to compete with the traditional electronic device,because the speed of ions inside the solution is less than one millionth of that of electron or hole inside the silicon[101].Nevertheless,the chance to use a chemical or biological way to manipulate the logical circuit is a fascinating thought for the automation process.

The specific properties of nanofluidics make it a ubiquitous method for the separation process,and the advanced nanotechnology permits the better manufacture and control of the structure of the nanodevices,which improve the efficiency and performance of the separation process and even create new techniques for separation. Ji et al.reviews the recent studies on the nanofiltration membranes[102].Liu summarized the most recent progress in the emerging 2D molecular sieve membranes for separation[103].

As an important macromolecule in biology,DNA carries the genetic information of creatures.Purification of DNA is quite important,because it is the first and usually expensive step to analyze and modify the molecule.Traditional methods require huge investment and are unable to separate DNA in acceptable time for analysis of individual information.Nanofluidics system is a promising platform to manipulate single cells and DNA [104]. When a parabolic velocity profile exists in a nanochannel,the larger molecules are confined in the center,which move faster [105]. Nano-devices then can be used to separate DNA molecules with different lengths by incorporating pressure difference as shown in Fig. 6. The hydrodynamic chromatography utilizes this phenomenon to separate nanoparticles or macromolecules with sizes around 10 nm[16],and is a precise and efficient method to separate DNA [106]. Because of the steric exclusion effect, the orientation or conformation of the macromolecule influences whether it can pass the filtration or not. For non-spherical macromolecules, it is required to satisfy the channel size by rotation or change of conformation,which induces the change of entropy.Microcavities,i.e.entropic traps,combined with nanochannels,are widely used in many nano-devices to separate DNA with specific orders [107-109].For DNA molecules with a bulk hydrodynamics radius larger than the capillary radius, it cannot be separated as the result of deforming into cylinder inside the narrow capillary and keeping in the middle of the channel.This problem can be solved by a wider capillary [110], which is not able to deal with small DNA fragment.Therefore,a combination of different sizes of capillary is a promising method for separation of DNA molecules with a wide range of lengths[111].Fu et al.[108]use anisotropic nanofilter array and develop it for continuous-flow separation of DNA and proteins by size or charge,which makes it possible for downstream analysis to receive purified biomolecules continuously.In addition to the usage of steric effect,electrophoresis is conducted through nanochannels to separate DNA[112-114].

Fig. 6. DNA separation using nano-devices. (a) schematic illusion of DNA separation mechanism, (b)Result of Chromatography separation of a mixture of GeneRuler 1 kb plus DNA ladder and λ DNA.(Adapted from Wang et al.J.Am.Chem.Soc.134(17)(2012)7400-7405)

Ion separation is time-consuming and shows low efficiency by using traditional methods.The distinct phenomena of fast water flow and ion selection in nano-devices,however,encourage the application of ion separation by nanofluidics.Based on the experimental and theoretical results on the electric double layer,charge-selective nanochannels or nanopores can allow the passage of counter-ions,but prohibit that of co-ions[115,116].By using an angstrom-scale nanoslit with atomically flat planes and little surface charge,Esfandiar et al.found that its confinement leads to notable asymmetric mobility between anions and cations of the same diameter[71].For usage of graphene oxide membrane in the separation, one big challenge is the variable size of interlayer spacing between graphene oxide sheets. Liang Chen et al. overcome this problem by cationic control of the interlayer spacing with angstrom precising using K+,Na+,Ca+,Li+or Mg2+ions and therefore make it applicable for ion separation [117]. Yang et al. reported the efficient and fast filtration of organic solutions composed of small molecular dyes by using graphene or graphene oxide with selectivity of over 99.9%.They attribute these permeation and sieving properties to randomly distributed pinholes with a width of 1 nm interconnected by short graphene[118].

Water desalination is gradually urgent as the result of the decrease of the drinking water,the increase of population and the effect of greenhouse.Membrane-based water purification on different scales is illuminated in Fig.7.

By introducing nanofluidics into this area,many previous unsolvable problems become easy to overcome and the investment on nanodevices grows fast in recent years.The graphene nanomaterials are an optimum choice because of their unique physicochemical properties with water and ions[119].Different mechanisms of separation between water and ions are exhibited in membranes of monolayer graphene and multilayer graphene with stacked sheets as shown in Fig.8.

For desalination, graphene can be derived from different forms,such as pristine graphene, graphene oxide and reduced graphene oxide [120]. By spray coating an aqueous dispersion of graphene oxide/few-layered graphene/deoxycholate, Morelos-Gomez et al.prepared a graphene-based membrane realizing the scalability and high salt rejection for the long time periods in a strong cross flow,with near 85%for NaCl rejection and 96%for an anionic dye[121].Xu et al. utilize self-assembly to form ultrathin and high-performance graphene oxide membranes with 2.5-4 times higher water flux and suitable for water purification [122]. Abraham et al. make graphene oxide membrane applicable for water purification by using physical confinement to control the interlayer spacing and achieve accurate and tunable ion sieving,and exhibit 97%rejection for NaCl[123].

Fig.7.Schematic illustration of various membrane process involved in water purification.(Adapted from Lee et al.Environmental Science:Water Research&Technology 2(1)(2016)17-42)

Gas separation is another promising application of nanofluidics,as the size of the nano-devices is on the same order as the free path of the gas.By incorporating nanofluidics phenomena into the system of gas separation,the separation of some gases becomes economically or technically available.For example,graphene and nanotube membranes have been investigated for separation of oxygen with nitrogen,helium with nitrogen and purification of hydrogen and carbon dioxide[124].Knudsen diffusion suggests that the single component selectivity exhibits an inverse-square-root scaling with molecular mass. Holt et al.studied hydrocarbons and they are exceptional to this equation and exhibit higher selectivities[125].MoS2membranes manufactured by vacuum filtration process are found to have a hydrogen and carbon dioxide selectivity of 3.4 with high permeation rate[126].Danke Chen et al. confine an ionic liquid in the 2D channels of MoS2-laminated membranes by an infiltration process.The membrane exhibits excellent carbon dioxide separation performance with high permeation rate and selectivity for CO2/N2(131.42),CO2/CH4(43.52),and CO2/H2(14.95)[127].As for 2D zeolites and MOF,they exhibit high permeation and selectivity of gas because of their well-defined pores.For zeolites,high selectivity and permeation rate of xylene- and butane-isomers are found[128].For MOF,it can be used for separation of hydrogen and carbon dioxide with a selectivity of 291[129].Li Ding et al.found lamellar stacked MXene membranes with aligned had excellent gas separation with hydrogen permeability larger than 2200 Barrer and selectivity of hydrogen and carbon dioxide larger than 160 as the result of abundant surface-terminating groups on the MXene nanosheets[130].

Fig.8.Different separation mechanisms for(a)single layer graphene membrane and(b)multilayer graphene membrane with stacked sheets.(Adapted from Perreault et al.Chemical Society Reviews 44(16)(2015)5861-5896)

5.Conclusion and Perspective

Because of its interdisciplinary nature, nanofluidics is widely encountered and studied in the physical,chemical,biological and engineering fields.Recent years have witnessed the rapid development of nanofluidics and nano-devices and their many applications.The development of manufacture of nano-devices provides more precise and reproducible fundamental results for models.Theoretical models and computer simulation methods become more mature and achieve business applications gradually,as the result of the improvement of precision and computational capabilities. These theoretical results then guide the application of nano-devices on many practical problems,especially for separation processes,like desalination,separation of biological macromolecules,drug purification and many other fields.

Nanofluidics may still have more unknown phenomena and forces that may have influenced nature and our life significantly.To better understand nanofluidics,theories,simulations and experiments should be further studied.Traditional theory can only be applied to nanofluidics on the relatively large scale(larger than 10 nm).The small size,high specific surface area,surface reaction etc.make the experimental results of nanofluidics deviate those from theories seriously.The lack of applicable theories still restricts the development of the utilization of the nanofluidics. The lack of theories on the nanoscale still restricts the application of these specific phenomena on solving the related problems by the traditional methods.Molecular simulation with more accurate models and higher computational efficacy also needs to be developed,which helps us comprehend the difference and the reason in nanofluidics. Technologies of fabricating nano-devices with high accuracy and low cost are under development,and many researchers devote themselves into this promising field.More important,it is urgent to use these nano-devices into modern industries,improving efficiencies of energy conversion and separation for chemical engineering.Although there is a long way for the maturation of nanofluidics in both theories and applications,we believe it shows a great promising way to solve the problems in the chemical industry,especially for separation engineering.