Introduction
Mass transport through nanoscale pores has been studied for many years in disciplines as diverse as membrane science, soil permeability, and cell physiology. In these fields, emphasis has been placed on the macroscopic outcome, while molecular-level effects on fluid behavior have often been neglected. In the last 10 years, however, the focus has shifted to the effects on fluid behavior of intermolecular interactions between the fluid and the walls of the channel that it flows through. Interest in this field, called nanofluidics, has dramatically increased with the widespread availability of carbon nanotubes (CNTs) and, more recently, graphene, with potential applications to filtration and separation (e.g., water desalination). Initial insights into nanoscale steady-state flow were obtained by numerical simulations, Reference Hummer, Rasaiah and Noworyta1 followed by experiments in small membranes of aligned tubes, Reference Majumder, Chopra, Andrews and Hinds2,Reference Holt, Park, Wang, Stadermann, Artyukhin, Grigoropoulos, Noy and Bakajin3 and measurements of flow through single nanotubes. Reference Agrawal, Drahushuk and Strano4 These results have been extensively reviewed elsewhere. Reference Whitby and Quirke5,Reference Mattia and Gogotsi6
A key concept in nanofluidics is flow enhancement, defined as the ratio of the measured flow to an ideal no-slip Poiseuille flow. The latter assumes that the fluid molecules closest to the channel’s surface have zero velocity, in other words, they stick to the surface. Reference Whitby and Quirke5,Reference Mattia and Gogotsi6 Experimental and modeling results have reported flow enhancements ranging from 10 to 100,000 for water flow inside nanotubes made of carbon and other materials. Reference Mattia and Gogotsi6
While a full understanding of the physical origins of flow enhancement has yet to be achieved, some aspects are now generally accepted:
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• A 2-nm threshold exists below which the conventional continuum fluid mechanics model can no longer be applied. Reference Thomas and McGaughey7
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• The presence of a reduced viscosity or depletion layer near the tube wall is due to solid–liquid molecular interactions. Reference Joseph and Aluru8
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• Frictional losses are mainly confined to the entrance region of the nanochannel. Reference Sisan and Lichter9
Other aspects are still unclear and represent active areas of research, including the effective dependence of flow enhancement on the nanochannel length; whether a maximum flow enhancement value exists based on the nanochannel’s geometric characteristics and surface chemistry and structure; Reference Walther, Ritos, Cruz-Chu, Megaridis and Koumoutsakos10–Reference Mattia and Calabrò13 and the physical state of liquid molecules under nanoscale confinement. Reference Thomas and McGaughey14 For example, water in nanotubes with diameters ranging from 1.1 to 2.1 nm displays strong structural anisotropy. Notably, the diffusivity and viscosity in the axial direction are much larger than in the radial direction, leading to an ordered, helical structure inside a (10,10) CNT. Reference Thomas and McGaughey7
Nanochannel material and flow enhancement
Experiments and simulations have both shown that the surface structure and chemistry of a nanochannel have a significant effect on liquid flow and flow enhancement. Molecular dynamics (MD) simulations have shown that imposing hydrophilic potentials on a CNT structure significantly reduces the flow enhancement, Reference Joseph and Aluru8 though a certain amount of slip would still occur. Reference Ho, Papavassiliou, Lee and Striolo15 This prediction was confirmed by experimental measurements of small water flow enhancement in hydrophilic alumina nanochannels. Reference Lee, Leese and Mattia16 While experimental evidence of flow enhancement in nanotubes other than in carbon nanotubes is scarce, more studies have been done with MD, although some results are contradictory. For example, both higher and lower flow enhancements compared to CNTs have been predicted for silicon carbide nanotubes, Reference Khademi and Sahimi17,Reference Ritos, Mattia, Calabrò and Reese18 a material more hydrophilic than carbon. Another interesting example is boron nitride, whose contact angle with water is similar to that of carbon, but for which MD simulations have shown a significantly lower flow enhancement. Reference Joseph and Aluru8,Reference Ritos, Mattia, Calabrò and Reese18
A change in flow enhancement can also be obtained by modifying the surface chemistry or structure of the nanochannel. For example, hydrophilic functionalization of CNT tips can ease capillary filling while reducing flow enhancement. Reference Majumder, Chopra and Hinds19 A reduction in flow enhancement has also been observed in MD simulations of water flow through CNTs containing defects. Reference Nicholls, Borg, Lockerby and Reese20 On the other hand, graphitization of amorphous CNTs changed their wetting behavior from hydrophilic to hydrophobic, inhibiting imbibition, or entry, of water. Reference Mattia, Rossi, Kim, Korneva, Bau and Gogotsi21 Surface modification of CNTs has also been used to control their ability to imbibe liquids other than water, with different polarity or viscosity. Reference Majumder and Corry22 Similarly, functionalization of CNT tips can be used to control selective permeation of ions through CNT membranes according to MD simulations. Reference Corry23
These results highlight the strong effect that the properties of wall materials have on flow enhancement in nanochannels. Numerous theoretical models have been developed to account for the strength of solid–liquid interactions on fluid flow, relating the flow enhancement to the wetting behavior via the slip length, Reference Neto, Evans, Bonaccurso, Butt and Craig24 friction coefficient, Reference Kannam, Todd, Hansen and Daivis11 work of adhesion between the flowing liquid and channel wall, Reference Mattia and Calabrò13 or reduced fluid viscosity at the wall. Reference Thomas, McGaughey and Kuter-Arnebeck25
Fertile ground for experimental and modeling collaborations
Much of the progress in nanofluidics is due to substantial improvements in both experimental and computer simulation methods. Fluid behavior can now be probed in channel sizes on the order of 1–10 nm, where nanoscale confinement effects become important. Nanomaterials can be fabricated with increasing accuracy in terms of size, surface chemistry, and structure, while simulation methods have become powerful enough to produce useful insights at the length scales captured in experimental observations. These advances have resulted in a convergence of experiments and modeling, quickening progress in the field. The articles in this issue highlight the importance of this collaborative process and provide practical steps to achieving this result. On the experimental side, careful design is needed so that measurements can be directly compared to simulation predictions. This alignment requires control of materials chemistry and structure, as well pore size, particularly in the 1–2 nm range—the region where continuum fluid theory breaks down. On the modeling side, simulations need to be applied consistently and be carefully validated. An example is the porting of interatomic potentials calibrated on the water contact angle at the macroscale to study flow in the interior of a nanochannel.
In this issue
The articles in this issue of MRS Bulletin describe the origin of flow enhancement under nanoscale confinement and the design of nanomaterials with tailored enhanced behavior for a range of applications. In his article, Calabrò provides an overview of the material structure and chemistry factors that affect nanoscale flows. Kannam et al. provide a detailed description of the underlying fluid mechanics formulation for describing slip flow, and survey predictions of slip length from atomistic simulations. In their article, Majumder et al. present an overview of experimental efforts to observe enhanced fluid flow in one-dimensional (1D) (e.g., nanotubes) and two-dimensional (2D) (e.g., stacked graphene sheets) nanochannels.
Borg and Reese describe a multiscale modeling framework for predicting the behavior of nanotube membranes at experimental length scales and time scales. Min et al. then detail the characterization of flow in single nanotubes, with focus on measurement platforms and detection techniques. The Corry article describes how nanochannels can be used to control ion transport through the underlying physical mechanisms of size, hydration, and chemical functionalization.
Final considerations
While the concept of flow enhancement is useful to understand the fundamental relationship between channel wall material properties and the flowing liquid, it must be converted into a quantity, such as permeability or permeance, to allow for comparing performance with other porous materials used for filtration. Such a comparison is often hindered by the fact that many studies on flow enhancement in 1D and 2D nanochannels, particularly modeling, do not report the necessary information to calculate permeability or permeance. We hope that this issue will spur readers to provide the necessary information in their future publications to make this comparison possible. These include the channels’ and membranes’ geometry (channel length and diameter and membrane porosity and tortuosity) and surface chemistry (presence of functional groups or defects), fluid properties (viscosity, density, and temperature), and flow parameters (flow rate or Reynolds number and applied pressure).
Alan McGaughey is a professor of mechanical engineering at Carnegie Mellon University (CMU) and a Fellow of The American Society of Mechanical Engineers. He earned a B.Eng. degree in mechanical engineering from McMaster University, Canada, in 1998, a M.A.Sc. degree in mechanical and industrial engineering from the University of Toronto, Canada, in 2000, and a PhD degree in mechanical engineering from the University of Michigan in 2004. He was a Harrington Faculty Fellow at the University of Texas at Austin from 2012 to 2013, was awarded CMU’s Teare Teaching Award in 2014, and was named an Outstanding Referee by the American Physical Society in 2015. His research focuses on the modeling of nanoscale transport phenomena. McGaughey can be reached by phone at 412-268-9605 or by email at [email protected].
Davide Mattia is a professor of chemical engineering at the University of Bath, UK. He earned a MSc degree in materials engineering from the University of Naples Federico II, Italy, in 2002, and a PhD degree in materials science and engineering from Drexel University in 2007. He is a chartered engineer; a Fellow of the IChemE; and a past Royal Academy of Engineering research fellow. His research interests focus on the development of novel one- and two-dimensional hybrid membranes for water-treatment processes and understanding the effects of nanoscale confinement on fluid flow. Mattia can be reached by phone at +44 (0) 1225 383961 or by email at [email protected].
