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    Cao, Wei Wang, Jin and Ma, Ming 2018. Carbon nanostructure based mechano-nanofluidics. Journal of Micromechanics and Microengineering, Vol. 28, Issue. 3, p. 033001.




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        Materials enabling nanofluidic flow enhancement
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        Materials enabling nanofluidic flow enhancement
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This issue of MRS Bulletin focuses on materials that enable nanofluidic systems with unusually high mass fluxes, termed “enhancement factor” or “slip flow.” There is now ample evidence of such flow enhancement in nanochannels, with sizes ranging from subnanometer to a few nanometers. Most of the studies to date, both experimental and modeling, have focused on carbon nanotubes and, more recently, on graphene. Different fabrication methods result in different structures, surface chemistries, and defects, with a significant effect on flow enhancement. As new one-dimensional and two-dimensional nanomaterials are synthesized, a deeper understanding of the nanoscale transport physics is needed, particularly in the relationship between material properties and flow behavior. Herein, authors at the forefront of experimental, modeling, and theoretical developments in nanofluidic flow describe the state of the art in materials development and characterization.


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, 1 followed by experiments in small membranes of aligned tubes, 2,3 and measurements of flow through single nanotubes. 4 These results have been extensively reviewed elsewhere. 5,6

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. 5,6 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. 6

While a full understanding of the physical origins of flow enhancement has yet to be achieved, some aspects are now generally accepted:

  • A 2-nm threshold exists below which the conventional continuum fluid mechanics model can no longer be applied. 7

  • The presence of a reduced viscosity or depletion layer near the tube wall is due to solid–liquid molecular interactions. 8

  • Frictional losses are mainly confined to the entrance region of the nanochannel. 9

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; 1013 and the physical state of liquid molecules under nanoscale confinement. 14 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. 7

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, 8 though a certain amount of slip would still occur. 15 This prediction was confirmed by experimental measurements of small water flow enhancement in hydrophilic alumina nanochannels. 16 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, 17,18 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. 8,18

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. 19 A reduction in flow enhancement has also been observed in MD simulations of water flow through CNTs containing defects. 20 On the other hand, graphitization of amorphous CNTs changed their wetting behavior from hydrophilic to hydrophobic, inhibiting imbibition, or entry, of water. 21 Surface modification of CNTs has also been used to control their ability to imbibe liquids other than water, with different polarity or viscosity. 22 Similarly, functionalization of CNT tips can be used to control selective permeation of ions through CNT membranes according to MD simulations. 23

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, 24 friction coefficient, 11 work of adhesion between the flowing liquid and channel wall, 13 or reduced fluid viscosity at the wall. 25

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).


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3. Holt, J.K., Park, H.G., Wang, Y., Stadermann, M., Artyukhin, A.B., Grigoropoulos, C.P., Noy, A., Bakajin, O., Science 312, 1034 (2006).
4. Agrawal, K.V., Drahushuk, L.W., Strano, M.S., Philos. Trans. R. Soc. Lond. A 374, 20150357 (2016).
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6. Mattia, D., Gogotsi, Y., Microfluid. Nanofluid. 5, 289 (2008).
7. Thomas, J.A., McGaughey, A.J.H., Phys. Rev. Lett. 102, 184502 (2009).
8. Joseph, S., Aluru, N.R., Nano Lett. 8, 452 (2008).
9. Sisan, T., Lichter, S., Microfluid. Nanofluid. 11, 787 (2011).
10. Walther, J.H., Ritos, K., Cruz-Chu, E., Megaridis, C.M., Koumoutsakos, P., Nano Lett. 13, 1910 (2013).
11. Kannam, S.K., Todd, B.D., Hansen, J.S., Daivis, P.J., J. Chem. Phys. 138, 094701 (2013).
12. Nicholls, W., Borg, M., Lockerby, D., Reese, J., Microfluid. Nanofluid. 12, 257 (2012).
13. Mattia, D., Calabrò, F., Microfluid. Nanofluid. 13, 125 (2012).
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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 .

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 .