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Abstract

Nanofluidics has firmly established itself as a new field in fluid mechanics, as novel properties have been shown to emerge in fluids at the nanometric scale. Thanks to recent developments in fabrication technology, artificial nanofluidic systems are now being designed at the scale of biological nanopores. This ultimate step in scale reduction has pushed the development of new experimental techniques and new theoretical tools, bridging fluid mechanics, statistical mechanics, and condensed matter physics. This review is intended as a toolbox for fluids at the nanometer scale. After presenting the basic equations that govern fluid behavior in the continuum limit, we show how these equations break down and new properties emerge in molecular-scale confinement. A large number of analytical estimates and physical arguments are given to organize the results and different limits.

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2021-01-05
2024-12-11
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Literature Cited

  1. Algara-Siller G, Lehtinen O, Wang FC, Nair RR, Kaiser U et al. 2015. Square ice in graphene nanocapillaries. Nature 519:443–45
    [Google Scholar]
  2. Andelman D. 1995. Electrostatic properties of membranes: the Poisson-Boltzmann theory. Handbook of Biological Physics 1 R Lipowsky, E Sackmann 603–42 Amsterdam: Elsevier
    [Google Scholar]
  3. Aris R. 1956. On the dispersion of a solute in a fluid flowing through a tube. Proc. R. Soc. A 235:67–77
    [Google Scholar]
  4. Barrat JL, Hansen JP. 2003. Chapter 7: the density functional approach. Basic Concepts for Simple and Complex Liquids179–212 Cambridge, UK: Cambridge Univ. Press
    [Google Scholar]
  5. Beenakker CW. 1991. Theory of Coulomb-blockade oscillations in the conductance of a quantum dot. Phys. Rev. B 44:1646–56
    [Google Scholar]
  6. Berezhkovskii A, Hummer G. 2002. Single-file transport of water molecules through a carbon nanotube. Phys. Rev. Lett. 89:064503
    [Google Scholar]
  7. Bezrukov SM, Winterhalter M. 2000. Examining noise sources at the single-molecule level: noise of an open maltoporin channel. Phys. Rev. Lett. 85:202–5
    [Google Scholar]
  8. Biesheuvel PM, Bazant MZ. 2016. Analysis of ionic conductance of carbon nanotubes. Phys. Rev. E 94:78–81
    [Google Scholar]
  9. Bocquet L. 2014. Nanofluidics: bubbles as osmotic membranes. Nat. Nanotechnol. 9:249–51
    [Google Scholar]
  10. Bocquet L. 2020. Nanofluidics coming of age. Nat. Mater. 19:254–56
    [Google Scholar]
  11. Bocquet L, Barrat JL. 2007. Flow boundary conditions from nano- to micro-scales. Soft Matter 3:6685–93
    [Google Scholar]
  12. Bocquet L, Barrat JL. 2013. On the Green-Kubo relationship for the liquid-solid friction coefficient. J. Chem. Phys. 139:044704
    [Google Scholar]
  13. Bocquet L, Charlaix E. 2010. Nanofluidics, from bulk to interfaces. Chem. Soc. Rev. 39:1073–95
    [Google Scholar]
  14. Bonthuis DJ, Gekle S, Netz RR 2011. Dielectric profile of interfacial water and its effect on double-layer capacitance. Phys. Rev. Lett. 107:166102
    [Google Scholar]
  15. Bonthuis DJ, Gekle S, Netz RR 2012. Profile of the static permittivity tensor of water at interfaces: consequences for capacitance, hydration interaction and ion adsorption. Langmuir 28:7679–94
    [Google Scholar]
  16. Buyukdagli S, Manghi M, Palmeri J 2010. Ionic capillary evaporation in weakly charged nanopores. Phys. Rev. Lett. 105:158103
    [Google Scholar]
  17. Celebi K, Buchheim J, Wyss RM, Droudian A, Gasser P et al. 2014. Ultimate permeation across atomically thin porous graphene. Science 344:289–92
    [Google Scholar]
  18. Cheng L, Fenter P, Nagy KL, Schlegel ML, Sturchio NC 2001. Molecular-scale density oscillations in water adjacent to a mica surface. Phys. Rev. Lett. 87:156103
    [Google Scholar]
  19. Chmiola J, Yushin G, Gogotsi Y, Portet C, Simon P, Taberna PL 2006. Anomalous increase in carbon at pore sizes less than 1 nanometer. Science 313:1760–63
    [Google Scholar]
  20. Choi W, Ulissi ZW, Shimizu SF, Bellisario DO, Ellison MD, Strano MS 2013. Diameter-dependent ion transport through the interior of isolated single-walled carbon nanotubes. Nat. Commun. 4:2397
    [Google Scholar]
  21. Chou T. 1998. How fast do fluids squeeze through microscopic single-file pores. ? Phys. Rev. Lett. 80:85–88
    [Google Scholar]
  22. Chou T. 1999. Kinetics and thermodynamics across single-file pores: solute permeability and rectified osmosis. J. Chem. Phys. 110:606–15
    [Google Scholar]
  23. Cruz-Chú ER, Papadopoulou E, Walther JH, Popadić A, Li G et al. 2017. On phonons and water flow enhancement in carbon nanotubes. Nat. Nanotechnol. 12:1106–8
    [Google Scholar]
  24. Dagan Z, Weinbaum S, Pfeffer R 1982. An infinite-series solution for the creeping motion through an orifice of finite length. J. Fluid Mech. 115:505–23
    [Google Scholar]
  25. Daldrop JO, Kowalik BG, Netz RR 2017. External potential modifies friction of molecular solutes in water. Phys. Rev. X 7:041065
    [Google Scholar]
  26. Dekker C. 2007. Solid-state nanopores. Nat. Nanotechnol. 2:209–15
    [Google Scholar]
  27. Detcheverry F, Bocquet L. 2012. Thermal fluctuations in nanofluidic transport. Phys. Rev. Lett. 109:024501
    [Google Scholar]
  28. Detcheverry F, Bocquet L. 2013. Thermal fluctuations of hydrodynamic flows in nanochannels. Phys. Rev. E 88:012106
    [Google Scholar]
  29. Eijkel JC, van den Berg A 2005. Nanofluidics: What is it and what can we expect from it. ? Microfluid. Nanofluid. 1:249–67
    [Google Scholar]
  30. Epsztein R, Shaulsky E, Qin M, Elimelech M 2019. Activation behavior for ion permeation in ion-exchange membranes: role of ion dehydration in selective transport. J. Membr. Sci. 580:316–26
    [Google Scholar]
  31. Falk K, Coasne B, Pellenq R, Ulm FJ, Bocquet L 2015. Subcontinuum mass transport of condensed hydrocarbons in nanoporous media. Nat. Commun. 6:6949
    [Google Scholar]
  32. Falk K, Sedlmeier F, Joly L, Netz RR, Bocquet L 2010. Molecular origin of fast water transport in carbon nanotube membranes: superlubricity versus curvature dependent friction. Nano Lett 10:4067–73
    [Google Scholar]
  33. Faucher S, Aluru N, Bazant MZ, Blankschtein D, Brozena AH et al. 2019. Critical knowledge gaps in mass transport through single-digit nanopores: a review and perspective. J. Phys. Chem. C 123:21309–26
    [Google Scholar]
  34. Feng J, Graf M, Liu K, Ovchinnikov D, Dumcenco D et al. 2016a. Single-layer MoS2 nanopores as nanopower generators. Nature 536:197–200
    [Google Scholar]
  35. Feng J, Liu K, Graf M, Dumcenco D, Kis A et al. 2016b. Observation of ionic Coulomb blockade in nanopores. Nat. Mater. 15:850–55
    [Google Scholar]
  36. Feng J, Liu K, Graf M, Lihter M, Bulushev RD et al. 2015. Electrochemical reaction in single layer MoS2: nanopores opened atom by atom. Nano Lett 15:3431–38
    [Google Scholar]
  37. Finkelstein A. 1987. Water Movement Through Lipid Bilayers, Pores, and Plasma Membranes New York: Wiley
    [Google Scholar]
  38. Fouad AM, Gawlinski ET. 2017. Anomalous and nonanomalous behaviors of single-file dynamics. Phys. Lett. A 381:2906–11
    [Google Scholar]
  39. Fox RF, Uhlenbeck GE. 1970. Contributions to non-equilibrium thermodynamics. I. Theory of hydrodynamical fluctuations. Phys. Fluids 13:1893–902
    [Google Scholar]
  40. Fumagalli L, Esfandiar A, Fabregas R, Hu S, Ares P et al. 2018. Anomalously low dielectric constant of confined water. Science 360:1339–42
    [Google Scholar]
  41. Futamura R, Iiyama T, Takasaki Y, Gogotsi Y, Biggs MJ et al. 2017. Partial breaking of the Coulombic ordering of ionic liquids confined in carbon nanopores. Nat. Mater. 16:1225–32
    [Google Scholar]
  42. Garaj S, Hubbard W, Reina A, Kong J, Branton D, Golovchenko JA 2010. Graphene as a subnanometre trans-electrode membrane. Nature 467:190–93
    [Google Scholar]
  43. Ghosh S, Sood AK, Kumar N 2003. Carbon nanotube flow sensors. Science 299:1042–44
    [Google Scholar]
  44. Gopinadhan K, Hu S, Esfandiar A, Lozada-Hidalgo M, Wang FC et al. 2019. Complete steric exclusion of ions and proton transport through confined monolayer water. Science 363:145–48
    [Google Scholar]
  45. Gravelle S, Joly L, Detcheverry F, Ybert C, Cottin-Bizonne C, Bocquet L 2013. Optimizing water permeability through the hourglass shape of aquaporins. PNAS 110:16367–72
    [Google Scholar]
  46. Gravelle S, Netz RR, Bocquet L 2019. Adsorption kinetics in open nanopores as a source of low-frequency noise. Nano Lett 19:7265–72
    [Google Scholar]
  47. Gravelle S, Ybert C, Bocquet L, Joly L 2016. Anomalous capillary filling and wettability reversal in nanochannels. Phys. Rev. E 93:033123
    [Google Scholar]
  48. Grosjean B, Bocquet ML, Vuilleumier R 2019. Versatile electrification of two-dimensional nanomaterials in water. Nat. Commun. 10:1656
    [Google Scholar]
  49. Hall JE. 1975. Access resistance of a small circular pore. J. Gen. Physiol. 66:531–32
    [Google Scholar]
  50. Hauge EH, Martin-Lof A. 1973. Fluctuating hydrodynamics and Brownian motion. J. Stat. Phys. 7:259–81
    [Google Scholar]
  51. Hille B. 1968. Pharmacological modifications of the sodium channels of frog nerve. J. Gen. Physiol. 51:199–219
    [Google Scholar]
  52. Holt JK, Park HG, Wang Y, Stadermann M, Artyukhin AB et al. 2006. Fast mass transport through sub-2-nanometer carbon nanotubes. Science 312:1034–37
    [Google Scholar]
  53. Hooge FN. 1969. noise is no surface effect. Phys. Lett. A 29:139–40
    [Google Scholar]
  54. Hoogerheide DP, Garaj S, Golovchenko JA 2009. Probing surface charge fluctuations with solid-state nanopores. Phys. Rev. Lett. 102:5–8
    [Google Scholar]
  55. Horner A, Pohl P. 2018a. Comment on “Enhanced water permeability and tunable ion selectivity in subnanometer carbon nanotube porins.”. Science 359:eaap9173
    [Google Scholar]
  56. Horner A, Pohl P. 2018b. Single-file transport of water through membrane channels. Faraday Discuss 209:9–33
    [Google Scholar]
  57. Horner A, Zocher F, Preiner J, Ollinger N, Siligan C et al. 2015. The mobility of single-file water molecules is governed by the number of H-bonds they may form with channel-lining residues. Sci. Adv. 1:e1400083
    [Google Scholar]
  58. Hummer G, Rasaiah JC, Noworyta JP 2001. Water conduction through the hydrophobic channel of a carbon nanotube. Nature 414:188–90
    [Google Scholar]
  59. Israelachvili JN. 2011. Electrostatic forces between surfaces in liquids. Intermolecular and Surface Forces291–340 Burlington, MA: Academic. , 3rd. ed.
    [Google Scholar]
  60. Israelachvili JN, Pashley RM. 1983. Molecular layering of water at surfaces and origin of repulsive hydration forces. Nature 306:249–50
    [Google Scholar]
  61. Jain T, Rasera BC, Guerrero RJS, Boutilier MS, O'Hern SC et al. 2015. Heterogeneous sub-continuum ionic transport in statistically isolated graphene nanopores. Nat. Nanotechnol. 10:1053–57
    [Google Scholar]
  62. Kaiser V, Bramwell ST, Holdsworth PC, Moessner R 2013. Onsager's Wien effect on a lattice. Nat. Mater. 12:1033–37
    [Google Scholar]
  63. Kalra A, Garde S, Hummer G 2003. Osmotic water transport through carbon nanotube membranes. PNAS 100:10175–80
    [Google Scholar]
  64. Kappler J, Daldrop JO, Brünig FN, Boehle MD, Netz RR 2018. Memory-induced acceleration and slowdown of barrier crossing. J. Chem. Phys. 148:014903
    [Google Scholar]
  65. Kaufman IK, McClintock PV, Eisenberg RS 2015. Coulomb blockade model of permeation and selectivity in biological ion channels. New J. Phys. 17:083021
    [Google Scholar]
  66. Kavokine N, Marbach S, Siria A, Bocquet L 2019. Ionic Coulomb blockade as a fractional Wien effect. Nat. Nanotechnol. 14:573–78
    [Google Scholar]
  67. Keerthi A, Geim AK, Janardanan A, Rooney AP, Esfandiar A et al. 2018. Ballistic molecular transport through two-dimensional channels. Nature 558:420–23
    [Google Scholar]
  68. Keyser UF, Koeleman BN, van Dorp S, Krapf D, Smeets RM et al. 2006. Direct force measurements on DNA in a solid-state nanopore. Nat. Phys. 2:473–77
    [Google Scholar]
  69. Khair AS, Squires TM. 2008. Surprising consequences of ion conservation in electro-osmosis over a surface charge discontinuity. J. Fluid Mech. 615:323–34
    [Google Scholar]
  70. Knudsen M. 1909. Die Gesetze der Molekularströmung und der inneren Reibungsströmung der Gase durch Röhren. Ann. Phys. 333:75–130
    [Google Scholar]
  71. Koenig SP, Wang L, Pellegrino J, Bunch JS 2012. Selective molecular sieving through porous graphene. Nat. Nanotechnol. 7:728–32
    [Google Scholar]
  72. Köfinger J, Hummer G, Dellago C 2011. Single-file water in nanopores. Phys. Chem. Chem. Phys. 13:15403–17
    [Google Scholar]
  73. Kondrat S, Kornyshev A. 2011. Superionic state in double-layer capacitors with nanoporous electrodes. J. Phys. Condens. Matter 23:022201
    [Google Scholar]
  74. Kralchevsky PA, Denkov ND. 1995. Analytical expression for the oscillatory structural surface force. Chem. Phys. Lett. 240:385–92
    [Google Scholar]
  75. Landau L, Lifshitz E. 1977. IX. Hydrodynamic fluctuations. Statistical Physics: Part 2360–84 Elmsford, NY: Pergamon
    [Google Scholar]
  76. Lauga E, Brenner M, Stone H 2007. Microfluidics: the no-slip boundary condition. Springer Handbook of Experimental Fluid Mechanics C Tropea, AL Yarin, JF Foss 1219–40 Berlin: Springer-Verlag
    [Google Scholar]
  77. Lee AA, Kondrat S, Kornyshev AA 2014. Single-file charge storage in conducting nanopores. Phys. Rev. Lett. 113:048701
    [Google Scholar]
  78. Lee C, Joly L, Siria A, Biance AL, Fulcrand R, Bocquet L 2012. Large apparent electric size of solid-state nanopores due to spatially extended surface conduction. Nano Lett 12:4037–44
    [Google Scholar]
  79. Lee CY, Choi W, Han JH, Strano MS 2010. Coherence resonance in a single-walled carbon nanotube ion channel. Science 329:1320–24
    [Google Scholar]
  80. Lee J, Laoui T, Karnik R 2014. Nanofluidic transport governed by the liquid/vapour interface. Nat. Nanotechnol. 9:317–23
    [Google Scholar]
  81. Lei W, Rigozzi MK, McKenzie DR 2016. The physics of confined flow and its application to water leaks, water permeation and water nanoflows: a review. Rep. Prog. Phys. 79:025901
    [Google Scholar]
  82. Levin Y. 2002. Electrostatic correlations: from plasma to biology. Rep. Prog. Phys. 65:1577–632
    [Google Scholar]
  83. Levin Y. 2006. Electrostatics of ions inside the nanopores and trans-membrane channels. Europhys. Lett. 76:163–69
    [Google Scholar]
  84. Levine S, Marriott JR, Robinson K 1975. Theory of electrokinetic flow in a narrow parallel-plate channel. J. Chem. Soc. Faraday Trans. 2 71:1–11
    [Google Scholar]
  85. Levitt DG. 1973. Dynamics of a single-file pore: non-Fickian behavior. Phys. Rev. A 8:3050–54
    [Google Scholar]
  86. Levy A, Pedro de Souza J, Bazant M 2020. Breakdown of electroneutrality in nanopores. arXiv:1905.05789 [cond-mat.soft]
  87. Li W, Wang W, Zhang Y, Yan Y, Dai C, Zhang J 2017. Gated water transport through graphene nanochannels: from ionic coulomb blockade to electroosmotic pump. J. Phys. Chem. C 121:17523–29
    [Google Scholar]
  88. Liu H, He J, Tang J, Liu H, Pang P et al. 2010. Translocation of single-stranded DNA through single-walled carbon nanotubes. Science 327:64–67
    [Google Scholar]
  89. Liu L, Yang C, Zhao K, Li J, Wu HC 2013. Ultrashort single-walled carbon nanotubes in a lipid bilayer as a new nanopore sensor. Nat. Commun. 4:2989
    [Google Scholar]
  90. Loche P, Ayaz C, Schlaich A, Uematsu Y, Netz RR 2019. Giant axial dielectric response in water-filled nanotubes an effective electrostatic ion–ion interactions from a tensorial dielectric model. J. Phys. Chem. B 123:10850–57
    [Google Scholar]
  91. Ma M, Grey F, Shen L, Urbakh M, Wu S et al. 2015. Water transport inside carbon nanotubes mediated by phonon-induced oscillating friction. Nat. Nanotechnol. 10:692–95
    [Google Scholar]
  92. MacKinnon R. 2004. Potassium channels and the atomic basis of selective ion conduction. Biosci. Rep. 24:75–100
    [Google Scholar]
  93. Maduar SR, Belyaev AV, Lobaskin V, Vinogradova OI 2015. Electrohydrodynamics near hydrophobic surfaces. Phys. Rev. Lett. 114:118301
    [Google Scholar]
  94. Mahan G. 2000. Homogeneous electron gas. Many-Particle Physics295–374 New York: Springer. , 3rd. ed.
    [Google Scholar]
  95. Majumder M, Smalley RE, Hinds BJ 2008. Mass transport through carbon nanotube membranes in three different regimes: ionic, liquid and gas Paper presented at the AIChE 2008 Annual Meeting Philadelphia, PA: Nov. 18
    [Google Scholar]
  96. Malgaretti P, Pagonabarraga I, Rubi JM 2014. Entropic electrokinetics: recirculation, particle separation, and negative mobility. Phys. Rev. Lett. 113:128301
    [Google Scholar]
  97. Mamatkulov SI, Allolio C, Netz RR, Bonthuis DJ 2017. Orientation-induced adsorption of hydrated protons at the air–water interface. Angew. Chem. Int. Ed. 56:15846–51
    [Google Scholar]
  98. Manghi M, Palmeri J, Yazda K, Henn F, Jourdain V 2018. Role of charge regulation and flow slip in the ionic conductance of nanopores: an analytical approach. Phys. Rev. E 98:012605
    [Google Scholar]
  99. Marbach S, Dean DS, Bocquet L 2018. Transport and dispersion across wiggling nanopores. Nat. Phys. 14:1108–13
    [Google Scholar]
  100. Marcotte A, Mouterde T, Niguès A, Siria A, Bocquet L 2020. Mechanically activated ionic transport across single-digit carbon nanotubes. Nat. Mater. 19:1057–61
    [Google Scholar]
  101. Mashiyama KT, Mori H. 1978. Origin of the Landau-Lifshitz hydrodynamic fluctuations in nonequilibrium systems and a new method for reducing the Boltzmann equation. J. Stat. Phys. 18:385–407
    [Google Scholar]
  102. Merlet C, Rotenberg B, Madden PA, Taberna PL, Simon P et al. 2012. On the molecular origin of supercapacitance in nanoporous carbon electrodes. Nat. Mater. 11:306–10
    [Google Scholar]
  103. Misra RP, Blankschtein D. 2017. Insights on the role of many-body polarization effects in the wetting of graphitic surfaces by water. J. Phys. Chem. C 121:28166–79
    [Google Scholar]
  104. Mouhat F, Coudert FX, Bocquet ML 2020. Structure and chemistry of graphene oxide in liquid water from first principles. Nat. Commun. 11:1566
    [Google Scholar]
  105. Mouterde T, Bocquet L. 2018. Interfacial transport with mobile surface charges and consequences for ionic transport in carbon nanotubes. Eur. Phys. J. E 41:148
    [Google Scholar]
  106. Mouterde T, Keerthi A, Poggioli AR, Dar SA, Siria A et al. 2019. Molecular streaming and its voltage control in ångström-scale channels. Nature 567:87–90
    [Google Scholar]
  107. Murata K, Mitsuoka K, Hiral T, Walz T, Agre P et al. 2000. Structural determinants of water permeation through aquaporin-1. Nature 407:599–605
    [Google Scholar]
  108. Neek-Amal M, Lohrasebi A, Mousaei M, Shayeganfar F, Radha B, Peeters FM 2018. Fast water flow through graphene nanocapillaries: a continuum model approach involving the microscopic structure of confined water. Appl. Phys. Lett. 113:083101
    [Google Scholar]
  109. Neek-Amal M, Peeters FM, Grigorieva IV, Geim AK 2016. Commensurability effects in viscosity of nanoconfined water. ACS Nano 10:3685–92
    [Google Scholar]
  110. Nicholson D, Quirke N. 2003. Ion pairing in confined electrolytes. Mol. Simul. 29:287–90
    [Google Scholar]
  111. O'Hern SC, Stewart CA, Boutilier MS, Idrobo JC, Bhaviripudi S et al. 2012. Selective molecular transport through intrinsic defects in a single layer of CVD graphene. ACS Nano 6:10130–38
    [Google Scholar]
  112. Onsager L. 1934. Deviations from Ohm's law in weak electrolytes. J. Chem. Phys. 2:599–615
    [Google Scholar]
  113. Pang P, He J, Park JH, Krstić PS, Lindsay S 2011. Origin of giant ionic currents in carbon nanotube channels. ACS Nano 5:7277–83
    [Google Scholar]
  114. Parsegian A. 1969. Energy of an ion crossing a low dielectric membrane: solutions to four relevant electrostatic problems. Nature 221:844–46
    [Google Scholar]
  115. Perram JW, Hunter RJ, Wright HJ 1973. Charge and potential at the oxide/solution interface. Chem. Phys. Lett. 23:265–69
    [Google Scholar]
  116. Portella G, Pohl P, De Groot BL 2007. Invariance of single-file water mobility in gramicidin-like peptidic pores as function of pore length. Biophys. J. 92:3930–37
    [Google Scholar]
  117. Rabinowitz J, Cohen C, Shepard KL 2020. An electrically actuated, carbon-nanotube-based biomimetic ion pump. Nano Lett 20:21148–53
    [Google Scholar]
  118. Radha B, Esfandiar A, Wang FC, Rooney AP, Gopinadhan K et al. 2016. Molecular transport through capillaries made with atomic-scale precision. Nature 538:222–25
    [Google Scholar]
  119. Reguera D, Rubí JM. 2001. Kinetic equations for diffusion in the presence of entropic barriers. Phys. Rev. E 64:061106
    [Google Scholar]
  120. Renkin EM. 1954. Filtration, diffusion, and molecular sieving through porous cellulose membranes. J. Gen. Physiol. 38:225–43
    [Google Scholar]
  121. Richards LA, Schäfer AI, Richards BS, Corry B 2012. The importance of dehydration in determining ion transport in narrow pores. Small 8:1701–9
    [Google Scholar]
  122. Sahu S, Zwolak M. 2019. Ionic phenomena in nanoscale pores through 2D materials. Rev. Mod. Phys. 91:021004
    [Google Scholar]
  123. Sampson R. 1891. On Stokes's current function. Philos. Trans. R. Soc. Lond. 182:449–518
    [Google Scholar]
  124. Saparov SM, Pfeifer JR, Al-Momani L, Portella G, De Groot BL et al. 2006. Mobility of a one-dimensional confined file of water molecules as a function of file length. Phys. Rev. Lett. 96:148101
    [Google Scholar]
  125. Schlaich A, Kappler J, Netz RR 2017. Hydration friction in nanoconfinement: from bulk via interfacial to dry friction. Nano Lett 17:5969–75
    [Google Scholar]
  126. Schlaich A, Knapp EW, Netz RR 2016. Water dielectric effects in planar confinement. Phys. Rev. Lett. 117:048001
    [Google Scholar]
  127. Schoch RB, Han J, Renaud P 2008. Transport phenomena in nanofluidics. Rev. Mod. Phys. 80:839–83
    [Google Scholar]
  128. Secchi E, Marbach S, Niguès A, Stein D, Siria A, Bocquet L 2016a. Massive radius-dependent flow slippage in carbon nanotubes. Nature 537:210–13
    [Google Scholar]
  129. Secchi E, Niguès A, Jubin L, Siria A, Bocquet L 2016b. Scaling behavior for ionic transport and its fluctuations in individual carbon nanotubes. Phys. Rev. Lett. 116:154501
    [Google Scholar]
  130. Silkina EF, Asmolov ES, Vinogradova OI 2019. Electro-osmotic flow in hydrophobic nanochannels. Phys. Chem. Chem. Phys. 21:23036–43
    [Google Scholar]
  131. Siria A, Poncharal P, Biance AL, Fulcrand R, Blase X et al. 2013. Giant osmotic energy conversion measured in a single transmembrane boron nitride nanotube. Nature 494:455–58
    [Google Scholar]
  132. Siwy Z, Fuliński A. 2002. Origin of noise in membrane channel currents. Phys. Rev. Lett. 89:158101
    [Google Scholar]
  133. Smeets RMM, Keyser UF, Dekker NH, Dekker C 2008. Noise in solid-state nanopores. PNAS 105:417–21
    [Google Scholar]
  134. Smoluchowski M. 1910. Zur kinetischen Theorie der Transpiration und Diffusion verdünnter Gase. Ann. Phys. 338:1559–70
    [Google Scholar]
  135. Sparreboom W, van den Berg A, Eijkel JC 2010. Transport in nanofluidic systems: a review of theory and applications. New J. Phys. 12:015004
    [Google Scholar]
  136. Steckelmacher W. 1966. A review of the molecular flow conductance for systems of tubes and components and the measurement of pumping speed. Vacuum 16:561–84
    [Google Scholar]
  137. Tasserit C, Koutsioubas A, Lairez D, Zalczer G, Clochard MC 2010. Pink noise of ionic conductance through single artificial nanopores revisited. Phys. Rev. Lett. 105:260602
    [Google Scholar]
  138. Taylor G. 1953. Dispersion of soluble matter in solvent flowing slowly through a tube. Proc. R. Soc. A 219:186–203
    [Google Scholar]
  139. Teber S. 2005. Translocation energy of ions in nano-channels of cell membranes. J. Stat. Mech. Theory Exp. 2005:P07001
    [Google Scholar]
  140. Thomas JA, McGaughey AJ. 2009. Water flow in carbon nanotubes: transition to subcontinuum transport. Phys. Rev. Lett. 102:184502
    [Google Scholar]
  141. Travis KP, Todd BD, Evans DJ 1997. Departure from Navier-Stokes hydrodynamics in confined liquids. Phys. Rev. E 55:4288–95
    [Google Scholar]
  142. Tunuguntla RH, Henley RY, Yao YC, Pham TA, Wanunu M, Noy A 2017. Enhanced water permeability and tunable ion selectivity in subnanometer carbon nanotube porins. Science 357:792–96
    [Google Scholar]
  143. Tunuguntla RH, Zhang Y, Henley RY, Yao YC, Pham TA et al. 2018. Response to Comment on “Enhanced water permeability and tunable ion selectivity in subnanometer carbon nanotube porins.”. Science 359:eaaq1241
    [Google Scholar]
  144. Uematsu Y, Bonthuis DJ, Netz RR 2019. Impurity effects at hydrophobic surfaces. Curr. Opin. Electrochem. 13:166–73
    [Google Scholar]
  145. Uematsu Y, Netz RR, Bocquet L, Bonthuis DJ 2018. Crossover of the power-law exponent for carbon nanotube conductivity as a function of salinity. J. Phys. Chem. B 122:2992–97
    [Google Scholar]
  146. Vlassiouk I, Siwy ZS. 2007. Nanofluidic diode. Nano Lett 7:552–56
    [Google Scholar]
  147. Walker MI, Ubych K, Saraswat V, Chalklen EA, Braeuninger-Weimer P et al. 2017. Extrinsic cation selectivity of 2D membranes. ACS Nano 11:1340–46
    [Google Scholar]
  148. Weissberg HL. 1962. End correction for slow viscous flow through long tubes. Phys. Fluids 5:1033
    [Google Scholar]
  149. Wohnsland F, Benz R. 1997. -Noise of open bacterial porin channels. J. Membr. Biol. 158:77–85
    [Google Scholar]
  150. Won CY, Aluru NR. 2007. Water permeation through a subnanometer boron nitride nanotube. J. Am. Chem. Soc. 129:2748–49
    [Google Scholar]
  151. Wu J, Lewis AH, Grandl J 2017. Touch, tension, and transduction—the function and regulation of Piezo ion channels. Trends Biochem. Sci. 42:57–71
    [Google Scholar]
  152. Xie Y, Fu L, Niehaus T, Joly L 2020. Liquid-solid slip on charged walls: the dramatic impact of charge distribution. Phys. Rev. Lett. 125:014501
    [Google Scholar]
  153. Yazda K, Tahir S, Michel T, Loubet B, Manghi M et al. 2017. Voltage-activated transport of ions through single-walled carbon nanotubes. Nanoscale 9:11976–86
    [Google Scholar]
  154. Zhang C, Gygi F, Galli G 2013. Strongly anisotropic dielectric relaxation of water at the nanoscale. J. Phys. Chem. Lett. 4:2477–81
    [Google Scholar]
  155. Zhang J, Kamenev A, Shklovskii BI 2006. Ion exchange phase transitions in water-filled channels with charged walls. Phys. Rev. E 73:051205
    [Google Scholar]
  156. Zhang J, Todd BD, Travis KP 2004. Viscosity of confined inhomogeneous nonequilibrium fluids. J. Chem. Phys. 121:10778–86
    [Google Scholar]
  157. Zhu F, Tajkhorshid E, Schulten K 2004. Collective diffusion model for water permeation through microscopic channels. Phys. Rev. Lett. 93:224501
    [Google Scholar]
  158. Zorkot M, Golestanian R, Bonthuis DJ 2016. The power spectrum of ionic nanopore currents: the role of ion correlations. Nano Lett 16:2205–12
    [Google Scholar]
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