Microfluidics and Nanofluidics

, Volume 3, Issue 6, pp 723–728 | Cite as

Hydrodynamic dispersion of neutral solutes in nanochannels: the effect of streaming potential

  • Xiangchun Xuan
  • David Sinton
Short Communication


An analytical model is developed to account for the effect of streaming potential on the hydrodynamic dispersion of neutral solutes in pressure-driven flow. The pressure-driven flow and the resulting electroosmotic backflow exhibit coupled dispersion effects in nanoscale channels where the hydraulic diameter is on the order of the electrical double layer thickness. An effective diffusion coefficient for this regime is derived. The influence of streaming potential on hydrodynamic dispersion is found to be mainly dependent on an electrokinetic parameter, previously termed the “figure of merit”. Results indicate that streaming potential decreases the effective diffusion coefficient of the solute, while increasing the dispersion coefficient as traditionally defined. This discrepancy arises from the additional effect of streaming potential on average solute velocity, and discussed herein.


Hydrodynamic dispersion Nanochannel Streaming potential Neutral solutes Electroviscous effect 



The authors are grateful for financial support from Clemson University to X.X. and from the Natural Sciences and Engineering Research Council (NSERC) of Canada to D.S. The authors also thank S. Griffiths for helpful discussions.


  1. Aris R (1956) On the dispersion of a solute in a fluid flowing through a tube. Proc R Soc Lond A 235:67–77Google Scholar
  2. Brenner H, Edwards DA (1993) Macrotransport processes. Butterworth-Heinemann, BostonGoogle Scholar
  3. Burgreen D, Nakache FR (1964) Electrokinetic flow in ultrafine capillary slits. J Phys Chem 68:1084–1091CrossRefGoogle Scholar
  4. Datta R (1990) Theoretical analysis of capillary electrophoresis performance. Biotechnol Prog 6:485–493CrossRefGoogle Scholar
  5. Datta R, Kotamarthi VR (1990) Electrokinetic dispersion in capillary electrophoresis. AICHE J 36:916–926CrossRefGoogle Scholar
  6. De Leebeeck A, Sinton D (2006) Ionic dispersion in nanofluidics. Electrophoresis 27:4999–5008CrossRefGoogle Scholar
  7. Dutta D, Leighton DT (2003) Dispersion reduction in open-channel liquid electrochromatographic columns via pressure-driven back flow. Anal Chem 75:3352–3359CrossRefGoogle Scholar
  8. Dutta D, Ramachandran A, Leighton DT (2006) Effect of channel geometry on solute dispersion in pressure-driven microfluidic devices. Microfluid Nanofluid 2:275–290CrossRefGoogle Scholar
  9. Garcia AL, Ista LK, Petsev DN et al (2005) Electrokinetic molecular separation in nanoscale fluidic channels. Lab Chip 5:1271–1276CrossRefGoogle Scholar
  10. Gas B, Kenndler E (2002) Peak broadening in microchip electrophoresis: a discussion of the theoretical background. Electrophoresis 23:3817–3826CrossRefGoogle Scholar
  11. Ghosal S (2004) Fluid mechanics of electroosmotic flow and its effect on band broadening in capillary electrophoresis. Electrophoresis 25:214–228CrossRefGoogle Scholar
  12. Ghosal S (2006) Electrokinetic flow and dispersion in capillary electrophoresis. Annu Rev Fluid Mech 38:309–338CrossRefMathSciNetGoogle Scholar
  13. Griffiths SK, Nilson RH (1999) Hydrodynamic dispersion of a neutral nonreacting solute in electroosmotic flow. Anal Chem 71:5522–5529CrossRefGoogle Scholar
  14. Griffiths SK, Nilson RH (2005) The efficiency of electrokinetic pumping at a condition of maximum work. Electrophoresis 26:351–361CrossRefGoogle Scholar
  15. Griffiths SK, Nilson RH (2006) Charged species transport, separation, and dispersion in nanoscale channels: autogenous electric field-flow fractionation. Anal Chem 78:8134–8141CrossRefGoogle Scholar
  16. Hildreth D (1970) Electrokinetic flow in fine capillary channels. J Phys Chem 74:2006–2015CrossRefGoogle Scholar
  17. Hunter RJ (1981) Zeta potential in colloid science, principles and applications. Academic, New YorkGoogle Scholar
  18. Li D (2001) Electro-viscous effects on pressure-driven liquid flow in microchannels. Colloid Surf A 191:35–57CrossRefGoogle Scholar
  19. Li D (2004) Electrokinetics in microfluidics. Elsevier Academic Press, BurlingtonCrossRefGoogle Scholar
  20. Morrison FA, Osterle JF (1965) Electrokinetic energy conversion in untrafine capillaries. J Chem Phys 43:2111–2115CrossRefGoogle Scholar
  21. Pennathur S, Santiago JG (2005a) Electrokinetic transport in nanochannels: 1. Theory. Anal Chem 77:6772–6781CrossRefGoogle Scholar
  22. Pennathur S, Santiago JG (2005b) Electrokinetic transport in nanochannels: 2. Experiments. Anal Chem 77:6782–6789CrossRefGoogle Scholar
  23. Probstein RF (1995) Physicochemical hydrodynamics. Willey, New YorkGoogle Scholar
  24. Taylor GI (1953) Dispersion of soluble matter in solvent flowing slowly through a tube. Prof R Soc Lond A 219:186–203CrossRefGoogle Scholar
  25. Xuan X (2007) Revisit of Joule heating in capillary electrophoresis: the contribution of surface conductance. Electrophoresis (in press)Google Scholar
  26. Xuan X, Li D (2006a) Thermodynamic analysis of electrokinetic energy conversion. J Power Sources 156:677–684CrossRefGoogle Scholar
  27. Xuan X, Li D (2006b) Electrokinetic transport of charged solutes in micro- and nanochannels, the influence of transverse electromigration. Electrophoresis 27:5020–5031CrossRefGoogle Scholar
  28. Xuan X, Li D (2007) Solute separation in nanofluidic channels, pressure-driven or electric field-driven. Electrophoresis 28:627–634CrossRefGoogle Scholar
  29. Zholkovskij EK, Masliyah JH (2004) Hydrodynamic dispersion due to combined pressure-driven and electroosmotic flow through microchannels with a thin double layer. Anal Chem 76:2708–2718CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2007

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringClemson UniversityClemsonUSA
  2. 2.Department of Mechanical EngineeringUniversity of VictoriaVictoriaCanada

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