Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-19T06:11:46.150Z Has data issue: false hasContentIssue false
  • English
  • Français

Surprising consequences of ion conservation in electro-osmosis over a surface charge discontinuity

Published online by Cambridge University Press:  25 November 2008

ADITYA S. KHAIR  and
TODD M. SQUIRES
ADITYA S. KHAIR
Affiliation:
Department of Chemical Engineering, University of California, Santa Barbara, CA 93106-5080, USA
TODD M. SQUIRES
Affiliation:
Department of Chemical Engineering, University of California, Santa Barbara, CA 93106-5080, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

A variety of microfluidic technologies utilise electrokinetic transport over rigid surfaces possessing rapid variations in charge. Here, as a paradigmatic model system for such situations, we consider electro-osmosis past a flat plate possessing a discontinuous jump in surface charge. Although the problem is relatively simple to pose, our analysis highlights a number of interesting and somewhat surprising features. Notably, the standard assumption that the electric field outside the diffuse screening layer is equal to the uniform applied field leads to a violation of ion conservation, since the applied field drives an ionic surface current along the diffuse layer downstream of the jump, whereas there is zero surface current upstream. Instead, at the surface charge discontinuity, field lines are drawn into the diffuse layer to supply ions from the bulk electrolyte, thereby ensuring ion conservation. A simple charge conservation argument reveals that the length-scale over which this process occurs is of the order of the ratio of surface-to-bulk electrolyte conductivities, LH=σs/σb. For a highly charged surface, LH can be several orders of magnitude greater than the Debye screening length λD, which is typically nanometres in size. Remarkably, therefore, nano-scale surface conduction may cause micrometre-scale gradients in the bulk electric field. After a distance O(LH) downstream, the bulk field ‘heals’ and is once again equal to the applied field. Scaling all distances with the ‘healing length’ LH yields a universal set of equations for the bulk field and fluid flow, which are solved numerically. Finally, we discuss the role of surface conduction in driving a non-uniform ion distribution, or concentration polarization, in the bulk electrolyte.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 615 , 25 November 2008 , pp. 323 - 334
Copyright
Copyright © Cambridge University Press 2008

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Ajdari, A. 1995 Electro-osmosis on inhomogeneously charge surfaces. Phys. Rev. Lett. 75, 755.CrossRefGoogle Scholar
Anderson, J. L. 1985 Effect of non-uniform zeta potential on particle movement in electric fields. J. Colloid Interface Sci. 105, 45.CrossRefGoogle Scholar
Anderson, J. L. & Idol, W. K. 1985 Electroosmosis through pores with nonuniformly charged walls. Chem. Engng Commun. 38, 93.CrossRefGoogle Scholar
Bazant, M. Z. & Squires, T. M. 2004 Induced-charge electrokinetic phenomena: theory and microfluidic applications. Phys. Rev. Lett. 92, 066010.CrossRefGoogle ScholarPubMed
Bikerman, J. J. 1940 Electrokinetic equations and surface conductance, a survery of the diffuse double layer theory of colloidal solutions. Trans. Faraday Soc. 36, 154.CrossRefGoogle Scholar
Chu, K. T. & Bazant, M. Z. 2007 Nonlinear electrochemical relaxation around conductors. Phys. Rev. E 74, 011501.Google Scholar
Deryaguin, B. V. & Dukhin, S. S. 1969 Theory of surface conductance. Colloid J. USSR 31, 277.Google Scholar
Dukhin, S. S. 1993 Non-equilibrium electric surface phenomena. Adv. Colloid Interface Sci. 44, 1.CrossRefGoogle Scholar
Dukhin, S. S. & Deryaguin, B. V. 1974 Electrokinetic phenomena. Surface and Colloid Science 7 (ed. Matijevic, E.). Wiley.Google Scholar
Gamayunov, N. I., Murtsovkin, V. A. & Dukhin, A. S. 1986 Pair interaction of particles in electric field. 1. Features of hydrodynamic interaction of polarized particles. Colloid J. USSR 48, 197.Google Scholar
Gangwal, S., Cayre, O. J., Bazant, M. Z. & Velev, O. D. 2008 Induced-charge electrophoresis of metallodielectric particles. Phys. Rev. Lett. 100, 058302.CrossRefGoogle ScholarPubMed
Ghosal, S. 2006 Electrokinetic flow and dispersion in capillary electrophoresis. Annu. Rev. Fluid Mech. 38, 309.CrossRefGoogle Scholar
González, A., Ramos, A., Green, N. G., Castellanos, A. & Morgan, H. 2000 Fluid flow induced by nonuniform ac electric fields in electrolytes on microelectrodes. II. A linear double-layer analysis. Phys. Rev. E 61, 4019.Google Scholar
van der Heyden, F. H. J., Bonthuis, D. J., Stein, D., Meyer, C. & Dekker, C. 2006 Electrokinetic energy conversion efficiency in nanofluidic channels. Nano. Lett. 6, 2232.CrossRefGoogle ScholarPubMed
van der Heyden, F. H. J., Bonthuis, D. J., Stein, D., Meyer, C. & Dekker, C. 2007 Power generation by pressure-driven transport of ions in nanofluidic channels. Nano. Lett. 7, 1022.CrossRefGoogle ScholarPubMed
Khair, A. S. & Squires, T. M. 2008 Fundamental aspects of concentration polarization arising from non-uniform electrokinetic transport. Phys. Fluids 20, 087102.CrossRefGoogle Scholar
Khandurina, J. & Guttman, A. 2003 Microscale separation and analysis. Curr. Opin. Chem. Biol. 7, 595.CrossRefGoogle ScholarPubMed
Kilic, M. S., Bazant, M. Z. & Ajdari, A. 2007 Steric effects in the dynamics of electrolytes at large applied voltages. I. Double-layer charging. Phys. Rev. E 75, 021502.Google ScholarPubMed
Kim, S. J., Wang, Y. C., Lee, J. H., Jang, H. & Han, J. 2007 Concentration polarization and nonlinear electrokinetic flow near a nanofluidic channel. Phys. Rev. Lett. 99, 044501.CrossRefGoogle Scholar
Levitan, J. A., Devasenathipathy, S., Studer, V., Ben, Y., Thorsen, T., Squires, T. M. & Bazant, M. Z. 2005 Experimental observation of induced-charge electro-osmosis around a metal wire in a microchannel. Colloids Surfaces A 267, 122.CrossRefGoogle Scholar
Long, D. & Ajdari, A. 1998 Symmetry properties of the electrophoretic motion of patterned colloidal particles. Phys. Rev. Lett. 81, 1529.CrossRefGoogle Scholar
Long, D., Stone, H. A. & Ajdari, A. 1999 Electroosmotic flows created by surface defects in capillary electrophoresis. J. Colloid Interface Sci. 212, 338.CrossRefGoogle ScholarPubMed
Lyklema, J. 1995 Fundamentals of Interface and Colloid Science. Volume II: Solid–Liquid Interfaces. Academic.Google Scholar
Murtsovkin, V. A. 1996 Nonlinear flows near polarized disperse particles. Colloid J. Russ. Acad. Sci. 53, 947.Google Scholar
O'Brien, R. W. 1983 The solution of the electrokinetic equations for colloidal particles with thin double layers. J. Colloid Interface Sci. 92, 204.CrossRefGoogle Scholar
O'Brien, R. W. & White, L. R. 1978 Electrophoretic mobility of a spherical colloidal particle. J. Chem. Soc. Faraday Trans. II 74, 1607.CrossRefGoogle Scholar
Pennathur, S., Eijkel, J. C. T. & van der Berg, A. 2007 Energy conversion in microsystems: is there a role for micro/nanofluidics? Lab. Chip 7, 1234.Google Scholar
Press, W. H., Teukolsky, S. A., Vetterling, W. T. & Flannery, B. P. 1992 Numerical Recipes in FORTRAN, 2nd edn.Cambridge University Press.Google Scholar
Prieve, D. C, Anderson, J. L., Ebel, J. P. & Lowell, M. E. 1984 Motion of a particle generated by chemical gradients. Part 2. Electrolytes. J. Fluid Mech. 148, 247.CrossRefGoogle Scholar
Ramos, A., Morgan, H., Green, N. G. & Castellanos, A. 1998 AC electrokinetics: a review of forces in microelectrode structures. J. Phys. D 31, 2338.Google Scholar
Reuss, F. 1809 Sur un nouvel effet de le électricité glavanique. Mém. Soc. Imp. Nat. Mosc. 2, 327.Google Scholar
Rice, C. & Whitehead, R. 1965 Electrokinetic flow in a narrow cylindrical capillary. J. Phys. Chem. 69, 4017.CrossRefGoogle Scholar
Russel, W. B., Saville, D. A. & Schowalter, W. R. 1989 Colloidal Dispersions. Cambridge University Press.CrossRefGoogle Scholar
Soni, G., Squires, T. M. & Meinhart, C. D. 2007 Nonlinear effects in induced charge electroosmosis. Proc. IMECE2007, Paper IMECE2007-41468, 2007 ASME International Mechanical Engineering Congress and Exposition, Seattle, WA, USA.CrossRefGoogle Scholar
Squires, T. M. & Bazant, M. Z. 2004 Induced-charge electro-osmosis. J. Fluid Mech. 509, 217.CrossRefGoogle Scholar
Squires, T. M. & Bazant, M. Z. 2006 Breaking symmetries in induced-charge electro-osmosis and electrophoresis. J. Fluid Mech. 560, 65.CrossRefGoogle Scholar
Squires, T. M. & Quake, S. 2005 Microfluidics: fluid physics at the nanoliter scale. Rev. Mod. Phys. 77, 977.CrossRefGoogle Scholar
Stone, H. A., Stroock, A. D. & Ajdari, A. 2004 Engineering flows in small devices: microfluidics toward a lab-on-a-chip. Annu. Rev. Fluid Mech. 36, 381.CrossRefGoogle Scholar
Storey, B. D., Edwards, L. R., Sabri Kilic, M. & Bazant, M. Z. 2008 Steric effects on ac electro-osmosis in dilute electrolytes. Phys. Rev. E 77, 036317.Google ScholarPubMed
Stroock, A. D., Weck, M., Chiu, D. T., Huck, W. T. S., Kenis, P. J. A., Ismagilov, R. F. & Whitesides, G. M. 2000 Patterning electro-osmotic flow with patterned surface charge. Phys. Rev. Lett. 84 (15), 3314.CrossRefGoogle ScholarPubMed
Teubner, M. 1982 The motion of charge colloidal particles in electric fields. J. Chem. Phys. 76, 5564.CrossRefGoogle Scholar
Wang, Y., Stevens, A. & Han, J. 2005 Million-fold preconcentration of proteins and peptides by nanofluidic filter. Anal. Chem. 77, 4293.CrossRefGoogle ScholarPubMed
Yariv, E. 2004 Electro-osmotic flow near a surface charge discontinuity. J. Fluid Mech. 521, 181.CrossRefGoogle Scholar