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A continuum approach to predicting electrophoretic mobility reversals

Published online by Cambridge University Press:  04 July 2014

Robert F. Stout and
Aditya S. Khair
Robert F. Stout
Affiliation:
Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
Aditya S. Khair*
Affiliation:
Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 15213, USA
*
†Email address for correspondence: akhair@andrew.cmu.edu
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Abstract

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We present a continuum approach to predicting the electrophoretic mobility of a charged dielectric colloidal particle in a concentrated multivalent electrolyte. Our model takes into account steric (excluded volume) hindrance between ions via Bikerman’s approach (Philos. Mag., vol. 33, 1942, p. 384) and ion–ion electrostatic (Coulombic) correlations via the work of Bazant et al. (Phys. Rev. Lett., vol. 106, 2011, 046102). The latter can result in the prediction of an electrophoretic mobility reversal, that is, the migration velocity of a particle switches direction with increasing ion concentration. Our model predictions compare favourably with experiments that observe mobility reversals in multivalent electrolytes.

JFM classification

Complex Fluids: ColloidsLow-Reynolds-number flows: Low-Reynolds-number flowsMicro-/Nano-fluid dynamics: Micro-/Nano-fluid dynamics

Information

Type
Rapids
Information
Journal of Fluid Mechanics , Volume 752 , 10 August 2014, R1
Copyright
© 2014 Cambridge University Press 

References

Attard, P., Mitchell, D. J. & Ninham, B. W. 1988 Beyond Poisson Boltzmann: images and correlations in the electric double layer. I. Counterions only. J. Chem. Phys. 88, 4987–4996.CrossRefGoogle Scholar
Bazant, M. Z., Kilic, M. S., Storey, B. D. & Ajdari, A. 2009 Towards an understanding of induced-charge electrokinetics at large applied voltages in concentrated solutions. Adv. Colloid Interface Sci. 152, 48–88.CrossRefGoogle ScholarPubMed
Bazant, M. Z., Storey, B. D. & Kornyshev, A. A. 2011 Double layer in ionic liquids: overscreening versus crowding. Phys. Rev. Lett. 106, 046102.Google Scholar
Bazant, M. Z., Storey, B. D. & Kornyshev, A. A. 2012 Erratum: Double layer in ionic liquids: overscreening versus crowding. Phys. Rev. Lett. 109, 149903.Google Scholar
Bikerman, J. J. 1942 XXXIX. Structure and capacity of electrical double layer. Phil. Mag. 33, 384–397.Google Scholar
Dorfman, K. D. 2010 DNA electrophoresis in microfabricated devices. Rev. Mod. Phys. 82, 2903–2947.Google Scholar
Dukhin, S. S. & Deryaguin, B. V. 1974 Electrokinetic phenomena. In Surface and Colloid Science (ed. Matijevic, E.), vol. 7. Wiley.Google Scholar
Elbashir, A. A. & Aboul-Enein, H. Y. 2013 Capillary electrophoresis and molecular modeling as a complementary technique for chiral recognition mechanism. Crit. Rev. Anal. Chem. 43, 131–137.CrossRefGoogle Scholar
Elimelech, M. & O’Melia, C. R. 1990 Effect of electrolyte type on the electrophoretic mobility of polystyrene latex colloids. Colloid Surf. 44, 165–178.CrossRefGoogle Scholar
Ennis, J., Marcelja, S. & Kjellander, R. 1996 Effective surface charge for symmetric electrolytes in the primitive model double layer. Electrochim. Acta 41, 2115–2124.Google Scholar
Fedorov, M. V. & Kornyshev, A. A. 2008 Ionic liquid near a charged wall: structure and capacitance of the electrical double-layer. J. Phys. Chem. B 112, 11868–11872.Google Scholar
Gillespie, D., Khair, A. S., Bardhan, J. P. & Pennathur, S. 2011 Efficiently accounting for ion correlations in electrokinetic nanofluidic devices using density functional theory. J. Colloid Interface Sci. 359, 520–529.Google Scholar
Gonzales-Tovar, E., Lozada-Cassou, M. & Henderson, D. 1985 Hypernetted chain approximation for the distribution of ions around a cylindrical electrode. II. Numerical solution for a model cylindrical polyelectrolyte. J. Chem. Phys. 83, 361–372.CrossRefGoogle Scholar
Grosberg, A. Y., Nguyen, T. T. & Shklovskii, B. I. 2002 Colloquium: the physics of charge inversion in chemical and biological systems. Rev. Mod. Phys. 74, 329–345.CrossRefGoogle Scholar
Hatlo, M. M. & Lue, L. 2010 Electrostatic interactions of charged bodies from the weak- to the strong-coupling regime. Europhys. Lett. 89, 25002.CrossRefGoogle Scholar
Hatlo, M. M., van Roij, R. & Lue, L. 2012 The electric double layer at high surface potentials: the influence of excess ion polarizability. Europhys. Lett. 89, 28010.Google Scholar
Henry, D. C. 1931 The cataphoresis of suspended particles. Part I. The equation of cataphoresis. Proc. R. Soc. Lond. A 133, 106–129.Google Scholar
Hückel, E. 1924 Die Kataphorese der Kugel. Phys. Z. 25, 204–210.Google Scholar
Khair, A. S. & Squires, T. M. 2009 Ion steric effects on electrophoresis of a colloidal particle. J. Fluid Mech. 640, 343–356.Google Scholar
Kilic, M. S., Bazant, M. Z. & Ajdari, A. 2007a Steric effects in the dynamics of electrolytes at large applied voltages. I. Double-layer charging. Phys. Rev. E 75, 021502.Google Scholar
Kilic, M. S., Bazant, M. Z. & Ajdari, A. 2007b Steric effects in the dynamics of electrolytes at large applied voltages. II. Modified Poisson–Nernst–Planck equations. Phys. Rev. E 75, 021503.Google ScholarPubMed
Kim, S. & Karrila, S. J. 2005 Microhydrodynamics: Principles and Selected Applications. Dover.Google Scholar
Kjellander, R. & Marcelja, S. 1986 Double-layer interaction in the primitive model and the corresponding Poisson–Boltzmann description. J. Phys. Chem. 90, 1230–1232.CrossRefGoogle Scholar
Levin, Y. 2002 Electrostatic correlations: from plasma to biology. Rep. Prog. Phys. 65, 1577–1632.Google Scholar
Lozada-Cassou, M., González-Tovar, E. & Olivares, W. 1999 Nonlinear effects in the electrophoresis of a spherical colloidal particle. Phys. Rev. E 60, R17–R20.CrossRefGoogle ScholarPubMed
Martín-Molina, A., Maroto-Centeno, J. A., Hidalgo-Alvarez, R. & Quesada-Pérez, M. 2008 Charge reversal in real colloids: experiments, theory and simulations. Colloid Surf. A 319, 103–108.CrossRefGoogle Scholar
Martín-Molina, A., Quesada-Pérez, M., Galisteo-González, F. & Hidalgo-Álvarez, R. 2003 Looking into overcharging in model colloids through electrophoresis: asymmetric electrolytes. J. Chem. Phys. 118, 4183–4189.Google Scholar
Martín-Molina, A., Rodríguez-Beas, C., Hidalgo-Álvarez, R. & Quesada-Pérez, M. 2009 Effect of surface charge on colloidal charge reversal. J. Phys. Chem. B 113, 6834–6839.Google Scholar
Mezger, M., Schroder, H., Reichert, H., Schramm, S., Okasinski, J. S., Schoder, S., Honkimaki, V., Deutsch, M., Ocko, B. M., Ralston, J., Rohwerder, M., Stratmann, M. & Dosch, H. 2008 Molecular layering of fluorinated ionic liquids at a charged sapphire (0001) surface. Science 322, 424–428.Google Scholar
Netz, R. R. & Orland, H. 2000 Beyond Poisson Boltzmann: fluctuation effects and correlation functions. Eur. Phys. J. E 1, 203–214.CrossRefGoogle Scholar
O’Brien, R. W. 1983 The solution of the electrokinetic equations for colloidal particles with thin double layers. J. Colloid Interface Sci. 92, 204–216.Google Scholar
O’Brien, R. W. & White, L. R. 1978 Electrophoretic mobility of a spherical colloid. J. Chem. Soc. Faraday Trans. 2 74, 1607–1626.Google Scholar
Ohtaki, H. & Radnai, T. 1993 Structure and dynamics of hydrated ions. Chem. Rev. 93, 1157–1204.Google Scholar
Quesada-Pèrez, M., Gonzàlez-Tovar, E., Martìn-Molina, A., Lozada-Cassou, M. & Hidalgo-Àlvarez, R. 2005 Ion size correlations and charge reversal in real colloids. Colloid Surf. A 267, 24–30.Google Scholar
Raafatnia, S., Hickey, O. A., Sega, M. & Holm, C. 2014 Computing the electrophoretic mobility of large spherical colloids by combining explicit ion simulations with the standard electrokinetic model. Langmuir 30, 1758–1767.CrossRefGoogle ScholarPubMed
Russel, W. B., Saville, D. A. & Schowalter, W. R. 1989 Colloidal Dispersions. Cambridge University Press.Google Scholar
Santangelo, C. D. 2006 Computing counterion densities at intermediate coupling. Phys. Rev. E 73, 041512.CrossRefGoogle ScholarPubMed
Schnitzer, O. & Yariv, E. 2012 Macroscale description of electrokinetic flows at large zeta potentials: nonlinear surface conduction. Phys. Rev. E 86, 021503.Google Scholar
Semenov, I., Raafatnia, S., Sega, M., Lobaskin, V., Holm, C. & Kremer, F. 2013 Electrophoretic mobility and charge inversion of a colloidal particle studied by single-colloid electrophoresis and molecular dynamics simulations. Phys. Rev. E 87, 022302.Google Scholar
Smoluchowski, M. M. 1903 Contribution à la théorie de l’endosmose électrique et de quelques phenomènes corrélatifs. Bull. Inst. Acad. Sci. Cracovie 8, 182–199.Google Scholar
Squires, T. M. & Quake, S. R. 2005 Microfluidics: fluid physics at the nanoliter scale. Rev. Mod. Phys. 77, 977–1026.Google Scholar
Storey, B. D. & Bazant, M. Z. 2012 Effects of electrostatic correlations on electrokinetic phenomena. Phys. Rev. E 86, 056303.CrossRefGoogle ScholarPubMed
Strauss, U. P., Gershfeld, N. L. & Spiera, H. 1954 Charge reversal of cationic poly-4-vinylpyridine derivatives in KBr solutions. J. Am. Chem. Soc. 76, 5909–5911.Google Scholar
Torrie, G. M. & Valleau, J. P. 1980 Electrical double layers. I. Monte Carlo study of a uniformly charged surface. J. Chem. Phys. 73, 5807–5816.Google Scholar
Vanýsek, P. 2012 CRC Handbook of Chemistry and Physics, 93rd edn (ed. Hayes, W. M.), p. 5. CRC Press.Google Scholar