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Electrokinetics at liquid/liquid interfaces

Published online by Cambridge University Press:  28 September 2011

Andrew J. Pascall  and
Todd M. Squires
Andrew J. Pascall
Affiliation:
Department of Chemical Engineering, University of California, Santa Barbara, CA 93106, USA
Todd M. Squires*
Affiliation:
Department of Chemical Engineering, University of California, Santa Barbara, CA 93106, USA
*
†Email address for correspondence: [email protected]
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Abstract

Electrokinetic effects at liquid/liquid interfaces have received considerably less attention than at solid/liquid interfaces. Because liquid/liquid interfaces are generally mobile, one might expect electrokinetic effects over a liquid/liquid interface to be faster than over an equivalent solid surface. The earliest predictions for the electrophoretic mobility of charged mercury drops – distinct approaches by Frumkin, along with Levich, and Booth – differed by , where is the radius of the drop and is the Debye length. Seeking to reconcile this rather striking discrepancy, Levine & O’Brien showed double-layer polarization to be the key ingredient. Without a physical mechanism by which electrokinetic effects are enhanced, however, it is difficult to know how general the enhancement is – whether it holds only for liquid metal surfaces, or more generally, for all liquid/liquid surfaces. By considering a series of systems in which a planar metal strip is coated with either a liquid metal or liquid dielectric, we show that the central physical mechanism behind the enhancement predicted by Frumkin is the presence of an unmatched electrical stress upon the electrolyte/liquid interface, which establishes a Marangoni stress on the droplet surface and drives it into motion. The source of the unbalanced electrokinetic stress on a liquid metal surface is clear – metals represent equipotential surfaces, so no field exists to drive an equal and opposite force on the surface charge. This might suggest that liquid metals represent a unique system, since dielectric liquids can support finite electric fields, which might be expected to exert an electrical stress on the surface charge that balances the electric stress. We demonstrate, however, that electrical and osmotic stresses on relaxed double layers internal to dielectric liquids precisely cancel, so that internal electrokinetic stresses generally vanish in closed, ideally polarizable liquids. The enhancement predicted by Frumkin for liquid mercury drops can thus be expected quite generally over ideally polarizable liquid drops. We then reconsider the electrophoretic mobility of spherical drops, and reconcile the approaches of Frumkin and Booth: Booth’s neglect of double-layer polarization leads to a standard electro-osmotic flow, without the enhancement, and Frumkin’s neglect of the detailed double-layer dynamics leads to the enhanced electrocapillary motion, but does not capture the (sub-dominant) electrophoretic motion. Finally, we show that, while the electrokinetic flow over electrodes coated with thin liquid films is faster than over solid/liquid interfaces, the Dukhin number, , which reflects the importance of surface conduction to bulk conduction, generally increases by a smaller amount [], where is the thickness of film and is the length of the electrode. This suggests that liquid/liquid interfaces may be utilized to enhance electrokinetic velocities in microfluidic devices, while delaying the onset of high- electrokinetic suppression.

JFM classification

Drops and Bubbles: Electrohydrodynamic effects Low-Reynolds-number flows: Low-Reynolds-number flows Micro-/Nano-fluid dynamics: Microfluidics
Type
Papers
Information
Journal of Fluid Mechanics , Volume 684 , 10 October 2011 , pp. 163 - 191
Copyright
Copyright © Cambridge University Press 2011

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References

1. Audry, M., Piednoir, A., Joseph, P. & Charlaix, E. 2010 Amplification of electro-osmotic flows by wall slippage: direct measurements on OTS-surfaces. Faraday Discuss. 146, 113–124.CrossRefGoogle ScholarPubMed
2. Bagotskaya, I. A. 1949 Dvizhenie zhidkikh i tverdykh metallicheskikh chastits v rastvorakh elektrolitov .5. opytnaya proverka uravnenii dvizheniya kapel rtuti v elektricheskom pole. Zh. Fiz. Khim. 23 (10), 1231–1238.Google Scholar
3. Bahga, S. S., Vinogradova, O. I. & Bazant, M. Z. 2010 Anisotropic electro-osmotic flow over super-hydrophobic surfaces. J. Fluid Mech. 644, 245–255.CrossRefGoogle Scholar
4. Baygents, J. C. & Saville, D. A. 1991 Electrophoresis of drops and bubbles. J. Chem. Soc. Faraday Trans. 87 (12), 1883–1898.CrossRefGoogle Scholar
5. Bazant, M. Z. & Squires, T. M. 2010 Induced-charge electrokinetic phenomena. Curr. Opin. Colloid Interface Sci. 15 (3), 203–213.CrossRefGoogle Scholar
6. Bocquet, L. & Charlaix, E. 2010 Nanofluidics, from bulk to interfaces. Chem. Soc. Rev. 39 (3), 1073.CrossRefGoogle ScholarPubMed
7. Booth, F. 1951 The cataphoresis of spherical fluid droplets in electrolytes. J. Chem. Phys. 19 (11), 1331–1336.CrossRefGoogle Scholar
8. Bouzigues, C. I., Tabeling, P. & Bocquet, L. 2008 Nanofluidics in the debye layer at hydrophilic and hydrophobic surfaces. Phys. Rev. Lett. 101 (11), 114503–4.CrossRefGoogle ScholarPubMed
9. Chu, K. T. & Bazant, M. Z. 2007 Surface conservation laws at microscopically diffuse interfaces. J. Colloid Interface Sci. 315 (1), 319–329.CrossRefGoogle ScholarPubMed
10. Churaev, N. V., Ralston, J., Sergeeva, I. P. & Sobolev, V. D. 2002 Electrokinetic properties of methylated quartz capillaries. Adv. Colloid Interface Sci. 96 (1–3), 265–278.CrossRefGoogle ScholarPubMed
11. Daiguji, H., Oka, Y. & Shirono, K. 2005 Nanofluidic diode and bipolar transistor. Nano Lett. 5 (11), 2274–2280.CrossRefGoogle ScholarPubMed
12. Daikhin, L. I. & Urbakh, M. 2003 Double layer capacitance and a microscopic structure of electrified liquid–liquid interfaces. J. Electroanalyt. Chem. 560 (1), 59–67.CrossRefGoogle Scholar
13. Davidson, C. & Xuan, X. 2008 Electrokinetic energy conversion in slip nanochannels. J. Power Sources 179 (1), 297–300.CrossRefGoogle Scholar
14. Dorfman, K. D. 2010 DNA electrophoresis in microfabricated devices. Rev. Mod. Phys. 82 (4), 2903.CrossRefGoogle Scholar
15. Dukhin, S. S. 1993 Nonequilibrium electric surface phenomena. Adv. Colloid Interface Sci. 44, 1–134.CrossRefGoogle Scholar
16. Frumkin, A. 1946 New electrocapillary phenomena. J. Colloid Sci. 1 (3), 277–291.CrossRefGoogle Scholar
17. Gamayunov, N. I., Mantrov, G. I. & Murtsovkin, V. A. 1992 Study of flows induced in the vicinity of conducting particles by an external electric-field. Colloid J. USSR 54 (1), 20–23.Google Scholar
18. Girault, H. & Schiffrin, D. 1989 Electrochemistry of liquid–liquid interfaces. In Electroanalytical Chemistry, vol. 15. Marcel-Dekker.Google Scholar
19. Görg, A., Weiss, W. & Dunn, M. J. 2004 Current two-dimensional electrophoresis technology for proteomics. Proteomics 4 (12), 3665–3685.CrossRefGoogle ScholarPubMed
20. Gorre, L., Ioannidis, E. & Silberzan, P. 1996 Rectified motion of a mercury drop in an asymmetric structure. Europhys. Lett. 33 (4), 267–272.CrossRefGoogle Scholar
21. Gorre-Talini, L. & Silberzan, P. 1997 Force-free motion of a mercury drop alternatively submitted to shifted asymmetric potentials. J. Phys. I 7 (11), 1475–1485.Google Scholar
22. Henry, D. C. 1931 The cataphoresis of suspended particles. Part 1. The equation of cataphoresis. Proc. R. Soc. Lond. A 133 (821), 106–129.Google Scholar
23. Joly, L., Ybert, C., Trizac, E. & Bocquet, L. 2006 Liquid friction on charged surfaces: from hydrodynamic slippage to electrokinetics. J. Chem. Phys. 125 (20).CrossRefGoogle ScholarPubMed
24. Karnik, R., Duan, C., Castelino, K., Daiguji, H. & Majumdar, A. 2007 Rectification of ionic current in a nanofluidic diode. Nano Lett. 7 (3), 547–551.CrossRefGoogle Scholar
25. Khair, A. S. & Squires, T. M. 2008a Fundamental aspects of concentration polarization arising from nonuniform electrokinetic transport. Phys. Fluids 20 (8), 087102–20.Google Scholar
26. Khair, A. S. & Squires, T. M. 2008b Surprising consequences of ion conservation in electro-osmosis over a surface charge discontinuity. J. Fluid Mech. 615, 323–334.CrossRefGoogle Scholar
27. Khair, A. S. & Squires, T. M. 2009a The influence of hydrodynamic slip on the electrophoretic mobility of a spherical colloidal particle. Phys. Fluids 21 (4), 042001–14.Google Scholar
28. Khair, A. S. & Squires, T. M. 2009b Ion steric effects on electrophoresis of a colloidal particle. J. Fluid Mech. 640, 343–356.CrossRefGoogle Scholar
29. Kim, S. J., Ko, S. H., Kang, K. H. & Han, J. 2010 Direct seawater desalination by ion concentration polarization. Nat. Nano. 5 (4), 297–301.Google Scholar
30. Landers, J. P. 2003 Molecular diagnostics on electrophoretic microchips. Analyt. Chem. 75 (12), 2919–2927.CrossRefGoogle ScholarPubMed
31. Larsen, R. J., Dickey, M. D., Whitesides, G. M. & Weitz, D. A. 2009 Viscoelastic properties of oxide-coated liquid metals. J. Rheol. 53 (6), 1305–1326.CrossRefGoogle Scholar
32. Lauga, E., Brenner, M. & Stone, H. 2007 Microfluidics: the no-slip boundary condition. In Handbook of Experimental Fluid Mechanics, pp. 1219–1240. Springer.Google Scholar
33. Leinweber, F. C., Eijkel, J. C. T., Bomer, J. G. & van den Berg, A. 2006 Continuous flow microfluidic demixing of electrolytes by induced charge electrokinetics in structured electrode arrays. Analyt. Chem. 78 (5), 1425–1434.CrossRefGoogle ScholarPubMed
34. Leinweber, F. C. & Tallarek, U. 2005 Concentration polarization-based nonlinear electrokinetics in porous media: induced-charge electroosmosis. J. Phys. Chem. B 109 (46), 21481–21485.CrossRefGoogle ScholarPubMed
35. Levich, V. G. 1962 Physicochemical Hydrodynamics. Prentice-Hall.Google Scholar
36. Levine, S. & O’Brien, R. N. 1973 Theory of electrophoresis of charged mercury drops in aqueous-electrolyte solution. J. Colloid Interface Sci. 43 (3), 616–629.Google Scholar
37. López-García, J., Aranda-Rascón, M. & Horno, J. 2008 Excluded volume effect on the electrophoretic mobility of colloidal particles. J. Colloid Interface Sci. 323 (1), 146–152.Google Scholar
38. Lyklema, J. 1995 Fundamentals of Interface and Colloid Science, vol. 2. Academic.Google Scholar
39. Lyklema, J. 2003 Electrokinetics after smoluchowski. Colloid Surf. A 222 (1–3), 5–14.CrossRefGoogle Scholar
40. Mani, A., Zangle, T. A. & Santiago, J. G. 2009 On the propagation of concentration polarization from microchannel–nanochannel interfaces part i: analytical model and characteristic analysis. Langmuir 25 (6), 3898–3908.CrossRefGoogle ScholarPubMed
41. Mansuripur, T. S., Pascall, A. J. & Squires, T. M. 2009 Asymmetric flows over symmetric surfaces: capacitive coupling in induced-charge electro-osmosis. New J. Phys. 11 (7), 075030.Google Scholar
42. Messinger, R. J. & Squires, T. M. 2010 Suppression of electro-osmotic flow by surface roughness. Phys. Rev. Lett. 105 (14), 144503.CrossRefGoogle ScholarPubMed
43. Monroe, C. W., Urbakh, M. & Kornyshev, A. A. 2009 Double-layer effects in electrowetting with two conductive liquids. J. Electrochem. Soc. 156 (1), P21.CrossRefGoogle Scholar
44. Muller, V., Sergeeva, I., Sobolev, V. & Churaev, N. 1986 Boundary effects in the theory of electrokinetic phenomena. Colloid J. USSR 48 (4), 606–614.Google Scholar
45. Murtsovkin, V. A. 1996 Nonlinear flows near polarized disperse particles. Colloid J. USSR 58 (3), 341–349.Google Scholar
46. O’Brien, R. W. 1983 The solution of the electrokinetic equations for colloidal particles with thin double layers. J. Colloid Interface Sci. 92 (1), 204–216.CrossRefGoogle Scholar
47. O’Brien, R. W. & White, L. R. 1978 Electrophoretic mobility of a spherical colloidal particle. J. Chem. Soc. Faraday Trans. 2 74, 1607–1626.Google Scholar
48. Ohshima, H. 1997 A simple expression for the electrophoretic mobility of charged mercury drops. J. Colloid Interface Sci. 189 (2), 376–378.CrossRefGoogle Scholar
49. Ohshima, H., Healy, T. W. & White, L. R. 1984 Electrokinetic phenomena in a dilute suspension of charged mercury drops. J. Chem. Soc. Faraday Trans. 2 80 (12), 1643–1667.Google Scholar
50. Pascall, A. J. & Squires, T. M. 2010a An automated, high-throughput experimental system for induced charge electrokinetics. Lab on a Chip 10 (18), 2350–2357.CrossRefGoogle ScholarPubMed
51. Pascall, A. J. & Squires, T. M. 2010b Induced charge electro-osmosis over controllably contaminated electrodes. Phys. Rev. Lett. 104 (8), 088301.CrossRefGoogle ScholarPubMed
52. Pennathur, S., Eijkel, J. C. T. & van den Berg, A. 2007 Energy conversion in microsystems: is there a role for micro/nanofluidics? Lab on a Chip 7 (10), 1234.Google Scholar
53. Poigin, B. N., Panfilov, A. M., Nemchenko, V. P. & Popel, S. I. 1977 Electrocapillary motion of mercury drops in strong electric-fields. Sov. Electrochem. 13 (3), 294–297.Google Scholar
54. Ren, Y. & Stein, D. 2008 Slip-enhanced electrokinetic energy conversion in nanofluidic channels. Nanotechnology 19 (19), 195707.Google Scholar
55. Russel, W. B., Saville, D. A. & Schowalter, W. R. 1989 Colloidal Dispersions. Cambridge University Press.Google Scholar
56. Schoch, R. B., Han, J. & Renaud, P. 2008 Transport phenomena in nanofluidics. Rev. Mod. Phys. 80 (3), 839–883.Google Scholar
57. So, J. & Dickey, M. D. 2011 Inherently aligned microfluidic electrodes composed of liquid metal. Lab on a Chip 11 (5), 905.CrossRefGoogle ScholarPubMed
58. Squires, T. M. 2008 Electrokinetic flows over inhomogeneously slipping surfaces. Phys. Fluids 20 (9), 092105.CrossRefGoogle Scholar
59. Squires, T. M. & Bazant, M. Z. 2004 Induced-charge electro-osmosis. J. Fluid Mech. 509, 217–252.CrossRefGoogle Scholar
60. Squires, T. M. & Quake, S. R. 2005 Microfluidics: fluid physics at the nanoliter scale. Rev. Mod. Phys. 77 (3), 977–1026.CrossRefGoogle Scholar
61. Tandon, V. & Kirby, B. J. 2008 Zeta potential and electroosmotic mobility in microfluidic devices fabricated from hydrophobic polymers: 2. Slip and interfacial water structure. Electrophoresis 29 (5), 1102–1114.Google Scholar
62. Velev, O. D. & Bhatt, K. H. 2006 On-chip micromanipulation and assembly of colloidal particles by electric fields. Soft Matt. 2 (9), 738.CrossRefGoogle ScholarPubMed
63. Vlassiouk, I., Smirnov, S. & Siwy, Z. 2008 Ionic selectivity of single nanochannels. Nano Lett. 8 (7), 1978–1985.CrossRefGoogle ScholarPubMed
64. Wang, Y., Stevens, A. L. & Han, J. 2005 Million-fold preconcentration of proteins and peptides by nanofluidic filter. Analyt. Chem. 77 (14), 4293–4299.Google Scholar
65. Zangle, T. A., Mani, A. & Santiago, J. G. 2009 On the propagation of concentration polarization from microchannel–nanochannel interfaces part II: numerical and experimental study. Langmuir 25 (6), 3909–3916.Google Scholar
66. Zhao, H. 2010 Electro-osmotic flow over a charged superhydrophobic surface. Phys. Rev. E 81 (6), 066314.Google Scholar