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Electro-hydrodynamic particle levitation on electrodes

Published online by Cambridge University Press:  22 February 2010

EHUD YARIV
EHUD YARIV*
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology, Haifa 32 000, Israel
*
†Email address for correspondence: udi@technion.ac.il
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Abstract

The thin-Debye-layer model is utilized to analyse the electro-hydrodynamic flow about a colloidal particle which is exposed to a direct ionic current, emitted by a proximate reactive electrode. This flow is driven by electro-osmotic slip on the particle, as well as a comparable slip on the electrode itself. The small particle–electrode separation allows for the use of singular perturbation. Thus, the electro-neutral bulk-fluid domain is decomposed into an ‘inner’ gap region, where the electric field and shear rate are large, and an ‘outer’ region, consisting of the remaining bulk domain, where they are moderate. Matched asymptotic expansions in both regions provide the requisite flow field. The intensive shear rate in the narrow gap region is associated with a lubrication-type pressure build-up, which is responsible for the leading-order hydrodynamic force on the particle. This force acts to repel the particle away from the electrode, thereby supporting it against gravity. Its magnitude is inversely proportional to the gap width. At large distances from the particle the fluid velocity decays with the third power of distance, while near the electrode it decays with the fourth power. The inward pointing flow near the electrode tend to entrain neighbouring particles, thereby resulting in two-dimensional particle clusters. For equal values of particle and anode zeta potentials, this process is dominated by the particle-slip contribution.

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Papers
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Journal of Fluid Mechanics , Volume 645 , 25 February 2010 , pp. 187 - 210
Copyright
Copyright © Cambridge University Press 2010

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References

REFERENCES

Bazant, M. Z., Chu, K. T. & Bayly, B. J. 2005 Current-voltage relations for electrochemical thin films. SIAM J. Appl. Math. 65, 1463–1484.CrossRefGoogle Scholar
Bazant, M. Z. & Squires, T. M. 2004 Induced-charge electrokinetic phenomena: theory and microfluidic applications. Phys. Rev. Lett. 92, 066101.CrossRefGoogle ScholarPubMed
Böhmer, M. 1996 In situ observation of 2-dimensional clustering during electrophoretic deposition. Langmuir 12, 5747–5750.CrossRefGoogle Scholar
Cox, R. G. 1997 Electroviscous forces on a charged particle suspended in a flowing liquid. J. Fluid Mech. 338, 1–34.CrossRefGoogle Scholar
Cox, R. G. & Brenner, H. 1967 The slow motion of a sphere through a viscous fluid towards a plane surface – II. Small gap widths, including inertial effects. Chem. Engng Sci. 22, 1753–1777.CrossRefGoogle Scholar
Dukhin, S. S. 1965 Diffusion-electrical theory of electrophoresis. In wentieth Intl Cong. on Pure and Applied Chemistry, vol. A72, p. 68, Moscow.Google Scholar
van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic Press.Google Scholar
Fagan, J. A., Sides, P. J. & Prieve, D. C. 2002 Vertical oscillatory motion of a single colloidal particle adjacent to an electrode in an ac electric field. Langmuir 18, 7810–7820.CrossRefGoogle Scholar
Fagan, J. A., Sides, P. J. & Prieve, D. C. 2004 Vertical motion of a charged colloidal particle near an AC polarized electrode with a non-uniform potential distribution: theory and experimental evidence. Langmuir 20, 4823–4834.CrossRefGoogle Scholar
Fagan, J. A., Sides, P. J. & Prieve, D. C. 2006 Mechanism of rectified lateral motion of particles near electrodes in alternating electric fields below 1 kHz. Langmuir 22, 9846–9852.CrossRefGoogle ScholarPubMed
Goldman, A. J., Cox, R. & Brenner, H. 1967 Slow viscous motion of a sphere parallel to a plane wall – I. Motion through a quiescent fluid. Chem. Engng Sci. 22, 637–651.CrossRefGoogle Scholar
Gong, T. & Marr, D. W. M. 2001 Electrically switchable colloidal ordering in confined geometries. Langmuir 17, 2301–2304.CrossRefGoogle Scholar
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.Google Scholar
Hinch, E. J. 1991 Perturbation Methods. Cambridge University Press.CrossRefGoogle Scholar
Jeffrey, D. J. 1978 The temperature field or electric potential around two almost touching spheres. J. Inst. Math. Appl. 22, 337–351.CrossRefGoogle Scholar
Jeffrey, D. J. & Chen, H. S. 1977 The virtual mass of a sphere moving towards a plane wall. J. Appl. Mech. 44, 166–167.CrossRefGoogle Scholar
Keh, H. J. & Anderson, J. L. 1985 Boundary effects on electrophoretic motion of colloidal spheres. J. Fluid Mech. 153, 417–439.CrossRefGoogle Scholar
Keh, H. J. & Lien, L. C. 1989 Electrophoresis of a dielectric sphere normal to a large conducting plane. J. Chin. Inst. Chem. Engng 20, 283–290.Google Scholar
Keller, J. B. 1963 Conductivity of a medium containing a dense array of perfectly conducting spheres or cylinders or nonconducting cylinders. J. Appl. Phys. 34, 991–993.CrossRefGoogle Scholar
Kim, J., Anderson, J. L., Garoff, S. & Sides, P. J. 2002 a Effects of zeta potential and electrolyte on particle interactions on an electrode under ac polarization. Langmuir 18 (14), 5387–5391.CrossRefGoogle Scholar
Kim, J., Guelcher, S. A., Garoff, S. & Anderson, J. L. 2002 b Two-particle dynamics on an electrode in ac electric fields. Adv. Colloid Interface 96, 131–142.CrossRefGoogle Scholar
Levich, V. G. 1962 Physicochemical Hydrodynamics. Prentice-Hall.Google Scholar
Loewenberg, M. & Davis, R. H. 1995 Near-contact electrophoretic particle motion. J. Fluid Mech. 288, 103–122.CrossRefGoogle Scholar
Lumsdon, S. O., Kaler, E. W., Williams, J. P. & Velev, O. D. 2003 Dielectrophoretic assembly of oriented and switchable two-dimensional photonic crystals. Appl. Phys. Lett. 82, 949–951.CrossRefGoogle Scholar
Moon, P. & Spencer, D. E. 1988 Field Theory Handbook. Springer.CrossRefGoogle Scholar
Nadal, F., Argoul, F., Hanusse, P., Pouligny, B. & Ajdari, A. 2002 Electrically induced interactions between colloidal particles in the vicinity of a conducting plane. Phys. Rev. E 65 (6), 61409.CrossRefGoogle ScholarPubMed
Newman, J. S. 1973 Electrochemical Systems. Prentice-Hall.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 (1), 204–216.CrossRefGoogle Scholar
Reed, L. D. & Morrison, F. A. 1976 Hydrodynamic interactions in electrophoresis. J. Colloid Interface Sci. 54, 117–133.CrossRefGoogle Scholar
Ristenpart, W. D., Aksay, I. A. & Saville, D. A. 2004 Assembly of colloidal aggregates by electrohydrodynamic flow: kinetic experiments and scaling analysis. Phys. Rev. E 69, 21405.CrossRefGoogle ScholarPubMed
Ristenpart, W. D., Aksay, I. A. & Saville, D. A. 2007 a Electrically driven flow near a colloidal particle close to an electrode with a Faradaic current. Langmuir 23, 4071–4080.CrossRefGoogle Scholar
Ristenpart, W. D., Aksay, I. A. & Saville, D. A. 2007 b Electrohydrodynamic flow around a colloidal particle near an electrode with an oscillating potential. J. Fluid Mech. 575, 83–109.CrossRefGoogle Scholar
Rubinstein, I. & Shtilman, L. 1979 Voltage against current curves of cation exchange membranes. J. Chem. Soc. Faraday Trans. 2 75, 231–246.CrossRefGoogle Scholar
Rubinstein, I. & Zaltzman, B. 2000 Electro-osmotically induced convection at a permselective membrane. Phys. Rev. E 62, 2238–2251.CrossRefGoogle Scholar
Rubinstein, I. & Zaltzman, B. 2001 Electro-osmotic slip of the second kind and instability in concentration polarization at electrodialysis membranes. Math. Models Methods Appl. Sci. 11, 263–300.CrossRefGoogle Scholar
Rubinstein, I., Zaltzman, B. & Kedem, O. 1997 Electric fields in and around ion-exchange membranes. J. Membr. Sci. 125, 17–21.CrossRefGoogle Scholar
Russel, W. B., Saville, D. A. & Schowalter, W. R. 1989 Colloidal Dispersions. Cambridge University Press.CrossRefGoogle Scholar
Sides, P. J. 2001 Electrohydrodynamic particle aggregation on an electrode driven by an alternating electric field normal to it. Langmuir 17, 5791–5800.CrossRefGoogle Scholar
Sides, P. J. 2003 Calculation of electrohydrodynamic flow around a single particle on an electrode. Langmuir 19, 2745–2751.CrossRefGoogle Scholar
Sides, P. J. & Tobias, C. W. 1980 Primary potential and current distribution around a bubble on an electrode. J. Electrochem. Soc. 127, 288–291.CrossRefGoogle Scholar
Sneddon, I. N. 1972 The Use of Integral Transforms. McGraw-Hill.Google Scholar
Solomentsev, Y., Böhmer, M. & Anderson, J. L. 1997 Particle clustering and pattern pormation during electrophoretic deposition: a hydrodynamic model. Langmuir 13, 6058–6068.CrossRefGoogle Scholar
Solomentsev, Y., Guelcher, S. A., Bevan, M. & Anderson, J. L. 2000 Aggregation dynamics for two particles during electrophoretic deposition under steady fields. Langmuir 16, 9208–9216.CrossRefGoogle Scholar
Squires, T. M. & Bazant, M. Z. 2004 Induced-charge electro-osmosis. J. Fluid Mech. 509, 217–252.CrossRefGoogle Scholar
Trau, M., Saville, D. A. & Aksay, I. A. 1996 Field-induced layering of colloidal crystals. Science 272, 706.CrossRefGoogle ScholarPubMed
Trau, M., Saville, D. A. & Aksay, I. A. 1997 Assembly of colloidal crystals at electrode interfaces. Langmuir 13, 6375–6381.CrossRefGoogle Scholar
Velev, O. & Kaler, E. 1999 In situ assembly of colloidal particles into miniaturized biosensors. Langmuir 15, 3693–3698.CrossRefGoogle Scholar
Wong, E. M. & Searson, P. C. 1999 ZnO quantum particle thin films fabricated by electrophoretic deposition. Appl. Phys. Lett. 74, 2939–2941.CrossRefGoogle Scholar
Yariv, E. 2008 Nonlinear electrophoresis of ideally polarizable spherical particles. Europhys. Lett. 82, 54004.CrossRefGoogle Scholar
Yariv, E. 2010 An asymptotic derivation of the thin-Debye-layer limit for electrokinetic phenomena. Chem. Engng Commun. 197, 3–17.CrossRefGoogle Scholar
Zaltzman, B. & Rubinstein, I. 2007 Electro-osmotic slip and electroconvective instability. J. Fluid Mech. 579, 173–226.CrossRefGoogle Scholar