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Induced-charge electrokinetic flows about polarizable nano-particles: the thick-Debye-layer limit

Published online by Cambridge University Press:  25 May 2009

MOHAMMAD ABU HAMED  and
EHUD YARIV
MOHAMMAD ABU HAMED
Affiliation:
Department of Mathematics, Technion - Israel Institute of Technology, Haifa 32000, Israel
EHUD YARIV*
Affiliation:
Department of Mathematics, Technion - Israel Institute of Technology, Haifa 32000, Israel
*
†Email address for correspondence: yarive@technion.ac.il
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Abstract

Using the standard weak-field approximation, we analyse the steady-state electrokinetic flow about an uncharged ideally polarizable spherical particle for the case of a Debye thickness which is large compared with the particle size. The dimensionless problem is governed by two parameters: β, the applied field magnitude (normalized with the thermal scale), and λ, the Debye thickness (normalized with particle size). The double limit β ≪ 1 and λ ≫ 1 is singular, and the resolution of the flow field requires the use of inner–outer asymptotic expansions in the spirit of Proudman & Pearson (J. Fluid Mech., vol. 2, 1957, p. 237). Two asymptotic limits are identified: the ‘moderately thick’ limit βλ ≪ 1, in which the outer domain is characterized by the Debye thickness, and the ‘super-thick’ limit βλ ≫ 1, in which the outer domain represents the emergence of electro-migration in the leading-order ionic-transport process. The singularity is stronger in the comparable two-dimensional flow about a circular cylinder, where a switchback mechanism in the moderately thick limit modifies the familiar O(β2) leading-order flow to O(β2 ln λ).

Type
Papers
Information
Journal of Fluid Mechanics , Volume 627 , 25 May 2009 , pp. 341 - 360
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions, 3rd edn. Dover.Google Scholar
Acrivos, A. & Taylor, T. D. 1962 Heat and mass transfer from single spheres in stokes flow. Phys. Fluids 5 (4), 387–394.CrossRefGoogle Scholar
Ajdari, A. 2000 Pumping liquids using asymmetric electrode arrays. Phys. Rev. E 61 (1), R45–R48.CrossRefGoogle ScholarPubMed
Anderson, J. L. 1989 Colloid transport by interfacial forces. Annu. Rev. Fluid Mech. 30, 139–165.CrossRefGoogle Scholar
Bazant, M. Z. & Squires, T. M. 2004 Induced-charge electrokinetic phenomena: theory and microfluidic applications. Phys. Rev. Lett. 92 (6).CrossRefGoogle ScholarPubMed
Ben, Y. & Chang, H. C. 2002 Nonlinear Smoluchowski slip velocity and micro-vortex generation. J. Fluid Mech. 461, 229–238.CrossRefGoogle Scholar
Ben, Y., Demekhin, E. A. & Chang, H. C. 2004 Nonlinear electrokinetics and “superfast” electrophoresis. J. Colloid Interface Sci. 276, 483–497.CrossRefGoogle ScholarPubMed
Böhmer, M. 1996 In situ observation of 2-dimensional clustering during electrophoretic deposition. Langmuir 12, 5747–5750.CrossRefGoogle Scholar
Brown, A. B. D., Smith, C. G. & Rennie, A. R. 2000 Pumping of water with ac electric fields applied to asymmetric pairs of microelectrodes. Phys. Rev. E 63 (1), 016305.CrossRefGoogle ScholarPubMed
Chu, K. T. & Bazant, M. Z. 2006 Nonlinear electrochemical relaxation around conductors. Phys. Rev. E 74, 11501.CrossRefGoogle ScholarPubMed
Dukhin, A. S. 1986 Pair interaction of disperse particles in electric-field. 3. Hydrodynamic interaction of ideally polarizable metal particles and dead biological cells. Colloid J. USSR 48, 376–381.Google Scholar
Dukhin, S. S. 1991 Electrokinetic phenomena of the 2nd kind and their applications. Adv. Colloid Interface 35, 173–196.CrossRefGoogle Scholar
Dukhin, A. S., Vincent, B. & Mozes, N. 1993 Biospecific mechanism of double layer formation and peculiarities of cell electrophoresis. Colloid Surface A 73, 29–48.CrossRefGoogle Scholar
Eijkel, J. & Berg, A. 2005 Nanofluidics: what is it and what can we expect from it? Microfluid. Nanofluid. 1, 249–267.CrossRefGoogle 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 (2), 197–203.Google Scholar
Gangwal, S., Cayre, O., Bazant, M. & Velev, O. 2008 Induced-charge electrophoresis of metallodielectric particles. Phys. Rev. Lett. 100, 58302.CrossRefGoogle ScholarPubMed
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 (4), 4019–4028.CrossRefGoogle Scholar
Green, N. G., Ramos, A., González, A., Morgan, H. & Castellanos, A. 2000 Fluid flow induced by nonuniform ac electric fields in electrolytes on microelectrodes. I. Experimental measurements. Phys. Rev. E 61 (4), 4011–4018.CrossRefGoogle ScholarPubMed
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice-HallGoogle Scholar
Harnett, C., Templeton, J., Dunphy-Guzman, K., Senousy, Y. & Kanouff, M. 2008 Model based design of a microfluidic mixer driven by induced charge electroosmosis. Lab Chip 8 (4), 565–572.CrossRefGoogle ScholarPubMed
Hinch, E. J. 1991 Perturbation Methods. Cambridge University Press.CrossRefGoogle Scholar
Hückel, E. 1924 The cataphoresis of the sphere. Phys. Z. 25, 204–210.Google 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. & Chen, S. 1993 Diffusiophoresis and electrophoresis of colloidal cylinders. Langmuir 9 (4), 1142–1149.CrossRefGoogle Scholar
Keh, H., Horng, K. & Kuo, J. 2006 Boundary effects on electrophoresis of colloidal cylinders. J. Fluid Mech. 231, 211–228.CrossRefGoogle Scholar
Levich, V. G. 1962 Physicochemical Hydrodynamics. Prentice-Hall.Google Scholar
Levitan, J., Devasenathipathy, S., Studer, V., Ben, Y., Thorsen, T., Squires, T. & Bazant, M. 2005 Experimental observation of induced-charge electro-osmosis around a metal wire in a microchannel. Colloids Surface A 267 (1–3), 122–132.CrossRefGoogle Scholar
Miloh, T. 2008 Dipolophoresis of nanoparticles. Phys. Fluids 20, 107105.CrossRefGoogle Scholar
Murtsovkin, V. A. 1996 Nonlinear flows near polarized disperse particles. Colloid J. 58 (3), 341–349.Google Scholar
Natarajan, R. & Schechter, R. S. 1986 The solution of the nonlinear Poisson-Boltzmann equation for thick, spherical double-layers. J. Colloid Interface Sci. 113 (1), 241–247.CrossRefGoogle Scholar
Proudman, I. & Pearson, J. R. A. 1957 Expansions at small Reynolds number for the flow past a sphere and a circular cylinder. J. Fluid Mech. 2, 237–531.CrossRefGoogle Scholar
Ramos, A., Morgan, H., Green, N. & Castellanos, A. 1998 AC electrokinetics: a review of forces in microelectrode structures. J. Phys. D: Appl. Phys. 31, 2338–2353.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
Rose, K., Meier, J., Dougherty, G. & Santiago, J. 2007 Rotational electrophoresis of striped metallic microrods. Phys. Rev. E 75, 11503.CrossRefGoogle ScholarPubMed
Rubinstein, I. & Shtilman, L. 1979 Voltage against current curves of cation exchange membranes. J. Chem. Soc. Farad. T. 2 75, 231–246.CrossRefGoogle Scholar
Rubinstein, I. & Zaltzman, B. 2001 Electro-osmotic slip of the second kind and instability in concentration polarization at electrodialysis membranes. Math. Mod. Meth. Appl. S. 11, 263–300.CrossRefGoogle Scholar
Saintillan, D. 2008 Nonlinear interactions in electrophoresis of ideally polarizable particles. Phys. Fluids 20, 067104.CrossRefGoogle Scholar
Saintillan, D. In preparation. Nonlinear effects in electrophoresis of polarizable particles near rigid boundaries.Google Scholar
Saintillan, D., Darve, E. & Shaqfeh, E. S. G. 2006 a Hydrodynamic interactions in the induced-charge electrophoresis of colloidal rod dispersions. J. Fluid Mech. 563, 223–259.CrossRefGoogle Scholar
Saintillan, D., Shaqfeh, E. S. G. & Darve, E. 2006 b Stabilization of a suspension of sedimenting rods by induced-charge electrophoresis. Phys. Fluids 18 (12), 121503.CrossRefGoogle Scholar
Saville, D. A. 1977 Electrokinetic effects with small particles. Annu. Rev. Fluid Mech. 9, 321–337.CrossRefGoogle Scholar
Schoch, R., Han, J. & Renaud, P. 2008 Transport phenomena in nanofluidics. Rev. Mod. Phys. 80, 839–883.CrossRefGoogle Scholar
Shilov, V. N. & Simonova, T. S. 1981 Polarization of electric double-layer of disperse particles and dipolophoresis in a steady (dc) field. Colloid J. USSR 43 (1), 90–96.Google 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
Simonov, I. N. & Dukhin, S. S. 1973 Theory of electrophoresis of solid conducting particles in case of ideal polarization of a thin diffuse double-layer. Colloid J. USSR 35 (1), 191–193.Google Scholar
Simonova, T. S., Shilov, V. N. & Shramko, O. A. 2001 Low-frequency dielectrophoresis and the polarization interaction of uncharged spherical particles with an induced Debye atmosphere of arbitrary thickness. Colloid J. 63 (1), 108–115.CrossRefGoogle 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
Squires, T. M. & Bazant, M. Z. 2004 Induced-charge electro-osmosis. J. Fluid Mech. 509, 217–252.CrossRefGoogle Scholar
Squires, T. M. & Bazant, M. Z. 2006 Breaking symmetries in induced-charge electro-osmosis and electrophoresis. J. Fluid Mech. 560, 65–101.CrossRefGoogle Scholar
Stein, D., Kruithof, M. & Dekker, C. 2004 Surface-charge-governed ion transport in nanofluidic channels. Phys. Rev. Lett. 93, 35901.CrossRefGoogle ScholarPubMed
Subramanian, R. S. 1981 Slow migration of a gas bubble in a thermal gradient. AIChE J. 27, 646–654.CrossRefGoogle Scholar
Thamida, S. & Chang, H. C. 2002 Nonlinear electrokinetic ejection and entrainment due to polarization at nearly insulated wedges. Phys. Fluids 14, 4315.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
Van Dyke, M. 1964 Perturbation Methods in Fluid Mechanics. Academic pressGoogle Scholar
Wang, S., Chen, H., Lee, C., Yu, C. & Chang, H. 2006 AC electro-osmotic mixing induced by non-contact external electrodes. Biosensors and Bioelectronics 22 (4), 563–567.CrossRefGoogle ScholarPubMed
Yariv, E. 2005 Induced-charge electrophoresis of nonspherical particles. Phys. Fluids 17 (5), 051702.CrossRefGoogle Scholar
Yariv, E. 2008 a Nonlinear electrophoresis of ideally polarizable spherical particles. Europhys. Lett. 82, 54004.CrossRefGoogle Scholar
Yariv, E. 2008 b Slender-body approximations for electro-phoresis and electro-rotation of polarizable particles. J. Fluid Mech. 613, 85–94.CrossRefGoogle Scholar
Yariv, E. 2009 Boundary-induced electrophoresis of uncharged conducting particles: remote-wall approximations. Proc. R. Soc. A. 465, 709–723.CrossRefGoogle Scholar
Yariv, E. & Miloh, T. 2008 Electro-convection about conducing particles. J. Fluid Mech. 595, 163–172.CrossRefGoogle Scholar
Yossifon, G., Frankel, I. & Miloh, T. 2006 On electro-osmotic flows through microchannel junctions. Phys. Fluids 18, 117108.CrossRefGoogle Scholar
Yossifon, G., Frankel, I. & Miloh, T. 2007 Symmetry breaking in induced-charge electro-osmosis over polarizable spheroids. Phys. Fluids 19, 068105.CrossRefGoogle Scholar
Yossifon, G., Frankel, I. & Miloh, T. 2009 Macro-scale description of transient electro-kinetic phenomena over polarizable dielectric solids. J. Fluid Mech. 620, 241–262.CrossRefGoogle Scholar
Zaltzman, B. & Rubinstein, I. 2007 Electro-osmotic slip and electroconvective instability. J. Fluid Mech. 579, 173–226.CrossRefGoogle Scholar
Zhao, H. & Bau, H. 2007 a Microfluidic chaotic stirrer utilizing induced-charge electro-osmosis. Phys. Rev. E 75.CrossRefGoogle ScholarPubMed
Zhao, H. & Bau, H. 2007 b On the effect of induced electro-osmosis on a cylindrical particle next to a surface. Langmuir 23, 4053–4063.CrossRefGoogle ScholarPubMed