Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-19T18:07:08.492Z Has data issue: false hasContentIssue false

Electrokinetic instabilities of non-dilute colloidal suspensions

Published online by Cambridge University Press:  25 January 2009

GURU NAVANEETHAM
Affiliation:
Department of Mechanical Engineering, Arizona State University, Tempe, AZ, USA
JONATHAN D. POSNER*
Affiliation:
Department of Mechanical Engineering, Arizona State University, Tempe, AZ, USA Department of Chemical Engineering, Arizona State University, Tempe, AZ, USA
*
Email address for correspondence: [email protected]

Abstract

An experimental investigation of electrokinetic instabilities (EKIs) of non-dilute colloidal suspensions in microchannels is presented. The addition of charged colloidal particles to a solution can alter the solution's electrical conductivity and permittivity as well as the average particle electrophoretic mobility. In this work, a colloidal (500 nm polystyrene) volume fraction gradient is achieved at the intersection of a Y-shaped polydimethylsiloxane (PDMS) microchannel. The flow becomes unstable when the electroviscous stretching and folding of the conductivity and permittivity interfaces exceed the dissipative effects of viscous forces and particle diffusion. The suspension conductivity as a function of the particle volume fraction is presented. The critical conditions required for flow instability are measured along with a scaling analysis which shows that the flow becomes unstable due to a coupling of applied electric fields and the electrical conductivity and permittivity gradients in the flow. The flow becomes unstable at a critical electric Rayleigh number of Rae = 1.8 × 105 for a wide range of applied electric fields spanning three orders of magnitude and colloid volume fractions varying two orders of magnitude. EKIs of non-dilute colloidal suspensions may be important for applications such as the electrophoretic deposition of micropatterned colloidal assemblies, electrorheological devices and on-chip electrokinetic (EK) manipulation of colloids.

Type
Papers
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

Ahualli, S., Jimenez, M. L., Delgado, A. V., Arroyo, F. J. & Carrique, F. 2006 Electroacoustic and dielectric dispersion of concentrated colloidal suspensions. IEEE Trans. Dielec. Elec. Insul. 13, 657663.CrossRefGoogle Scholar
Arroyo, F. J., Carrique, F., Bellini, T. & Delgado, A. V. 1999 Dielectric dispersion of colloidal suspensions in the presence of stern layer conductance: particle size effects. J. Colloid Interface Sci. 210, 194199.CrossRefGoogle ScholarPubMed
Batchelor, G. K. 1977 Effect of Brownian-motion on bulk stress in a suspension of spherical-particles. J. Fluid Mech. 83, 97117.CrossRefGoogle Scholar
Baygents, J. & Baldessari, F. 1998 Electrohydrodynamic instability in a thin fluid layer with an electrical conductivity gradient. Phys. Fluids 10, 301311.CrossRefGoogle Scholar
Bazant, M. Z. & Squires, T. M. 2004 Induced-charge electrokinetic phenomena: theory and microfluidic applications. Phys. Rev. Lett. 92, 066101-1 to 066101-4.CrossRefGoogle ScholarPubMed
Bonincontro, A., Cametti, C. & Biasio, A. D. 1980 Effect of volume ion polarisations on Maxwell–Wagner dielectric dispersions. J. Phys. D. 13, 15291535.Google Scholar
Booth, F. 1950 The cataphoresis of spherical, solid non-conducting particles in a symmetrical electrolyte. Proc. R. Soc. Lond. A 203, 514.Google Scholar
Carrique, F., Arroyo, F. J. & Delgado, A. V. 2001 Electrokinetics of concentrated suspensions of spherical colloidal particles: effect of a dynamic stern layer on electrophoresis and DC conductivity. J. Colloid Interface Sci. 243, 351361.CrossRefGoogle Scholar
Carrique, F., Arroyo, F. J. & Delgado, A. V. 2002 Electrokinetics of concentrated suspensions of spherical colloidal particles with surface conductance, arbitrary zeta potential, and double-layer thickness in static electric fields. J. Colloid Interface Sci. 252, 126137.CrossRefGoogle ScholarPubMed
Carrique, F., Arroyo, F. J., Jimenez, M. L. & Delgado, A. V. 2003 a Dielectric response of concentrated colloidal suspensions. J. Chem. Phys. 118, 19451956.CrossRefGoogle Scholar
Carrique, F., Arroyo, F. J., Jimenez, M. L. & Delgado, A. V. 2003 b Influence of double-layer overlap on the electrophoretic mobility and DC conductivity of a concentrated suspension of spherical particles. J. Phys. Chem. B 107, 31993206.CrossRefGoogle Scholar
Chen, C. H., Lin, H., Lele, S. K. & Santiago, J. G. 2005 Convective and absolute electrokinetic instability with conductivity gradients. J. Fluid Mech. 524, 263303.CrossRefGoogle Scholar
de Kruif, C. G., van Iersel, E. M. F., Vrij, A. & Russel, W. B. 1986 Hard sphere colloidal dispersions: viscosity as a function of shear rate & volume fraction. J. Chem. Phys. 83, 47174725.CrossRefGoogle Scholar
Ding, J. M. & Keh, H. J. 2001 The electrophoretic mobility and electric conductivity of a concentrated suspension of colloidal spheres with arbitrary double-layer thickness. J. Colloid Interface Sci. 236, 180193.CrossRefGoogle ScholarPubMed
Duffy, D. C., McDonald, J. C., Schueller, O. J. A. & Whitesides, G. M. 1998 Rapid prototyping of microfluidic systems in poly(dimethylsiloxane). Analyt. Chem. 70, 49744984.CrossRefGoogle ScholarPubMed
Dukhin, S. & Derjaguin, B. V. 1974 Surface and Colloid Science. Wiley.Google Scholar
Dukhin, S. S. 1993 Nonequilibrium electric surface phenomena. Adv. Colloid Interface Sci. 44, 1134.CrossRefGoogle Scholar
Espin, M. J., Delgado, A. V. & Rejon, L. 2005 Electrorheologial properties of hematite/silicone oil suspensions under dc fields. J. Non-Newton. Fluid Mech. 125, 110.Google Scholar
Fabbian, L., Gotze, W., Sciortino, F., Tartaglia, P. & Thiery, F. 1999 Ideal glass–glass transitions and logarithmic decay of correlations in a simple system. Phys. Rev. E 59, R1347R1350.CrossRefGoogle Scholar
Franosch, T., Fuchs, M., Gotze, W., Mayr, M. R. & Singh, A. P. 1997 Theory for the reorientational dynamics in glass-forming liquids. Phys. Rev. E 56, 56595674.Google Scholar
Fuchs, M. & Cates, M. E. 2002 Theory of nonlinear rheology and yielding of dense colloidal suspensions. Phys. Rev. Lett. 89, 248304-1 to 248304-4.CrossRefGoogle ScholarPubMed
Gregory, A. P. & Clarke, R. N. 2005 Traceable measurements of the static permittivity of dielectric reference liquids over the temperature range 5–50 degrees C. Meas. Sci. Technol. 16, 15061516.CrossRefGoogle Scholar
Guth, E. & Gold, O. 1938 Physical Review 53, 322.Google Scholar
Hayward, R. C., Saville, D. A. & Aksay, I. A. 2000 Electrophoretic assembly of colloidal crystals with optically tunable micropatterns. Nature 404, 5659.CrossRefGoogle ScholarPubMed
Henry, D. C. 1931 The cataphoresis of suspended particles. Part 1. The equation of cataphoresis. Proc. R. Soc. of Lond. A 133, 106.Google Scholar
Hoburg, J. F. & Melcher, J. R. 1976 Internal electrohydrodynamic instability and mixing of fluids with orthogonal field and conductivity gradients. J. Fluid Mech. 73, 333351.CrossRefGoogle Scholar
Hollingsworth, A. D. & Saville, D. A. 2004 Dielectric spectroscopy and electrophoretic mobility measurements interpreted with the standard electrokinetic model. J. Colloid Interface Sci. 272, 235245.CrossRefGoogle ScholarPubMed
Homsy, G. M. 1987 Viscous fingering in porous-media. Ann. Rev. Fluid Mech. 19, 271311.CrossRefGoogle Scholar
Huckel, E. 1924 Die Kataphorese der Kugel. Physik. Z. 25, 204.Google Scholar
Hunter, R. J. 1981 Zeta Potential in Colloid Science. Academic.Google Scholar
Ikazaki, F., Kawai, A., Uchida, K., Kawakami, T., Edamura, K., Sakurai, K., Anzai, H. & Asako, Y. 1998 Mechanisms of electrorheology: the effect of the dielectric property. J. Phys. D 31, 336347.Google Scholar
Jang, S. P. & Choi, S. U. S. 2006 Cooling performance of a microchannel heat sink with nanofluids. Appl. Therm. Engng 26, 24572463.CrossRefGoogle Scholar
Jeffrey, D. J. 1973 Conduction through a random suspension of spheres. Proc. R. Soc. Lond. A 335, 355367.Google Scholar
Johnson, T. J. & Davis, E. J. 1999 An analysis of electrophoresis of concentrated suspensions of colloidal particles. J. Colloid Interface Sci. 215, 397408.CrossRefGoogle ScholarPubMed
Keh, H. J. & Hsu, W. T. 2002 Electric conductivity of a suspension of charged colloidal spheres with thin but polarized double layers. Colloid Polym. Sci. 280, 922928.CrossRefGoogle Scholar
Kijlstra, J., Vanleeuwen, H. P. & Lyklema, J. 1992 Effects of surface conduction on the electrokinetic properties of colloids. J. Chem. Soc., Faraday Trans. 88, 34413449.CrossRefGoogle Scholar
Kijlstra, J., Vanleeuwen, H. P. & Lyklema, J. 1993 Low-frequency dielectric-relaxation of hematite and silica sols. Langmuir 9, 16251633.CrossRefGoogle Scholar
Kirby, B. J. & Hasselbrink, E. F. 2004 a Zeta potential of microfluidic substrates. Part 1. Theory, experimental techniques, and effects on separations. Electrophoresis 25, 187202.CrossRefGoogle Scholar
Kirby, B. J. & Hasselbrink, E. F. 2004 b Zeta potential of microfluidic substrates. Part 2. Data for polymers. Electrophoresis 25, 187213.CrossRefGoogle Scholar
ozak, M. W. & Davis, E. J. 1989 Electrokinetics of concentrated suspensions and porous-media. Part 2. Moderately thick electrical double-layers. J. Colloid Interface Sci. 129, 166174.Google Scholar
Krieger, I. M. & Dougherty, T. J. 1959 A mechanism for non-Newtonian flow in suspensions of rigid spheres. Trans. Soc. Rheol. 3, 137.CrossRefGoogle Scholar
Kuwabara, S. 1959 The forces experienced by randomly distributed parellel circular cylinders or spheres in a viscous flow at small reynolds numbers. J. Phys. Soc. Jpn 14, 527532.CrossRefGoogle Scholar
Larson, R. G. 1999 The Structure and Rheology of Complex Fluids. Oxford University Press.Google Scholar
Lee, E., Chih, M. H. & Hsu, J. P. 2001 Conductivity of a concentrated spherical colloidal dispersion. J. Phys. Chem. B 105, 747753.CrossRefGoogle Scholar
Levine, S. & Neale, G. H. 1974 Prediction of electrokinetic phenomena within multiparticle systems. Part 1. Electrophoresis and electroosmosis. J. Colloid Interface Sc. 47, 520529.CrossRefGoogle Scholar
Levine, S., Neale, G. & Epstein, N. 1976 Prediction of electrokinetic phenomena within multiparticle systems. J. Colloid Interface Sci. 57, 424437.CrossRefGoogle Scholar
Lin, H., Storey, B. D., Oddy, M. H., Chen, C. H. & Santiago, J. G. 2004 Instability of electrokinetic microchannel flows with conductivity gradients. Phys. Fluids 16, 19221935.CrossRefGoogle Scholar
Lyklema, J. 2005 Fundamentals of Interface and Colloid Science. Elsevier Academic Press.Google Scholar
Mangelsdorf, C. S. & White, L. R. 1990 Effects of stern-layer conductance on electrokinetic transport-properties of colloidal particles. J. Chem. Soc., Faraday Trans. 86, 28592870.CrossRefGoogle Scholar
Maxwell, J. C. 1873 Electricity and Magnetism. Oxford University. Press.Google Scholar
McKenzie, D. R., McPhedran, R. C. & Derrick, G. H. 1978 Conductivity of lattices of spheres. Part 2. Body-centered and face-centered cubic lattices. Proc. R. Soc. Lond. A 362, 211232.Google Scholar
Melcher, J. R. & Taylor, G. I. 1969 Electrohydrodynamics: a review of the role of interfacial shear stress. Ann. Rev. Fluid Mech. 1, 111146.CrossRefGoogle Scholar
Mooney, M. 1951 The viscosity of a concentrated suspension of spherical particles. J. Colloid Sci. 6, 162.CrossRefGoogle Scholar
Navaneetham, G. 2007 Electrokinetic Instabilities in Non-Dilute Colloidal Suspensions. Arizona State University.Google Scholar
Obrien, R. W. 1981 The electrical-conductivity of a dilute suspension of charged-particles. J. Colloid Interface Sci. 81, 234248.CrossRefGoogle Scholar
Obrien, R. W. 1983 The solution of the electrokinetic equations for colloidal particles with thin double-layers. J. Colloid Interface Sci. 92, 204216.CrossRefGoogle Scholar
Obrien, R. W. & White, L. R. 1978 Electrophoretic mobility of a spherical colloidal particle. J. Chem. Soc. Faraday Trans. 74, 16071626.CrossRefGoogle Scholar
Oddy, M. H. & Santiago, J. G. 2005 Multiple-species model for electrokinetic instability. Phys. Fluids 17, 064108-1 to 064108-17.CrossRefGoogle Scholar
Oddy, M. H., Santiago, J. G. & Mikkelsen, J. C. 2001 Electrokinetic instability micromixing. Analyt. Chem. 73, 58225832.CrossRefGoogle ScholarPubMed
Ohshima, H. 1999 Electrical conductivity of a concentrated suspension of spherical colloidal particles. J. Colloid Interface Sci. 212, 443448.CrossRefGoogle ScholarPubMed
Ohshima, H. 2000 Electrical conductivity of a concentrated suspension of soft particles. J. Colloid Interface Sci. 229, 307309.CrossRefGoogle ScholarPubMed
Ohshima, H., Healy, T. W. & White, L. R. 1983 Approximate analytic expressions for the electrophoretic mobility of spherical colloidal particles and the conductivity of their dilute suspensions. J. Chem. Soc., Faraday Trans. 79, 16131628.CrossRefGoogle Scholar
O'Konski, C. T. 1960 Electric properties of macromolecules. Part 5 Theory of ionic polarizations in polyelectrolytes. 64, 605–619.Google Scholar
Overbeek, J. T. 1950 Quantitative interpretation of the electrophonetic velocity of colloids. Advan. Colloid Sci. 3, 97.Google Scholar
Ozen, O., Aubry, N., Papageorgiou, D. T. & Petropoulos, P. G. 2006 Electrohydrodynamic linear stability of two immiscible fluids in channel flow. Electrochim. Acta 51, 53165323.CrossRefGoogle Scholar
Perez, A. T. & Lemaire, E. 2004 Measuring the electrophoretic mobility of concentrated suspensions in nonaqueous media. J. Colloid Interface Sci. 279, 259265.CrossRefGoogle ScholarPubMed
Posner, J. D. & Santiago, J. G. 2006 Convective instability of electrokinetic flows in a cross-shaped microchannel. J. Fluid Mech. 555, 142.CrossRefGoogle Scholar
Preisler, J. & Yeung, E. S. 1996 Characterization of nonbonded poly(ethylene oxide) coating for capillary electrophoresis via continuous monitoring of electroosmotic flow. Analyt. Chem. 68, 28852889.CrossRefGoogle ScholarPubMed
Probstein, R. F. 1994 Physicochemical Hydrodynamics: An Introduction. John Wiley.CrossRefGoogle Scholar
Rosen, L. A. & Saville, D. A. 1991 Dielectric-spectroscopy of colloidal dispersions: Comparisons between experiment and theory. Langmuir 7, 3642.CrossRefGoogle Scholar
Russel, W. B., Saville, D. A. & Schowalter, W. R. 1989 Colloidal Dispersions. Cambridge University Press.CrossRefGoogle Scholar
Saffman, P. G. & Taylor, G. 1958 The penetration of a fluid into a porous medium or hele-shaw cell containing a more viscous liquid. Proc. R. Soc. Lond. A 245, 312–&.Google Scholar
Sangani, A. S. & Acrivos, A. 1983 The effective conductivity of a periodic array of spheres. Proc. R. Soc. Lond. A 386, 263275.Google Scholar
Saville, D. A. 1979 Electrical-conductivity of suspensions of charged-particles in ionic-solutions. J. Colloid Interface Sci. 71, 477490.CrossRefGoogle Scholar
Saville, D. A. 1997 Electrohydrodynamics: the Taylor–Melcher leaky dielectric model. Ann. Rev. Fluid Mech. 29, 2764.CrossRefGoogle Scholar
Sigurdson, M., Wang, D. & Meinhart, C. D. 2005 Electrothermal stirring for heterogeneous immunoassays. Lab Chip 5, 13661373.CrossRefGoogle ScholarPubMed
Simha, R. 1940 The influence of brownian movement on the viscosity of solutions. J. Phys. Chem. 44, 25.CrossRefGoogle Scholar
Smoluchowski, M. 1918 Versuch einer mathematischen theorie der koagulationskinetik koiloider lösungen. Z. Phys. Chem. 92, 129.CrossRefGoogle Scholar
Stone, H. A. & Kim, S. 2001 Microfluidics: basic issues, applications, and challenges. Aiche J. 47, 12501254.CrossRefGoogle Scholar
Storey, B. D., Tilley, B. S., Lin, H. & Santiago, J. G. 2005 Electrokinetic instabilities in thin microchannels. Phys. Fluids 17, 018103-1 to 018103-4.CrossRefGoogle Scholar
Stratton, J. A. 1941 Electromagnetic Theory. McGraw-Hill.Google Scholar
Tirado, M. C., Arroyo, F. J., Delgado, A. V. & Grosse, C. 2000 Measurement of the low-frequency dielectric properties of colloidal suspensions: comparison between different methods. J. Colloid Interface Sci. 227, 141146.CrossRefGoogle ScholarPubMed
Trau, M., Sankaran, S., Saville, D. A. & I. A., A. (1995). Electric field induced pattern formations in colloidal dispersions. Nature 374, 437439.CrossRefGoogle Scholar
Trau, M., Saville, D. A. & Aksay, I. A. 1996 Field-induced layering of colloidal crystals. Science 272, 706709.CrossRefGoogle ScholarPubMed
Vand, V. 1948 Viscosity of solutions and suspensions. Part 2. J. Phys. Chem. 52, 277.CrossRefGoogle Scholar
Voegtli, L. P. & Zukoski, C. F. 1991 Adsorption of ionic species to the surface of polystyrene latexes. J. Colloid Interface Sci. 141, 92108.CrossRefGoogle Scholar
Watillon, A. & Stone-Masui, J. 1972 Surface conductance in dispersions of spherical particles – study of monodisperse polystyrene latices. J. Electroanalyt. Chem. 37, 143160.CrossRefGoogle Scholar
Wereley, S. T., Meinhart, C. D., Santiago, J. G. & Adrian, R. J. 1998 Velocimetry for mems applications. In Proc. ASME/DSC (Micro-Fluidics Symposium), Anaheim, CA, USA.Google Scholar
Whitesides, G. M. & Grzybowski, B. 2002 Self-assembly at all scales. Science 295, 24182421.CrossRefGoogle ScholarPubMed
Wiersema, P. H., Loeb, A. L. & Overbeek, J. T. 1966 Calculation of electrophoretic mobility of a spherical colloid particle. J Colloid Interface Sci. 22, 78-&.CrossRefGoogle Scholar
Zukoski, C. F. & Saville, D. A. 1985 An experimental test of electrokinetic theory using measurements of electrophoretic mobility and electrical-conductivity. J Colloid Interface Sci. 107, 322333.CrossRefGoogle Scholar
Zukoski, C. F. & Saville, D. A. 1986 The interpretation of electrokinetic measurements using a dynamic-model of the stern layer. Part 1. The dynamic-model. J. Colloid Interface Sci. 114, 3244.CrossRefGoogle Scholar
Zukoski, C. F. & Saville, D. A. 1987 Electrokinetic properties of particles in concentrated suspensions. J. Colloid Interface Sci. 115, 422436.CrossRefGoogle Scholar
Zukoski, C. F. & Saville, D. A. 1989 Electrokinetic properties of particles in concentrated suspensions–heterogeneous systems. J. Colloid Interface Sci. 132, 220229.CrossRefGoogle Scholar