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Dipolophoresis in large-scale suspensions of ideally polarizable spheres

  • JAE SUNG PARK (a1) and DAVID SAINTILLAN (a1)

Abstract

The nonlinear dynamics of uncharged ideally polarizable spheres freely suspended in a viscous electrolyte in a uniform electric field are analysed using theory and numerical simulations. When a sphere polarizes under the action of the field, it acquires a non-uniform surface charge, which results in an electro-osmotic flow near its surface that scales quadratically with the applied field magnitude. While this so-called induced-charge electrophoresis yields no net motion in the case of a single sphere, it can drive relative motions by symmetry breaking when several particles are present. In addition, Maxwell stresses in the fluid also result in non-zero dielectrophoretic forces, which also cause particle motions. The combination of these two nonlinear electrokinetic effects, termed dipolophoresis, is analysed in detail by using numerical simulations. An efficient simulation method based on our previous analysis of pair interactions is presented and accounts for both far-field and near-field electric and hydrodynamic interactions in the thin-Debye-layer limit, as well as steric interactions using a novel contact algorithm. Simulation results in large-scale suspensions with periodic boundary conditions are presented. While the dynamics under dielectrophoresis alone are shown to be characterized by particle chaining along the field direction, in agreement with previous investigations, chaining is not found to occur under dipolophoresis, which instead causes transient particle pairings and results in a non-uniform microstructure with large number of density fluctuations, as we demonstrate by calculating pair distribution functions and particle occupancy statistics. Dipolophoresis is also found to result in significant hydrodynamic dispersion and velocity fluctuations, and the dependence of these two effects on suspension volume fraction is investigated.

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Corresponding author

Email address for correspondence: dstn@illinois.edu

References

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Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables. Dover.
Abu Hamed, M. & Yariv, E. 2009 Boundary-induced electrophoresis of uncharged conducting particles: near-contact approximation. Proc. R. Soc. A 465, 19391948.
Acrivos, A., Jeffrey, D. J. & Saville, D. A. 1990 Particle migration in suspensions by thermocapillary or electrophoretic motion. J. Fluid Mech. 212, 95110.
Anderson, J. L. 1985 Droplet interactions in thermocapillary motion. Intl J. Multiph. Flow 11, 813824.
Bazant, M. Z. & Squires, T. M. 2004 Induced-charge electrokinetic phenomena: theory and microfluidic applications. Phys. Rev. Lett. 92, 066101.
Bazant, M. Z. & Squires, T. M. 2010 Induced-charge electrokinetic phenomena. Current Opin. Colloid Interface Sci. 15, 203213.
Bergougnoux, L. & Guazzelli, E. 2009 Non-Poisson statistics of settling spheres. Phys. Fluids 21, 091701.
Butler, J. E. & Shaqfeh, E. S. G. 2002 Dynamic simulations of the inhomogeneous sedimentation of rigid fibres. J. Fluid Mech. 468, 205237.
Chen, S. B. & Keh, H. J. 1988 Electrophoresis in a dilute dispersion of colloidal spheres. AIChE J. 34, 10751085.
Deserno, M. & Holm, C. 1997 How to mesh up Ewald sums. Part I. A theoretical and numerical comparison of various particle mesh routines. J. Chem. Phys. 109, 76787693.
Drazer, G., Koplik, J., Khusid, B. & Acrivos, A. 2002 Deterministic and stochastic behaviour of non-Brownian spheres in sheared suspensions J. Fluid Mech. 460, 307335.
Dukhin, A. S. 1986 Pair interaction of particles in electric field. Part 3. Hydrodynamic interaction of ideally polarizable metal particles and dead biological cells. Colloid J. USSR 48, 376381.
Dukhin, A. S. & Murtsovkin, V. A. 1986 Pair interaction of particles in electric field. Part 2. Influence of polarization of double layer of dielectric particles on their hydrodynamic interaction in a stationary electric field. Colloid J. USSR 48, 203209.
Essmann, U., Perera, L., Berkowitz, M. L., Darden, T., Lee, H. & Pedersen, L. G. 1995 A smooth particle mesh Ewald method. J. Chem. Phys. 103, 85778593.
Füredi, A. A. & Valentine, R. C. 1962 Factors involved in the orientation of microscopic particles in suspensions influenced by radio frequency fields. Biochim. Biophys. Acta 56, 3342.
Gamayunov, N. I., Murtsovkin, V. A. & Dukhin, A. S. 1986 Pair interaction of particles in electric field. Part I. Features of hydrodynamic interaction of polarized particles. Colloid J. USSR 48, 197203.
Ham, J. M. & Homsy, G. M. 1988 Hindered settling and hydrodynamic dispersion in quiescent sedimenting suspensions. Intl J. Multiph. Flow 14, 533546.
Happel, J. & Brenner, H. 1965 Low Reynolds Number Hydrodynamics. Prentice-Hall.
Hasimoto, H. 1959 On the periodic fundamental solutions of the Stokes equations and their application to viscous flow past a cubic array of spheres. J. Fluid Mech. 5, 317328.
Henry, D. C. 1931 The cataphoresis of suspended particles. Part I. The equation of cataphoresis. Proc. R. Soc. Lond. A 133, 106129.
Hiemenz, P. C. & Rajagopalan, R. 1997 Principles of Colloid and Surface Chemistry. CRC.
Hoffman, B. D. & Shaqfeh, E. S. G. 2009 The effect of Brownian motion on the stability of sedimenting suspensions of polarizable rods in an electric field. J. Fluid Mech. 624, 361388.
Jeffrey, D. J. 1973 Conduction through a random suspension of spheres. Proc. R. Soc. Lond. Ser. A 335, 355367.
Jeffrey, D. J. & Onishi, Y. 1984 Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow. J. Fluid Mech. 139, 261290.
Jones, T. B. 1995 Electromechanics of Particles. Cambridge University Press.
Kim, S. & Karrila, S. P. 1991 Microhydrodynamics: Principles and Selected Applications. Butterworth-Heinemann.
Lei, X., Ackerson, B. J., & Tong, P. 2001 Settling statistics of hard sphere particles. Phys. Rev. Lett. 86, 33003303.
Miloh, T. 2008 a Dipolophoresis of nanoparticles. Phys. Fluids 20, 063303.
Miloh, T. 2008 b A unified theory of dipolophoresis for nanoparticles. Phys. Fluids 20, 107105.
Miloh, T. 2009 Nonlinear alternating electric field dipolophoresis of spherical nanoparticles. Phys. Fluids 21, 072002.
Morrison, F. A. 1970 Electrophoresis of a particle of arbitrary shape. J. Colloid Interface Sci. 34, 210214.
Murtsovkin, V. A. 1996 Nonlinear flows near polarized disperse particles. Colloid J. USSR 58, 341349.
Nott, P. R. & Brady, J. F. 1994 Pressure-driven flow of suspensions: simulations and theory. J. Fluid Mech. 275, 157199.
Patankar, N. A. 2009 Are the hydrodynamic forces and torques zero during electrophoresis of multiparticle systems with thin Debye layers? Mech. Res. Commun. 36, 3945.
Pine, D. J., Gollub, J. P., Brady, J. F. & Leshansky, A. M. 2005 Chaos and threshold for irreversibility in sheared suspensions. Nature 438, 9971000.
Pohl, H. A. 1978 Dielectrophoresis. Cambridge University Press.
Pozrikidis, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge University Press.
Reed, L. D. & Morrison, F. A. 1975 Hydrodynamic interactions in electrophoresis. J. Colloid Interface Sci. 54, 117133.
Rose, K. A., Meier, J. A., Dougherty, G. M. & Santiago, J. G. 2007 Rotational electrophoresis of striped metallic microrods. Phys. Rev. E 75, 011503.
Rose, K. A., Hoffman, B., Saintillan, D., Shaqfeh, E. S. G. & Santiago, J. G. 2009 Hydrodynamic interactions in metal rodlike-particle suspensions due to induced charge electro-osmosis. Phys. Rev. E 79, 011402.
Russel, W. B., Saville, D. A. & Schowalter, W. R. 1989 Colloidal Dispersions. Cambridge University Press.
Saintillan, D. 2008 Nonlinear interactions in electrophoresis of ideally polarizable particles. Phys. Fluids 20, 067104.
Saintillan, D., Darve, E. & Shaqfeh, E. S. G. 2005 A smooth particle-mesh Ewald algorithm for Stokes suspension simulations: the sedimentation of fibers. Phys. Fluids 17, 033301.
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, 223259.
Saintillan, D., Shaqfeh, E. S. G. & Darve, E. 2006 b Stabilization of a suspension of sedimenting rods by induced-charge electrophoresis. Phys. Fluids 18, 121701.
Shilov, V. N. & Simonova, T. S. 1981 Polarization of electric-double-layer of dispersive particles and dipolophoresis in steady (DC) field. Colloid J. USSR 43, 9096.
Sierou, A. & Brady, J. F. 2001 Accelerated Stokesian dynamics simulations. J. Fluid Mech. 448, 115146.
Simonov, I. N. & Dukhin, A. S. 1973 Theory of electrophoresis of solid conducting particles in case of ideal polarization of a thin diffuse double layer. Colloid J. USSR 35, 173176.
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, 108115.
Smoluchowski, M. 1903 Contribution à la théorie de l'endosmose électrique et de quelques phénomènes corrélatifs. Bull. Intl Acad. Sci. Cracovie 8, 182200.
Squires, T. M. 2009 Induced-charge electro-kinetics: fundamental challenges and opportunities. Lab on a Chip 9, 24772483.
Squires, T. M. & Bazant, M. Z. 2004 Induced-charge electro-osmosis. J. Fluid Mech. 509, 217252.
Squires, T. M. & Bazant, M. Z. 2006 Breaking symmetries in induced-charge electro-osmosis and electrophoresis. J. Fluid Mech. 560, 65101.
Squires, T. M. & Quake, S. R. 2005 Microfluidics: fluid physics at the nanoliter scale. Rev. Mod. Phys. 77, 9771026.
Viovy, J. L. 2000 Electrophoresis of DNA and other polyelectrolytes: physical mechanisms. Rev. Mod. Phys. 72, 813872.
Wang, X., Wang, X.-B. & Gascoyne, P. R. C. 1997 General expressions for dielectrophoretic force and electrorotational torque derived using the Maxwell stress tensor method. J. Electrostat. 39, 277295.
Yariv, E. 2005 Induced-charge electrophoresis of nonspherical particles. Phys. Fluids 17, 051702.
Yariv, E. 2009 Boundary-induced electrophoresis of uncharged conducting particles: remote wall approximations. Proc. R. Soc. A 465, 709723.
Yossifon, G., Frankel, I. & Miloh, T. 2007 Symmetry breaking in induced-charge electro-osmosis over polarizable spheroids. Phys. Fluids 19, 068105.
Zhao, H. & Bau, H. H. 2007 On the effect of induced electro-osmosis on a cylindrical particle next to a surface. Langmuir 23, 40534063.
Zinchenko, A. Z. 1994 An efficient algorithm for calculating multiparticle thermal interaction in a concentrated dispersion of spheres. J. Comput. Phys. 111, 120135.
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JFM classification

Type Description Title
VIDEO
Movies

Park and Saintillan supplementary movie
Movie 1. Dynamics in a suspension of 100 spheres undergoing dielectrophoresis under a uniform external electric field, in a periodic box of dimensions 20 x 20 x 20 and at a volume fraction of 5.24%. The electric field points in the vertical direction. DEP forces give rise to the formation of particle chains in the direction of the field. The occasional particle flickers are a consequence of the periodic boundary conditions, by which a particle leaving the simulation box immediately reenters on the other side.

 Video (9.7 MB)
9.7 MB
VIDEO
Movies

Park and Saintillan supplementary movie
Movie 2. Dynamics in a suspension of 100 spheres undergoing dipolophoresis (combination of dielectrophoresis and induced-charge electrophoresis) under a uniform external electric field, in a periodic box of dimensions 20 x 20 x 20 and at a volume fraction of 5.24%. The electric field points in the vertical direction. DIP results in the formation of transient particle clusters, and also causes hydrodynamic diffusion. The occasional particle flickers are a consequence of the periodic boundary conditions, by which a particle leaving the simulation box immediately reenters on the other side.

 Video (9.3 MB)
9.3 MB
VIDEO
Movies

Park and Saintillan supplementary movie
Movie 3. Two-dimensional particle dynamics in a monolayer of 100 spheres undergoing dipolophoresis (combination of dielectrophoresis and induced-charge electrophoresis) under a uniform external electric field, in a periodic box of dimensions 50 x 3 x 50 and at a volume fraction of 5.59%. The electric field points in the vertical direction. DIP results in particle pairing events, as well as in the formation of transient particle clusters and clarified regions. It also causes hydrodynamic diffusion. The occasional particle flickers are a consequence of the periodic boundary conditions, by which a particle leaving the simulation box immediately reenters on the other side.

 Video (8.9 MB)
8.9 MB

Dipolophoresis in large-scale suspensions of ideally polarizable spheres

  • JAE SUNG PARK (a1) and DAVID SAINTILLAN (a1)

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