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Dipolophoresis in large-scale suspensions of ideally polarizable spheres

Published online by Cambridge University Press:  17 September 2010

JAE SUNG PARK  and
DAVID SAINTILLAN
JAE SUNG PARK
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
DAVID SAINTILLAN*
Affiliation:
Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA
*
†Email address for correspondence: [email protected]
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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.

JFM classification

Low-Reynolds-number flows: Stokesian dynamics Complex Fluids: Suspensions
Type
Papers
Information
Journal of Fluid Mechanics , Volume 662 , 10 November 2010 , pp. 66 - 90
Copyright
Copyright © Cambridge University Press 2010

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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.

Download Park and Saintillan supplementary movie(Video)
Video 9.7 MB

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.

Download Park and Saintillan supplementary movie(Video)
Video 9.3 MB

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.

Download Park and Saintillan supplementary movie(Video)
Video 8.9 MB