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Dipolophoresis in concentrated suspensions of ideally polarizable spheres

Published online by Cambridge University Press:  18 July 2019

Siamak Mirfendereski  and
Jae Sung Park Open the ORCID record for Jae Sung Park [Opens in a new window]
Siamak Mirfendereski
Affiliation:
Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE 68588-0526, USA
Jae Sung Park*
Affiliation:
Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE 68588-0526, USA
*
†Email address for correspondence: jaesung.park@unl.edu
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Abstract

The dynamics of ideally polarizable spherical particles in concentrated suspensions under the effects of nonlinear electrokinetic phenomena is analysed using large-scale numerical simulations. Particles are assumed to carry no net charge and considered to undergo the combination of dielectrophoresis and induced-charge electrophoresis termed dipolophoresis. Chaotic motion and resulting hydrodynamic diffusion are known to be driven by the induced-charge electrophoresis, which dominates the dielectrophoresis. Up to a volume fraction $\unicode[STIX]{x1D719}\approx 35\,\%$, the particle dynamics seems to be hindered by the increase in the magnitude of excluded volume interactions with concentration. However, a non-trivial suspension behaviour is observed in concentrated regimes, where the hydrodynamic diffusivity starts to increase with the volume fraction at $\unicode[STIX]{x1D719}\approx 35\,\%$, before reaching a local maximum, and then drastically decreases on approaching random close packing. Similar non-trivial behaviours are observed in the particle velocity and number-density fluctuations around volume fractions at which the non-trivial behaviour of the hydrodynamic diffusion is observed. We explain these non-trivial behaviours as a consequence of particle contacts, which are related to the dominant mechanism of particle pairings. The particle contacts are classified into attractive and repulsive classes by the nature of contacts, and in particular, the strong repulsive contact becomes predominant at $\unicode[STIX]{x1D719}>20\,\%$. Moreover, this transition is visible in the pair distribution functions, which also reveal the change in the suspension microstructure in concentrated regimes. It appears that strong and massive repulsive contacts along the direction perpendicular to an electric field promote the non-trivial suspension behaviours observed in concentrated regimes.

JFM classification

Complex Fluids: Suspensions Low-Reynolds-number flows: Stokesian dynamics Multiphase and Particle-laden Flows: Particle/fluid flow
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 875 , 25 September 2019 , R3
Copyright
© 2019 Cambridge University Press 

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References

Bazant, M. Z., Kilic, M. S., Storey, B. D. & Ajdari, A. 2009 Towards an understanding of induced-charge electrokinetics at large applied voltages in concentrated solutions. Adv. Colloid Interface Sci. 152 (1–2), 48–88.Google Scholar
Bergougnoux, L. & Guazzelli, É. 2009 Non-Poisson statistics of settling spheres. Phys. Fluids 21 (9), 091701.Google Scholar
Butler, J. E. & Snook, B. 2018 Microstructural dynamics and rheology of suspensions of rigid fibers. Annu. Rev. Fluid Mech. 50, 299–318.Google Scholar
Clarke, A. S. & Wiley, J. D. 1987 Numerical simulation of the dense random packing of a binary mixture of hard spheres: amorphous metals. Phys. Rev. B 35 (14), 7350.Google Scholar
Evans, A. A., Ishikawa, T., Yamaguchi, T. & Lauga, E. 2011 Orientational order in concentrated suspensions of spherical microswimmers. Phys. Fluids 23 (11), 111702.Google Scholar
Flyvbjerg, H. & Petersen, H. G. 1989 Error estimates on averages of correlated data. J. Chem. Phys. 91 (1), 461–466.Google Scholar
Guazzelli, É. & Pouliquen, O. 2018 Rheology of dense granular suspensions. J. Fluid Mech. 852, P1.Google Scholar
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 (2), 317–328.Google Scholar
Ishikawa, T., Locsei, J. T. & Pedley, T. J. 2010 Fluid particle diffusion in a semidilute suspension of model micro-organisms. Phys. Rev. E 82 (2), 021408.Google Scholar
Ishikawa, T., Simmonds, M. P. & Pedley, T. J. 2006 Hydrodynamic interaction of two swimming model micro-organisms. J. Fluid Mech. 568, 119–160.Google Scholar
Jodrey, W. S. & Tory, E. M. 1985 Computer simulation of close random packing of equal spheres. Phys. Rev. A 32 (4), 2347.Google Scholar
Kim, S. & Karrila, S. J. 2013 Microhydrodynamics: Principles and Selected Applications. Courier Corporation.Google Scholar
Lauga, E. & Powers, T. R. 2009 The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72 (9), 096601.Google Scholar
Liu, Y. D. & Choi, H. J. 2012 Electrorheological fluids: smart soft matter and characteristics. Soft Matt. 8 (48), 11961–11978.Google Scholar
Mari, R., Seto, R., Morris, J. F. & Denn, M. M. 2014 Shear thickening, frictionless and frictional rheologies in non-Brownian suspensions. J. Rheol. 58 (6), 1693–1724.Google Scholar
Melrose, J. R. & Heyes, D. M. 1993 Simulations of electrorheological and particle mixture suspensions: agglomerate and layer structures. J. Chem. Phys. 98 (7), 5873–5886.Google Scholar
Morris, J. F. 2018 Lubricated-to-frictional shear thickening scenario in dense suspensions. Phys. Rev. Fluids 3 (11), 110508.Google Scholar
Park, J. S. & Saintillan, D. 2010 Dipolophoresis in large-scale suspensions of ideally polarizable spheres. J. Fluid Mech. 662, 66–90.Google Scholar
Park, J. S. & Saintillan, D. 2011a Electric-field-induced ordering and pattern formation in colloidal suspensions. Phys. Rev. E 83 (4), 041409.Google Scholar
Park, J. S. & Saintillan, D. 2011b From diffusive motion to local aggregation: effect of surface contamination in dipolophoresis. Soft Matt. 7 (22), 10720–10727.Google Scholar
von Pfeil, K., Graham, M. D., Klingenberg, D. J. & Morris, J. F. 2002 Pattern formation in flowing electrorheological fluids. Phys. Rev. Lett. 88 (18), 188301.Google Scholar
Pohl, H. A. 1978 Dielectrophoresis: The Behavior of Neutral Matter in Nonuniform Electric Fields (Cambridge Monographs on Physics). Cambridge University Press.Google Scholar
Rintoul, M. D. & Torquato, S. 1996 Computer simulations of dense hard-sphere systems. J. Chem. Phys. 105 (20), 9258–9265.Google Scholar
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 electroosmosis. Phys. Rev. E 79 (1), 011402.Google Scholar
Russel, W. B., Saville, D. A. & Schowalter, W. R. 1991 Colloidal Dispersions. Cambridge University Press.Google Scholar
Saintillan, D. 2008 Nonlinear interactions in electrophoresis of ideally polarizable particles. Phys. Fluids 20 (6), 067104.Google Scholar
Saintillan, D. 2018 Rheology of active fluids. Annu. Rev. Fluid Mech. 50, 563–592.Google Scholar
Saintillan, D., Darve, E. & Shaqfeh, E. S. G. 2006 Hydrodynamic interactions in the induced-charge electrophoresis of colloidal rod dispersions. J. Fluid Mech. 563, 223–259.Google Scholar
Sheng, P. & Wen, W. 2012 Electrorheological fluids: mechanisms, dynamics, and microfluidics applications. Annu. Rev. Fluid Mech. 44, 143–174.Google Scholar
Sherman, Z. M., Ghosh, D. & Swan, J. W. 2018 Field-directed self-assembly of mutually polarizable nanoparticles. Langmuir 34 (24), 7117–7134.Google 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
Squires, T. M. & Bazant, M. Z. 2004 Induced-charge electro-osmosis. J. Fluid Mech. 509, 217–252.Google Scholar
Squires, T. M. & Bazant, M. Z. 2006 Breaking symmetries in induced-charge electro-osmosis and electrophoresis. J. Fluid Mech. 560, 65–101.Google Scholar
Stillinger, F. H. Jr, DiMarzio, E. A. & Kornegay, R. L. 1964 Systematic approach to explanation of the rigid disk phase transition. J. Chem. Phys. 40 (6), 1564–1576.Google Scholar
Tapia, F., Shaikh, S., Butler, J. E., Pouliquen, O. & Guazzelli, É. 2017 Rheology of concentrated suspensions of non-colloidal rigid fibres. J. Fluid Mech. 827, R5.Google Scholar

Mirfendereski and Park supplementary movie 1

Dynamics in a suspension 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 10%. The electric field points in the vertical direction. 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 Mirfendereski and Park supplementary movie 1(Video)
Video 9.9 MB

Mirfendereski and Park supplementary movie 2

Dynamics in a suspension 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 25%. The electric field points in the vertical direction. 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 Mirfendereski and Park supplementary movie 2(Video)
Video 9.6 MB

Mirfendereski and Park supplementary movie 3

Dynamics in a suspension 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 45%. The electric field points in the vertical direction. 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 Mirfendereski and Park supplementary movie 3(Video)
Video 10 MB

Mirfendereski and Park supplementary movie 4

Dynamics in a suspension 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 59%. The electric field points in the vertical direction. 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 Mirfendereski and Park supplementary movie 4(Video)
Video 8.8 MB