- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review Fluids

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Modeling chemo-hydrodynamic interactions of phoretic particles: A unified framework

Akhil Varma* and Sébastien Michelin†

  • LadHyX–Département de Mécanique, CNRS–Ecole Polytechnique, Institut Polytechnique de Paris, 91128 Palaiseau Cedex, France

  • *akhil.varma@ladhyx.polytechnique.fr
  • †sebastien.michelin@ladhyx.polytechnique.fr
PDF

Phys. Rev. Fluids 4, 124204 – Published 24 December, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.124204

Abstract

Phoretic particles exploit local self-generated physico-chemical gradients to achieve self-propulsion at the micron scale. The collective dynamics of a large number of such particles is currently the focus of intense research efforts, both from a physical perspective to understand the precise mechanisms of the interactions and their respective roles, as well as from an experimental point of view to explain the observations of complex dynamics as well as formation of coherent large-scale structures. However, an exact modeling of such multiparticle problems is difficult, and most efforts so far rely on the superposition of far-field approximations for each particle's signature, which are only valid asymptotically in the dilute suspension limit. A systematic and unified analytical framework based on the classical Method of Reflections (MoR) is developed here for both the Laplace and Stokes' problems to obtain the higher-order interactions and the resulting velocities of multiple phoretic particles, up to any order of accuracy in the radius-to-distance ratio ɛ of the particles. Beyond simple pairwise chemical or hydrodynamic interactions, this model allows us to account for the generic chemo-hydrodynamic couplings as well as N-particle interactions (N≥3). The ɛ5-accurate interaction velocities are then explicitly obtained, and the resulting implementation of this MoR model is discussed and validated quantitatively against exact solutions of a few canonical problems.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (91)

  1. S. Ramaswamy, The mechanics and statistics of active matter, Annu. Rev. Condens. Matter Phys. 1, 323 (2010).
  2. M. C. Marchetti, J. F. Joanny, S. Ramaswamy, T. B. Liverpool, J. Prost, Madan Rao, and R. Aditi Simha, Hydrodynamics of soft active matter, Rev. Mod. Phys. 85, 1143 (2013).
  3. D. Saintillan and M. J. Shelley, Emergence of coherent structures and large-scale flows in motile suspensions, J. R. Soc. Interface 9, 571 (2012).
  4. A. Zöttl and H. Stark, Emergent behavior in active colloids, J. Phys.: Condens. Matter 28, 253001 (2016).
  5. J. Elgeti, R. G. Winkler, and G. Gompper, Physics of microswimmers—Single particle motion and collective behavior: A review, Rep. Prog. Phys. 78, 056601 (2015).
  6. I. S. Aranson and L. S. Tsimring, Patterns and collective behavior in granular media: Theoretical concepts, Rev. Mod. Phys. 78, 641 (2006).
  7. J. Deseigne, O. Dauchot, and H. Chaté, Collective Motion of Vibrated Polar Disks, Phys. Rev. Lett. 105, 098001 (2010).
  8. M. E. Cates and J. Tailleur, Motility-induced phase separation, Annu. Rev. Condens. Matter Phys. 6, 219 (2015).
  9. É. Fodor and M. C. Marchetti, The statistical physics of active matter: From self-catalytic colloids to living cells, Physica A 504, 106 (2018).
  10. S. Zhou, A. Sokolov, O. D. Lavrentovich, and I. S. Aranson, Living liquid crystals, Proc. Natl. Acad. Sci. USA 111, 1265 (2014).
  11. A. P. Petroff, X.-L. Wu, and A. Libchaber, Fast-Moving Bacteria Self-Organize into Active Two-Dimensional Crystals of Rotating Cells, Phys. Rev. Lett. 114, 158102 (2015).
  12. F. Jülicher, K. Kruse, J. Prost, and J.-F. Joanny, Active behavior of the cytoskeleton, Phys. Rep. 449, 3 (2007).
  13. T. Sanchez, D. T. N. Chen, S. J. DeCamp, M. Heymann, and Z. Dogic, Spontaneous motion in hierarchically assembled active matter, Nature (London) 491, 431 (2012).
  14. S. P. Thampi, R. Golestanian, and J. M. Yeomans, Velocity Correlations in an Active Nematic, Phys. Rev. Lett. 111, 118101 (2013).
  15. P. G. de Gennes and J. Prost, The Physics of Liquid Crystals, Oxford Science Publications (Oxford University Press, Oxford, 1993).
  16. S. Herminghaus, C. C. Maass, C. Krüger, S. Thutupalli, L. Goehring, and C. Bahr, Interfacial mechanisms in active emulsions, Soft Matter 10, 7008 (2014).
  17. S. Thutupalli and S. Herminghaus, Tuning active emulsion dynamics via surfactants and topology, Eur. Phys. J. E. 36, 91 (2013).
  18. C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, and G. Volpe, Active particles in complex and crowded environments, Rev. Mod. Phys. 88, 045006 (2016).
  19. T. Vicsek, A. Czirók, E. Ben-Jacob, I. Cohen, and O. Shochet, Novel Type of Phase Transition in a System of Self-Driven Particles, Phys. Rev. Lett. 75, 1226 (1995).
  20. J. Toner and Y. Tu, Long-Range Order in a Two-Dimensional Dynamical XY Model: How Birds Fly Together, Phys. Rev. Lett. 75, 4326 (1995).
  21. G. S. Redner, M. F. Hagan, and A. Baskaran, Structure and Dynamics of a Phase-Separating Active Colloidal Fluid, Phys. Rev. Lett. 110, 055701 (2013).
  22. J. Tailleur and M. E. Cates, Statistical Mechanics of Interacting Run-and-Tumble Bacteria, Phys. Rev. Lett. 100, 218103 (2008).
  23. B. Liebchen, D. Marenduzzo, and M. E. Cates, Phoretic Interactions Generically Induce Dynamic Clusters and Wave Patterns in Active Colloids, Phys. Rev. Lett. 118, 268001 (2017).
  24. B. Liebchen and H. Löwen, Synthetic chemotaxis and collective behavior in active matter, Acc. Chem. Res. 51, 2982 (2018).
  25. A. G. Mark, J. G. Gibbs, T.-C. Lee, and P. Fischer, Hybrid nanocolloids with programmed three-dimensional shape and material composition, Nat. Mater. 12, 802 (2013).
  26. A. Walther and A. H. E. Müller, Janus particles: Synthesis, self-assembly, physical properties and applications, Chem. Rev. 113, 5194 (2013).
  27. P. Illien, R. Golestanian, and A. Sen, ‘Fuelled’ motion: Phoretic motility and collective behaviour of active colloids, Chem. Soc. Rev. 46, 5508 (2017).
  28. J. L. Moran and J. D. Posner, Phoretic self-propulsion, Ann. Rev. Fluid Mech. 49, 511 (2017).
  29. A. Ghosh and P. Fischer, Controlled propulsion of artificial magnetic nanostructured propellers, Nano Lett. 9, 2243 (2009).
  30. 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).
  31. M. Driscoll, B. Delmotte, S. Sacanna, A. Donev, and P. Chaikin, Unstable fronts and motile structures formed by microrollers, Nature (London) 13, 375 (2016).
  32. A. Kaiser, A. Snezhko, and I. S. Aranson, Flocking ferromagnetic colloids, Sci. Adv. 3, e1601469 (2017).
  33. W. F. Paxton, K. C. Kistler, C. C. Olmeda, A. Sen, S. K. St. Angelo, Y. Cao, T. E. Mallouk, P. E. Lammert, and V. H. Crespi, Catalytic nanomotors: Autonomous movement of striped nanorods, J. Am. Chem. Soc. 126, 13424 (2004).
  34. J. R. Howse, R. A. L. Jones, A. J. Ryan, T. Gough, R. Vafabakhsh, and R. Golestanian, Self-Motile Colloidal Particles: From Directed Propulsion to Random Walk, Phys. Rev. Lett. 99, 048102 (2007).
  35. I. Theurkauff, C. Cottin-Bizonne, J. Palacci, C. Ybert, and Bocquet. L, Dynamic Clustering in Active Colloidal Suspensions with Chemical Signaling, Phys. Rev. Lett. 108, 268303 (2012).
  36. S. Thutupalli, R. Seemann, and S. Herminghaus, Swarming behavior of simple model squirmers, New J. Phys. 13, 073021 (2011).
  37. Z. Izri, M. N. van der Linden, S. Michelin, and O. Dauchot, Self-Propulsion of Pure Water Droplets by Spontaneous Marangoni-Stress-Driven Motion, Phys. Rev. Lett. 113, 248302 (2014).
  38. C. Krüger, G. Klös, C. Bahr, and C. C. Maass, Curling Liquid Crystal Microswimmers: A Cascade of Spontaneous Symmetry Breaking, Phys. Rev. Lett. 117, 048003 (2016).
  39. S. J. Ebbens, Active colloids: Progress and challenges towards realising autonomous applications, Curr. Opin. Colloid Interface Sci. 21, 14 (2016).
  40. J. Li, I. Rozen, and J. Wang, Rocket science at the nanoscale, ACS Nano 10, 5619 (2016).
  41. G. Gallino, F. Gallaire, E. Lauga, and S. Michelin, Physics of bubble-propelled microrockets, Adv. Funct. Mater. 28, 1800686 (2018).
  42. S. Thutupalli, D. Geyer, R. Singh, R. Adhikari, and H. A. Stone, Flow-induced phase separation of active particles is controlled by boundary conditions, Proc. Natl. Acad. Sci. USA 115, 5403 (2018).
  43. E. Kanso and S. Michelin, Phoretic and hydrodynamic interactions of weakly confined autophoretic particles, J. Chem. Phys. 150, 044902 (2019).
  44. B. Liebchen and H. Löwen, Which interactions dominate in active colloids? J. Chem. Phys. 150, 061102 (2019).
  45. J. L. Anderson, Colloidal transport by interfacial forces, Annu. Rev. Fluid Mech 21, 61 (1989).
  46. R. Golestanian, T. B. Liverpool, and A. Ajdari, Designing phoretic micro- and nano-swimmers, New J. Phys. 9, 126 (2007).
  47. T. Ishikawa, M. P. Simmonds, and T. J. Pedley, Hydrodynamic interaction of two swimming model micro-organisms, J. Fluid Mech. 568, 119 (2006).
  48. T. D. Montenegro-Johnson, S. Michelin, and E. Lauga, A regularised singularity approach to phoretic problems, Eur. Phys. J. E 38, 139 (2015).
  49. W. E. Uspal, M. N. Popescu, S. Dietrich, and M. Tasinkevych, Self-propulsion of a catalytically active particle near a planar wall: From reflection to sliding and hovering, Soft Matter 11, 434 (2015).
  50. E. Lushi and C. S. Peskin, Modeling and simulation of active suspensions containing large numbers of interacting micro-swimmers, Computers Struct. 122, 239 (2013).
  51. R. A. Lambert, F. Picano, W.-P. Breugem, and L. Brandt, Active suspensions in thin films: Nutrient uptake and swimmer motion, J. Fluid Mech. 733, 528 (2013).
  52. B. Delmotte, E. E. Keaveny, F. Plouraboué, and E. Climent, Large-scale simulation of steady and time-dependent active suspensions with the force-coupling method, J. Comput. Phys. 302, 524 (2015).
  53. M. Yang, A. Wysocki, and M. Ripoll, Hydrodynamic simulations of self-phoretic microswimmers, Soft Matter 10, 6208 (2014).
  54. P. H. Colberg and R. Kapral, Many-body dynamics of chemically propelled nanomotors, J. Chem. Phys. 147, 064910 (2017).
  55. F. Alarcòn and I. Pagonabarraga, Spontaneous aggregation and global polar ordering in squirmer suspensions, J. Mol. Liq. 185, 56 (2013).
  56. J. F. Brady and G. Bossis, Stokesian dynamics, Ann. Rev. Fluid Mech. 20, 111 (1988).
  57. K. Ichiki and J. F. Brady, Many-body effects and matrix inversion in low-Reynolds-number hydrodynamics, Phys. Fluids 13, 350 (2001).
  58. A. Sierou and J. F. Brady, Accelerated Stokesian dynamics simulations, J. Fluid Mech. 448, 115 (2001).
  59. A. M. Fiore and J. W. Swan, Fast Stokesian dynamics, J. Fluid Mech. 878, 544 (2019).
  60. W. Yan and J. F. Brady, The behavior of active diffusiophoretic suspensions: An accelerated Laplacian dynamics study, J. Chem. Phys. 145, 134902 (2016).
  61. R. Singh and R. Adhikari, Generalized stokes laws for active colloids and their applications, J. Phys. Commun. 2, 025025 (2018).
  62. R. Singh, R. Adhikari, and M. E. Cates, Competing chemical and hydrodynamic effects in autophoretic colloidal suspensions, J. Chem. Phys. 151, 044901 (2019).
  63. G. Mo and A. S. Sangani, A method for computing stokes flow interactions among spherical objects and its application to suspensions of drops and porous particles, Phys. Fluids 6, 1637 (1994).
  64. A. S. Sangani and G. Mo, An O(N) algorithm for stokes and laplace interactions of particles, Phys. Fluids 8, 1990 (1996).
  65. S. Michelin and E. Lauga, Phoretic self-propulsion at finite Péclet numbers, J. Fluid Mech. 747, 572 (2014).
  66. S. Michelin and E. Lauga, Autophoretic locomotion from geometric asymmetry, Eur. Phys. J. E 38, 7 (2015).
  67. S. E. Spagnolie and E. Lauga, Hydrodynamics of self-propulsion near a boundary: Predictions and accuracy of far-field approximations, J. Fluid Mech. 700, 105 (2012).
  68. S. Saha, R. Golestanian, and S. Ramaswamy, Clusters, asters, and collective oscillations in chemotactic colloids, Phys. Rev. E 89, 062316 (2014).
  69. R. Soto and R. Golestanian, Self-Assembly of Catalytically-Active Colloidal Molecules: Tailoring Activity Through Surface Chemistry, Phys. Rev. Lett. 112, 068301 (2014).
  70. M. Smoluchowski, On the mutual action of spheres which move in a viscous liquid, Bull. Acad. Sci. Cracovie A 1, 28 (1911).
  71. G. J. Kynch, The slow motion of two or more spheres through a viscous liquid, J. Fluid Mech. 5, 193 (1959).
  72. H. J. Wilson, Stokes flow past three spheres, J. Comput. Phys. 245, 302 (2013).
  73. J. Happel and H. Brenner, Low Reynolds Number Hydrodynamics (Springer, Netherlands, 1965).
  74. J. H. C. Luke, Convergence of a multiple reflection method for calculating Stokes flow in a suspension, SIAM J. Appl. Math. 49, 1635 (1989).
  75. S. D. Traytak, Convergence of a reflection method for diffusion-controlled reactions on static sinks, Physica A 362, 240 (2006).
  76. S. Michelin, E. Guérin, and E. Lauga, Collective dissolution of microbubbles, Phys. Rev. Fluids 3, 043601 (2018).
  77. A. Varma, T. D. Montenegro-Johnson, and S. Michelin, Clustering-induced self-propulsion of isotropic autophoretic particles, Soft Matter 14, 7155 (2018).
  78. B. Rallabandi, F. Yang, and H. A. Stone, Motion of hydrodynamically interacting active particles, arXiv:1901.04311.
  79. W. Duan, W. Wang, S. Das, V. Yadav, T. E. Mallouk, and A. Sen, Synthetic nano- and micromachines in analytical chemistry: Sensing, migration, capture, delivery and separation, Annu. Rev. Anal. Chem. 8, 311 (2015).
  80. H. A. Stone and A. D. T. Samuel, Propulsion of microorganisms by surface distortions, Phys. Rev. Lett 77, 4102 (1996).
  81. J. R. Blake, A spherical envelope approach to ciliary propulsion, J. Fluid Mech. 46, 199 (1971).
  82. O. S. Pak and E. Lauga, Generalized squirming motion of a sphere, J. Eng. Math. 88, 1 (2014).
  83. M. Tătulea-Codrean and E. Lauga, Artificial chemotaxis of phoretic swimmers: Instantaneous and long-time behavior, J. Fluid Mech. 856, 921 (2018).
  84. S. Kim and S. Karrila, Microhydrodynamics: Principles and Selected Applications (Dover Publications, New York, 1991).
  85. B. Nasouri and G. J. Elfring, Higher-order force moments of active particles, Phys. Rev. Fluids 3, 044101 (2018).
  86. M. Lisicki, S. Y. Reigh, and E. Lauga, Autophoretic motion in three dimensions, Soft Matter 14, 3304 (2018).
  87. H. Lamb, Hydrodynamics, 6th ed. (Dover, New York, 1932).
  88. E. Yariv, Wall-induced self-diffusiophoresis of active isotropic colloids, Phys. Rev. Fluids 1, 032101 (2016).
  89. N. Sharifi-Mood, A. Mozaffari, and U. M. Cordova-Figueroa, Pair interaction of catalytically active colloids: From assembly to escape, J. Fluid Mech. 798, 910 (2016).
  90. G. M. Golusin, Auflösung eines ebenen Wärmeleitungsproblems in einem von isolierender schichte umgebenen mehrfachzusammenhängenden Kreisbereiche, Mat. Sb. 42, 191 (1935).
  91. M. Stimson and G. B. Jeffery, The motion of two spheres in a viscous fluid, Proc. R. Soc. London A 111, 757 (1926).

Outline

Information

Phys. Rev. Fluids 4, 124204– Published 24 December, 2019
  • Received 11 April 2019
Crossmark - Check for updates button

©2019 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation