Perils of ad hoc approximations for the activity function of chemically powered colloids

  • M. N. Popescu
  • W. E. Uspal
  • M. Tasinkevych
  • S. Dietrich
Regular Article

Abstract.

Colloids can achieve motility by promoting at their surfaces chemical reactions in the surrounding solution. A well-studied case is that of self-phoresis, in which motility arises due to the spatial inhomogeneities in the chemical composition of the solution and the distinct interactions of the solvent molecules and of the reaction products with the colloid. For simple models of such chemically active colloids, the steady-state motion in an unbounded solution can be derived analytically in closed form. In contrast, for such chemically active particles moving in the vicinity of walls, the derivation of closed-form and physically intuitive solutions of the equations governing their dynamics turns out to be a severe challenge even for simple models. Therefore, recent studies of these phenomena have employed numerical methods as well as approximate analytical approaches based on multipolar expansions. We discuss and clarify certain conceptual aspects concerning the latter type of approach, which arise due to ad hoc truncations of the underlying so-called activity function, which describes the distribution of chemical reactions across the surface of the particle.

Graphical abstract

Keywords

Soft Matter: Colloids and Nanoparticles 

References

  1. 1.
    S.J. Ebbens, J.R. Howse, Soft Matter 6, 726 (2010)ADSCrossRefGoogle Scholar
  2. 2.
    Y. Hong, D. Velegol, N. Chaturvedi, A. Sen, Phys. Chem. Chem. Phys. 12, 1423 (2010)CrossRefGoogle Scholar
  3. 3.
    S. Ebbens, M.H. Tu, J.R. Howse, R. Golestanian, Phys. Rev. E 85, 020401 (2012)ADSCrossRefGoogle Scholar
  4. 4.
    T.C. Lee, M. Alarcón-Correa, C. Miksch, K. Hahn, J.G. Gibbs, P. Fischer, Nano Lett. 14, 2407 (2014)ADSCrossRefGoogle Scholar
  5. 5.
    L. Baraban, M. Tasinkevych, M.N. Popescu, S. Sánchez, S. Dietrich, O.G. Schmidt, Soft Matter 8, 48 (2012)ADSCrossRefGoogle Scholar
  6. 6.
    S. Ebbens, D.A. Gregory, G. Dunderdale, J.R. Howse, Y. Ibrahim, T.B. Liverpool, R. Golestanian, EPL 106, 58003 (2014)ADSCrossRefGoogle Scholar
  7. 7.
    A. Brown, W. Poon, Soft Matter 10, 4016 (2014)ADSCrossRefGoogle Scholar
  8. 8.
    X. Wang, M. In, C. Blanc, M. Nobili, A. Stocco, Soft Matter 11, 7376 (2015)ADSCrossRefGoogle Scholar
  9. 9.
    R. Golestanian, T.B. Liverpool, A. Ajdari, Phys. Rev. Lett. 94, 220801 (2005)ADSCrossRefGoogle Scholar
  10. 10.
    R. Golestanian, T.B. Liverpool, A. Ajdari, New J. Phys. 9, 126 (2007)ADSCrossRefGoogle Scholar
  11. 11.
    G.R. Rückner, R. Kapral, Phys. Rev. Lett. 98, 150603 (2007)CrossRefGoogle Scholar
  12. 12.
    F. Jülicher, J. Prost, Eur. Phys. J. E 29, 27 (2009)CrossRefGoogle Scholar
  13. 13.
    M.N. Popescu, M. Tasinkevych, S. Dietrich, EPL 95, 28004 (2011)ADSCrossRefGoogle Scholar
  14. 14.
    R. Kapral, J. Chem. Phys. 138, 202901 (2013)CrossRefGoogle Scholar
  15. 15.
    B. ten Hagen, S. van Teeffelen, H. Löwen, J. Phys.: Condens. Matter 23, 194119 (2011)ADSGoogle Scholar
  16. 16.
    S. Michelin, E. Lauga, Eur. Phys. J. E 38, 7 (2015)CrossRefGoogle Scholar
  17. 17.
    B. ten Hagen, F. Kümmel, R. Wittkowski, D. Takagi, H. Löwen, C. Bechinger, Nat. Commun. 5, 4829 (2014)ADSCrossRefGoogle Scholar
  18. 18.
    J. Elgeti, R.G. Winkler, G. Gompper, Rep. Prog. Phys. 78, 056601 (2015)ADSCrossRefGoogle Scholar
  19. 19.
    A. Zöttl, H. Stark, J. Phys.: Condens. Matter 28, 253001 (2016)ADSGoogle Scholar
  20. 20.
    J. de Graaf, G. Rempfer, C. Holm, IEEE Trans. NanoBiosci. 14, 272 (2015)CrossRefGoogle Scholar
  21. 21.
    J.L. Anderson, Annu. Rev. Fluid Mech. 21, 61 (1989)ADSMathSciNetCrossRefGoogle Scholar
  22. 22.
    W.E. Uspal, M.N. Popescu, S. Dietrich, M. Tasinkevych, Soft Matter 11, 434 (2015)ADSCrossRefGoogle Scholar
  23. 23.
    J. Palacci, S. Sacanna, A.S. Steinberg, D.J. Pine, P.M. Chaikin, Science 339, 936 (2013)ADSCrossRefGoogle Scholar
  24. 24.
    S. Das, A. Garg, A.I. Campbell, J. Howse, A. Sen, D. Velegol, R. Golestanian, S.J. Ebbens, Nat. Commun. 6, 8999 (2015)ADSCrossRefGoogle Scholar
  25. 25.
    J. Simmchen, J. Katuri, W.E. Uspal, M.N. Popescu, M. Tasinkevych, S. Sánchez, Nat. Commun. 7, 10598 (2016)ADSCrossRefGoogle Scholar
  26. 26.
    A. Mozaffari, N. Sharifi-Mood, J. Koplik, C. Maldarelli, Phys. Fluids 28, 053107 (2016)ADSCrossRefGoogle Scholar
  27. 27.
    W.E. Uspal, M.N. Popescu, S. Dietrich, M. Tasinkevych, Phys. Rev. Lett. 117, 048002 (2016)ADSCrossRefGoogle Scholar
  28. 28.
    A.M. Leshansky, A.A. Golovin, A. Nir, Phys. Fluids 9, 2818 (1997)ADSCrossRefGoogle Scholar
  29. 29.
    A. Domínguez, P. Malgaretti, M.N. Popescu, S. Dietrich, Phys. Rev. Lett. 116, 078301 (2016)ADSCrossRefGoogle Scholar
  30. 30.
    W.E. Uspal, M.N. Popescu, S. Dietrich, M. Tasinkevych, Soft Matter 11, 6613 (2015)ADSCrossRefGoogle Scholar
  31. 31.
    A.I. Campbell, S.J. Ebbens, Langmuir 29, 14066 (2013)CrossRefGoogle Scholar
  32. 32.
    M. Enculescu, H. Stark, Phys. Rev. Lett. 107, 058301 (2011)ADSCrossRefGoogle Scholar
  33. 33.
    J.F. Brady, J. Fluid Mech. 667, 216 (2011)ADSMathSciNetCrossRefGoogle Scholar
  34. 34.
    D.G. Crowdy, J. Fluid Mech. 735, 473 (2013)ADSMathSciNetCrossRefGoogle Scholar
  35. 35.
    C. Pozrikidis, A Practical Guide to Boundary Element Methods with the Software Library BEMLIB (CRC Press, Boca Raton, 2002)Google Scholar
  36. 36.
    Y. Ibrahim, T.B. Liverpool, EPL 111, 48008 (2015)ADSCrossRefGoogle Scholar
  37. 37.
    S. Spagnolie, E. Lauga, J. Fluid Mech. 700, 105 (2012)MathSciNetCrossRefGoogle Scholar
  38. 38.
    S. Michelin, E. Lauga, J. Fluid Mech. 747, 572 (2014)ADSMathSciNetCrossRefGoogle Scholar
  39. 39.
    J.R. Blake, J. Fluid Mech. 46, 199 (1971)ADSCrossRefGoogle Scholar
  40. 40.
    Y. Ibrahim, T.B. Liverpool, arXiv:1607.08757

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • M. N. Popescu
    • 1
    • 2
  • W. E. Uspal
    • 1
    • 2
  • M. Tasinkevych
    • 1
    • 2
  • S. Dietrich
    • 1
    • 2
  1. 1.Max-Planck-Institut für Intelligente SystemeStuttgartGermany
  2. 2.IV. Institut für Theoretische PhysikUniversität StuttgartStuttgartGermany

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