Skip to main content

Conditions for the propulsion of a colloid surrounded by a mesoscale phase separation

The European Physical Journal E volume 45, Article number: 96 (2022) Cite this article

Abstract

We study a two-dimensional model of an active isotropic colloid whose propulsion is linked to the interactions between solute particles of the bath. The colloid catalyzes a chemical reaction in its vicinity, that yields a local phase separation of solute particles. The density fluctuations of solute particles result in the enhanced diffusion of the colloid. Using numerical simulations, we thoroughly investigate the conditions under which activity occurs, and we establish a state diagram for the activity of the colloid as a function of the parameters of the model. We use the generated data to unravel a key observable that controls the existence and the intensity of activity: The filling fraction of the reaction area. Remarkably, we finally show that propulsion also occurs in three-dimensional geometries, which confirms the interest of this mechanism for experimental applications.

Graphic abstract

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Data availability statement

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. E. Lauga, T.R. Powers, Rep. Prog. Phys. 72, 096601 (2009). https://doi.org/10.1088/0034-4885/72/9/096601. arXiv:0812.2887

    Article  ADS  Google Scholar 

  2. C. Bechinger, R. Di Leonardo, H. Löwen, C. Reichhardt, G. Volpe, G. Volpe, Rev. Mod. Phys. 88, 045006 (2016). https://doi.org/10.1103/RevModPhys.88.045006

    Article  ADS  Google Scholar 

  3. A. Zöttl, H. Stark, J. Phys. Condens. Matter 28, 253001 (2016). https://doi.org/10.1088/0953-8984/28/25/253001

    Article  ADS  Google Scholar 

  4. P. Illien, R. Golestanian, A. Sen, Chem. Soc. Rev. 46, 5508 (2017). https://doi.org/10.1039/C7CS00087A

    Article  Google Scholar 

  5. G. Rückner, R. Kapral, Phys. Rev. Lett. 98, 13 (2007). https://doi.org/10.1103/PhysRevLett.98.150603

    Article  Google Scholar 

  6. R. Golestanian, T.B. Liverpool, A. Ajdari, New J. Phys. 9, 126 (2007). https://doi.org/10.1088/1367-2630/9/5/126. arXiv:0701168 [cond-mat]

    Article  ADS  Google Scholar 

  7. S.J. Ebbens, J.R. Howse, Soft Matter 6, 726 (2010). https://doi.org/10.1039/b918598d

    Article  ADS  Google Scholar 

  8. S. Samin, R. Van Roij, Phys. Rev. Lett. 115, 1 (2015). https://doi.org/10.1103/PhysRevLett.115.188305. arXiv:1506.05695

    Article  Google Scholar 

  9. A. Würger, Phys. Rev. Lett. 115, 188304 (2015). https://doi.org/10.1103/PhysRevLett.115.188304. arXiv:1504.01522v1

    Article  ADS  Google Scholar 

  10. G. Volpe, I. Buttinoni, D. Vogt, H.-J. Kümmerer, C. Bechinger, H.-J. Kuemmerer, C. Bechinger, Soft Matter 7, 8810 (2011). https://doi.org/10.1039/c1sm05960b

    Article  ADS  Google Scholar 

  11. I. Buttinoni, G. Volpe, F. Kümmel, G. Volpe, C. Bechinger, J. Phys. Condens. Matter 24, 284129 (2012). https://doi.org/10.1088/0953-8984/24/28/284129. arXiv:1110.2202

    Article  Google Scholar 

  12. I. Buttinoni, J. Bialké, F. Kümmel, H. Löwen, C. Bechinger, T. Speck, Phys. Rev. Lett. 110, 238301 (2013). https://doi.org/10.1103/PhysRevLett.110.238301

    Article  ADS  Google Scholar 

  13. G. Oshanin, M.N. Popescu, S. Dietrich, J. Phys. A Math. Theor. 50, 134001 (2017)

    Article  ADS  Google Scholar 

  14. H.R. Jiang, N. Yoshinaga, M. Sano, Phys. Rev. Lett. 105, 1 (2010). https://doi.org/10.1103/PhysRevLett.105.268302. arXiv:1010.0470

    Article  Google Scholar 

  15. S. Safaei, A.Y. Archereau, S.C. Hendy, G.R. Willmott, Soft Matter 15, 6742 (2019). https://doi.org/10.1039/c9sm00694j

    Article  ADS  Google Scholar 

  16. A. Domínguez, M.N. Popescu, C.M. Rohwer, S. Dietrich, Phys. Rev. Lett. 125, 268002 (2020)

    Article  ADS  Google Scholar 

  17. R. Golestanian, Phys. Rev. Lett. 102, 188305 (2009). https://doi.org/10.1103/PhysRevLett.102.188305. arXiv:0904.3044

    Article  ADS  Google Scholar 

  18. C. Valeriani, R.J. Allen, D. Marenduzzo, J. Chem. Phys. 132, 204904 (2010). https://doi.org/10.1063/1.3428663

    Article  ADS  Google Scholar 

  19. R. Golestanian (2019). arXiv:1909.03747

  20. P. De Buyl, A.S. Mikhailov, R. Kapral, Europhys. Lett. 103, 60009 (2013). https://doi.org/10.1209/0295-5075/103/60009

    Article  Google Scholar 

  21. M. De Corato, I. Pagonabarraga, L.K.E.A. Abdelmohsen, S. Sánchez, M. Arroyo, Phys. Rev. Fluids 5, 122001 (2020). arXiv:2008.03251

    Article  ADS  Google Scholar 

  22. D. Boniface, C. Cottin-Bizonne, R. Kervil, C. Ybert, F. Detcheverry, Phys. Rev. E 99, 062605 (2019). https://doi.org/10.1103/PhysRevE.99.062605

    Article  ADS  Google Scholar 

  23. A.Y. Rednikov, Y.S. Ryazantsev, M.G. Velarde, Phys. Fluids 6, 451 (1994). https://doi.org/10.1016/0017-9310(94)90036-1

    Article  ADS  Google Scholar 

  24. S. Michelin, E. Lauga, D. Bartolo, Phys. Fluids 25, 061701 (2013)

    Article  ADS  Google Scholar 

  25. S. Michelin, E. Lauga, J. Fluid Mech. 747, 572 (2014). https://doi.org/10.1017/jfm.2014.158

    Article  ADS  Google Scholar 

  26. W.F. Hu, T.S. Lin, S. Rafai, C. Misbah, Phys. Rev. Lett. 123, 238004 (2019). https://doi.org/10.1103/PhysRevLett.123.238004

    Article  ADS  Google Scholar 

  27. A. Farutin, M.S. Rizvi, W.F. Hu, T.S. Lin, S. Rafaï, C. Misbah, 1 (2021). arXiv:2112.12023

  28. S. Thutupalli, R. Seemann, S. Herminghaus, New J. Phys. 13, 073021 (2011). https://doi.org/10.1088/1367-2630/13/7/073021

    Article  ADS  Google Scholar 

  29. Z. Izri, M.N. Van Der Linden, S. Michelin, O. Dauchot, Phys. Rev. Lett. 113, 248302 (2014). https://doi.org/10.1103/PhysRevLett.113.248302

    Article  ADS  Google Scholar 

  30. S. Herminghaus, C.C. Maass, C. Krüger, S. Thutupalli, L. Goehring, C. Bahr, Soft Matter 10, 7008 (2014). https://doi.org/10.1039/c4sm00550c

    Article  ADS  Google Scholar 

  31. C.C. Maass, C. Krüger, S. Herminghaus, C. Bahr, Annu. Rev. Condensed Matter Phys. 7, 171 (2016). https://doi.org/10.1146/annurev-conmatphys-031115-011517

    Article  ADS  Google Scholar 

  32. P. Illien, C. De Blois, Y. Liu, M.N. Van Der Linden, O. Dauchot, Phys. Rev. E 101, 0 40602 (2020). https://doi.org/10.1103/PhysRevE.101.040602

    Article  Google Scholar 

  33. A. Izzet, P.G. Moerman, P. Gross, J. Groenewold, A.D. Hollingsworth, J. Bibette, J. Brujic, Phys. Rev. X 10, 021035 (2020). https://doi.org/10.1103/PhysRevX.10.021035

    Article  Google Scholar 

  34. T. Zinn, L. Sharpnack, T. Narayanan, Phys. Rev. Res. 2, 033177 (2020). https://doi.org/10.1103/PhysRevResearch.2.033177

    Article  Google Scholar 

  35. R. Dattani, E.F. Semeraro, T. Narayanan, Soft Matter 13, 2817 (2017). https://doi.org/10.1039/C6SM02855A

    Article  ADS  Google Scholar 

  36. E.F. Semeraro, R. Dattani, T. Narayanan, J. Chem. Phys. 148, 014904 (2018). https://doi.org/10.1063/1.5008400

    Article  ADS  Google Scholar 

  37. A. Torres-Carbajal, S. Herrera-Velarde, R. Castañeda-Priego, Phys. Chem. Chem. Phys. 17, 19557 (2015). https://doi.org/10.1039/c5cp02777b

    Article  Google Scholar 

  38. A. Torres-Carbajal, R. Castañeda-Priego, Phys. Chem. Chem. Phys. 20, 6917 (2018). https://doi.org/10.1039/c7cp08302e

    Article  Google Scholar 

  39. J. Decayeux, V. Dahirel, M. Jardat, P. Illien, Phys. Rev. E 104, 1 (2021). https://doi.org/10.1103/PhysRevE.104.034602. arXiv:2103.13244

    Article  Google Scholar 

  40. R. Dattani, E.F. Semeraro, T. Narayanan, Soft Matter 13, 2817 (2017). https://doi.org/10.1039/C6SM02855A

    Article  ADS  Google Scholar 

  41. D.L. Ermak, J. Chem. Phys. 62, 4189 (1975)

    Article  ADS  Google Scholar 

  42. D. Frenkel, B. Smit, Understanding Molecular Simulation: From Algorithms to Simulations, 2nd edn. (Academic Press, Boston, 2002)

    MATH  Google Scholar 

  43. J. Bialké, T. Speck, H. Löwen, J. Non-Cryst. Solids 407, 367 (2015). https://doi.org/10.1016/j.jnoncrysol.2014.08.011. arXiv:1407.6828

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sorbonne Université, CNRS, Laboratoire PHENIX (Physicochimie des Electrolytes et Nanosystèmes Interfaciaux)), UMR 8234, F-75005 Paris, France

    Jeanne Decayeux, Marie Jardat, Pierre Illien & Vincent Dahirel

Authors
  1. Jeanne Decayeux
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marie Jardat
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pierre Illien
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Vincent Dahirel
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

JD made the investigation. JD did the data curation. All authors contributed to the methodology, the formal analysis, and writing.

Corresponding author

Correspondence to Vincent Dahirel.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Decayeux, J., Jardat, M., Illien, P. et al. Conditions for the propulsion of a colloid surrounded by a mesoscale phase separation. Eur. Phys. J. E 45, 96 (2022). https://doi.org/10.1140/epje/s10189-022-00247-6

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epje/s10189-022-00247-6